Class 12 Medical Physics - Electromagnetic Waves

A parallel plate capacitor (fig.) made of circular plates each of radius $R=6.0\ cm$ has a capacitance $C= 100 \mu F$ . The capacitor is connected to a $230\ V$ ac supply with a (angular) frequency of $300$ rad $s^{-1}$ .
Is the conduction current equal to the displacement current?

Given: A parallel plate capacitor made of circular plates each of radius R=6.0 cm has a capacitance

$C=100\mu F$ . The capacitor is connected to a 230 V ac supply with a (angular) frequency of

$300 rad s^{−1} .$

To find if the conduction current is equal to displacement current

Solution:

Radius of plates,

$R=6cm=6\times10^{-2}m$

Capacitance of capacitor,

$C=100\mu F=100\times10^{-6}F=10^{-4}F$

Voltage of capacitor,

$V=230V$

Frequency of capacitance,

$\omega=300rad/s$

Yes, the conduction current is equal to displacement current

By definition of the displacement current,

$I_d=\varepsilon_0\dfrac{d\phi_E}{dt}\\\implies I_d=\varepsilon_0\dfrac d{dt}(EA)\\\implies I_d=\varepsilon A\dfrac {dE}{dt}$

But

$E=\dfrac {\sigma}{\varepsilon_0}=\dfrac {Q}{\varepsilon_0 A}$

Substituting this in the abve equation, we get

$I_d=\varepsilon_0 A\dfrac d{dt}\left(\dfrac Q{\varepsilon_0 A}\right)\\\implies I_d=\varepsilon_0A.\dfrac 1{\varepsilon_0 A}.\dfrac {dQ}{dt}\\\implies I_d=\dfrac {dQ}{dt}=I$

Hence the conduction current is equal to displacement current

A parallel plate capacitor of plate separation $2\ mm$ is connected in an electric circuit having source voltage $400\ V$ . What is the value of the displacement current for $10^{-6}$ second if the plate area is $60\ cm^{2}$ .?

Given,

$d=2$ mm

$v=400$ v

$t=10^{-6}$

$A=60cm^2$

$t=0$ no charge on the capacitor, so potential drop across the capacitor

$=0$

$t=10^{-6}$ sec capacitor get fully charge to potential drop across capacitor

$=400$ v

$I_D=\varepsilon_o\dfrac{d\phi}{dt}=\varepsilon_o\dfrac{d}{dt}(EA)=\varepsilon_oA\dfrac{dE}{dt}=\dfrac{\varepsilon_oA}{dt}\left(\dfrac{dv}{dt}\right)$

$=\dfrac{\varepsilon_oA}{d}\dfrac{\Delta v}{\Delta t}=\dfrac{\varepsilon_oA}{d}\left(\dfrac{v_f-v_i}{f_f-t_i}\right)$

$=\dfrac{8.85\times 10^{-12}\times 60\times 10^{-4}}{2\times 10^{-3}}\left(\dfrac{400-0}{10^{-6}-0}\right)$

$=\dfrac{8.85\times 10^{-12+6}\times 60\times 10^{-4}\times 400}{2\times 10^{-3}}$

$=3\times 8.85\times 10$

$I_D=12\times 8.85\times 10^{-4}$

$I_D=1.06\times 10^2A$ .

How electromagnetic waves are produced ?

$\textbf{Explanation:}$

$\bullet$ Electromagnetic waves are the combination of electric and magnetic field waves produced by moving charges.

$\bullet$ The creation of all electromagnetic waves begins with a charged particle. This charged particle creates an electric field (which can exert a force on other nearby charged particles).

$\bullet$ When it accelerates as part of an oscillatory motion, the charged particle creates ripples, or oscillations, in its electric field, and also produces a magnetic field (as predicted by Maxwell’s equations).

$\bullet$ Once in motion, the electric and magnetic fields created by a charged particle are self-perpetuating time dependent changes in one field (electric or magnetic) produce the other.

$\bullet$ Both electric and magnetic fields in an electromagnetic wave will fluctuate in time, one causing the other to change.

$\bullet$ Electromagnetic waves (photons) are produced anytime by a charged particle experiences a change in velocity.

In which situation is there a displacement current but no conduction current?

During charging or discharging there is a displacement current but not conduction current between plates of capacitor.

What is ratio of electric field and magnetic field in $EM$ wave?

In electromagnetic waves the ratio of amplitudes of electric field and magnetic field is equal to. In electromagnetic waves the ratio of amplitudes of electric field and magnetic field is equal to the velocity of the electromagnetic waves in free space.

E/B = v

(i) What is main difference between electromagnetic waves theory and Planck's quantum theory.
(ii) Which rule is violated in the following orbital diagram:

(A) Electromagnetic theory

(1) Light Travels in the form of waves of very small wave length

(2) Energy of radiation is directly Proportional to intensity if radiation

This theory failed to explain black body radiation.

Plank's Quantum of Radiation:-

(1) Radiation has energy

(2) Energy of photon

$E = h v$

$E= nhv ,\,n=1,2,3$

(B) It is according to the rules of electronic configuration and it does not violate any rule.

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Answer the following questions:
(i) How are infrared waves produced? Write their one important use.
(ii) The thin Ozone layer on top of the stratosphere is crucial for human survival.

(i) Infrared waves are produced by hot bodies and molecules.
Important use:
(a) To treat muscular strains. (b) To reveal the secret writings on the ancient walls. (c) For producing dehydrated fruits (d) Solar heater (e) Solar cooker. (Any one)
(ii) Ozone layer protects us from harmful

$U-V$ rays.

State two properties of ultra violet radiations which differs from visible light.

(a) Ultraviolet radiations produce fluorescence on striking a zinc sulphide screen.

(b) They cause health hazards like cancer on the body.

(c)Ultra-violet radiations are of wavelength shorter than that of visible light.

(d)Ultra-violet radiations are more chemically active than the visible light.

What is meant displacement current?

Displacement current does not arise due to motion of charge carriers but it arises due to time variation of electric flux.

Analyse the diagram of solar spectrum and write answer.
a. Which radiation has a wavelength greater than visible light in this spectrum ?
b. Which color has the highest frequency in the visible part of the solar spectrum ?
c. Write one merit and demerit of infrared and ultraviolet radiations.

a.Infrared
b.Violet
c.Ultra violet - Vitamin D,Skin cancer Infrared - Distant photography,Makes sunlight Hot.

Write any two Maxwell's equation.

Gauss law of electrostatics: This law states that the electric flux through a closed surface S is

$\dfrac{1}{\in_o}$ times
the total changes q enclosed by the surface S.

$\oint \overset{\rightarrow} { E }. \overset{\rightarrow}{ds} = \dfrac{q}{\in_o}$
(2)Modified Ampere's law : This law states that the line integral of the magnetic field around any closed circuit C is equal to go times the total current (sum of conduction & displacement currents) threading the closed circuit.

$\oint \overset{\rightarrow}{B}. \overset{\rightarrow}{d\ell} = \mu_o[\sum I_c + \sum Id] = \mu_o[\sum I_c + \in_o\dfrac{d \phi}{dt}$

Name the characteristics of electromagnetic waves that
(i) increases
(ii) remains constant.
In the electromagnetic spectrum as one moves from radio wave region towards ultraviolet region.

(i) Frequency increases.

(ii) Speed in vacuum remains constant.

______ was the first scientist who produced electromagnetic waves in a laboratory.

Michael Faraday produced electromagnetic waves in laboratory in 1831.

Write a short note on sky wave propagation.

Sky wave propagation :-

It is a type of radio wave propagation. The wave which propagate through atmosphere and are reflected back by the ionosphere of earth's atmosphere is called as sky wave propagation.

These waves go from transmitter antenna to receiver antena travelling through sky. The sky waves are of practical importance at medium and high frequency for very long distance radio communication.

The table lists possible orders of magnitude of the wavelengths of some of the principal radiations
of the electromagnetic spectrum.
Which row shows the correct orders of magnitude of the wavelengths?

wavelength / m wavelength / m wavelength / m wavelength / m
microwaves infra-red ultraviolet X-rays
A $10^{-6}$ $10^{-10}$ $10^{-12}$ $10^{-14}$
B $10^{-4}$ $10^{-8}$ $10^{-10}$ $10^{-12}$
C $10^{-2}$ $10^{-6}$ $10^{-8}$ $10^{-10}$
D $10^{2}$ $10^{-4}$ $10^{-6}$ $10^{-8}$

Image result for orders of magnitude of the wavelengths of some of the principal radiations of the electromagnetic spectrum.

From the above fig. We can conclude that option C has correct matchings.

Which of thee following electromagnetic waves has (a) minimum wavelength, and (b) minimum frequency? Write one use of each of these two waves.
Infrared waves, Microwaves, y-rays and X-rays

The minimum wavelength or Maximum frequency has maximum energy and vise versa,

$\gamma$ - Ray has maximum energy so it has a minimum wavelength and Microwaves have minimum energy so it has a maximum frequency.

Use of electromagnetic waves :

Infrared waves: Heat-sensitive thermal imaging cameras, Remote controls.

Microwaves: microwave radio relay networks, radar, satellite, and spacecraft communication.

$\gamma$ -rays: Used as tracers in medicine, Astronomy.
X-rays: checking fractures

A pint charge is moving along a straight line with a constant velocity v. Consider a small area A perpendicular to the direction of motion of the charge (figure 40-E1). Calculate the displacement current through the area when its distance from the charge i x. The value of z is not large so that the electric field at any instant is essentially given by Coulomb's law.

$E = \dfrac{Kq}{x^{2}},$ [from coulomb's law]

$\phi _{E} = EA = \dfrac{KqA}{x^{2}}$

$l_{d} = \epsilon _{0}\dfrac{d_{\phi }E}{dt} = \epsilon _{0} \dfrac{d}{dt} \dfrac{kqA}{x^{2}} = \epsilon _{0}KqA = \dfrac{d}{dt}x^{-2}$

$= \epsilon _{0}\times \dfrac{1}{4\pi \epsilon _{0}}\times q\times A\times -2\times x^{-3}\times \dfrac{dx}{dt} = \dfrac{qAv}{2\pi x^{3}}$

The speed of electromagnetic waves (which include visible light, radio, and $x$ rays ) in vacuum is $3.0 \times 10^{8} \mathrm{m} / \mathrm{s}$ . X-ray wavelengths range from about $5.0 \mathrm{nm}$ to about $1.0 \times 10^{-2} \mathrm{nm} .$ What is the frequency range for x rays?

For X rays

$f_{\min }=\dfrac{c}{\lambda_{\max }}=\dfrac{3.0 \times 10^{8} \mathrm{m} / \mathrm{s}}{5.0 \times 10^{-9} \mathrm{m}}=6.0 \times 10^{16} \mathrm{Hz}$

and

$f_{\max }=\dfrac{c}{\lambda_{\min }}=\dfrac{3.0 \times 10^{8} \mathrm{m} / \mathrm{s}}{1.0 \times 10^{-11} \mathrm{m}}=3.0 \times 10^{19} \mathrm{Hz}$

Name the type of waves which are used by astronauts to communicate with one another on moon.

Astronauts use radio waves for communications, because radio wave in not mechanical wave, so it can travel in vacuum.

Monochromatic light (that is, light of a single wavelength) is to be absorbed by a sheet of photographic film and thus recorded on the film. Photon absorption will occur if the photon energy equals or exceeds $0.6 \mathrm{eV}$ , the smallest amount of energy needed to dissociate an AgBr molecule in the film.(a) What is the greatest wavelength of light that can be recorded by the film?(b) In what region of the electromagnetic spectrum is this wavelength located?

(a) The smallest amount of energy needed to dissociate an AgBr molecule in the film is

$0.6 eV$ , the energy of the photon equals the frequency of the photon multipliedby the Plank's Constant, that is:

$E= \dfrac{h c}{ \lambda}$

$\Rightarrow \lambda = \dfrac{hc}{E} = \dfrac{(4.136 \times 10^{-15} eV. s)(3 \times 10^8 m/s)}{0.6 eV} = 2.1 \times 10^{-6}$

(b) It is in the infrared region.

What is Maxwell's corkscrew rule ? For what purpose is it used ?

According to Maxwell's corkscrew in the direction of current, then the direction in which we turn its handle is the direction of magnetic field.
This rule is used to determine the direction of magnetic field around a straight-current carrying conductor.

Using $B = \mu _{0}H$ find the ratio $E_{0}/H_{0}$ for a plane electromagnetic wave propagating through vacuum. This ratio is a universal constant called the impedance of free space.

$B = \mu _{0}H$

$\Rightarrow H = \dfrac{B}{\mu _{0}}$

$\dfrac{E_{0}}{H_{0}} = \dfrac{B_{0}/(\mu _{0}\epsilon _{0}C)}{B_{0}/\mu _{0}} = \dfrac{1}{\epsilon _{0}C}$

$= \dfrac{1}{8.85\times 10^{-12}\times 3\times 10^{8}} = 376.6\,\Omega = 377\,\Omega$

The figure gives the variation
of an electric field that is perpendicular to a circular area of $2.0\, m^2$ .
During the time period shown, what
is the greatest displacement current
through the area?

Greatest displacement current would be there where slope is largest.

Because

$i_d=\epsilon_0A\dfrac{|\Delta \vec E|}{|\Delta t|}$

Ignoring points where the determination of the slope is problematic,

we find the interval of largest slope is

$6 \,μs < t < 7\, μs$ . During that time, we have,

$i_d=\epsilon_0A\dfrac{|\Delta \vec E|}{|\Delta t|}=\epsilon_0(2.0\,m^2)(2.0 \times 10^6\,V/m)$

which yields

$id = 3.5 \times 10^{–5} \,A$ .

Why are infra-red radiations referred to as heat waves? Name the radiations which are next to these radiations in the electromagnetic spectrum having (i) shorter wavelength (ii) longer wavelength.

Infrared waves are produced by hot bodies and molecules, so are referred to as heat waves.

(i)

$EM$ wave having short wavelength than infrared waves are visible

$UV, X-rays$ and

$\gamma-rays$ .

(ii)

$EM$ wave having longer wavelength than infrared waves are microwaves, radio waves.

Arrange the following electromagnetic waves in order of increasing frequency:
$\gamma-rays$ , microwaves, infrared rays and ultraviolet rays.

Electromagnetic radiation is classified into types according to the frequency of the wave. These types include, in order of increasing frequency, radio waves, microwaves, infrared radiation, visible light, ultraviolet radiation, X-rays and gamma rays.

The frequency is the inverse of wavelength.

Hence, in the order of increasing frequency, the waves are

$Microwave < Infrared < Ultraviolet < \gamma-rays$ .

Which part of the electromagnetic spectrum is absorbed from sunlight by ozone layer?

Ultraviolet light is absorbed by the ozone layer.

A parallel-plate capacitor with circular plates of radius $0.10$ m
is being discharged. A circular loop of radius $0.20$ m is concentric with the capacitor and halfway between the plates. The displacement current through the loop is $2.0$ A. At what rate is the electric
field between the plates changing?

We use Eq ,

$i_d=\epsilon_0A(dE/dt)$ . Note that, in this situation, A is the area over
which a changing electric field is present. In this case

$r > R$ , so

$A = πR^2$ . Thus,

$\dfrac{dE}{dt}=\dfrac{i_d}{\epsilon_0A}=\dfrac{i_d}{\epsilon_0\pi R^2}=\dfrac{2.0\,A}{\pi(8.85\times10^{-12}\,C^2/N.m^2)(0.10\,m)^2}=7.2\times10^{12}\,\dfrac{V}{m.s}$

Which part of the electromagnetic spectrum is used in operating a RADAR?

Microwaves are used in operating a RADAR.

Arrange the following electromagnetic waves in order of decreasing frequency:
$\gamma-rays$ , infrared rays, X-rays and microwaves.

The frequency is the inverse of wavelength.

Hence, in the order of decreasing frequency, the waves are

$Microwave > Infrared > X-rays > \gamma-rays$ .

Assume that lasers are available whose wavelengths can be precisely tuned to anywhere in the visible rangethat is, in the range $450 nm < \lambda < 650 nm$ . If every television channel occupies a bandwidth of 10 MHz, how many channels can be accommodated within this wavelength range?

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Name the electromagnetic waves, which (i) maintain the Earth's warmth and (ii) are used in aircraft nagivation.

(i) Infrared rays maintain the Earth's warmth.

(ii) Microwaves are used in aircraft nagivation.

A parallel-plate capacitor with circular plates is being charged. Consider a circular loop centered on the central axis and located between the plates. If the loop radius of $3.00$ cm is greater than the plate radius, what is the displacement current between the plates when the magnetic field along the loop has a magnitude $2.00 \mu T$ ?

It is known

$i_d=\dfrac{2\pi r\,B}{\mu_0}$

putting values according to question

$i_d=\dfrac{2\pi r\,B}{\mu_0}=\dfrac{2\pi(0.0300 \,m)(2.00 \times 10^{-6}\, T)}{4\pi \times 10^{-7}\,T.m/A}=0.300\,A$

Identify the part of the electromagnetic spectrum to which the following wavelengths belong:
(i) $10^{-1} m$
(ii) $10^{-12} m$ .

(i)

$10^{-1} m = 10\ cm$ belongs to short radio waves.

(ii)

$10^{-12} m = 0.01\overset {\circ}{A}$ belongs to gamma rays.

Which of the following radiations are (i) heat radiation and (ii) used for long distance transmission? Infrared rays, gamma rays, ultraviolet rays, microwaves.

Infrared rays are heat radiation, Microwaves are used for long distance transmission.

Which part of electromagnetic spectrum does the wavelength $10^{-10}m$ correspond to?

X-rays part of electromagnetic spectrum does the wavelength

$10^{−10}$ m correspond to.

Identify the type of waves which are produced by the following way and write one application for each:
(i) Radioactive decay of the nucleus
(ii) Rapid acceleration and decelerations of electrons in aerials
(iii) Bombarding a metal target by high energy electrons.

Type of wave Application

(i) Gamma rays Treatment of tumors

(ii) Radio waves Radio and television communication systems

(iii) X-rays Study of crystals

Which of the following has the minimum wavelength and which has the maximum wavelength?
Blue light, infrared rays, gamma rays, green light.

Out of the given wavelengths gamma rays have the minimum wavelength and infrared rays have the maximum wavelength.

Which of the following has the least wavelength? Gamma rays, blue light, infrared radiation and ultraviolet, radiation.

Gamma rays have the shortest wavelengths of the electromagnetic spectrum, and the highest energies.

How are $X-rays$ produced?

X-rays are produced when high energetic electron beam is made incident on a metallic target of high melting point and high atomic weight.

Name the part of the electromagnetic spectrum of wavelength $10^{-2}m$ and mention its one application.

Microwave is the part of the electromagnetic spectrum of wavelength

$10^{−2}$ m

Application : Used in RADAR system for aircraft navigation.

Identify the part of the electromagnetic spectrum to which the following wavelengths belong:
(i) $1\ mm$
(ii) $10^{-11} m$ .

(i) wavelength

$1\ mm$ belongs to the microwaves.

(ii) Wave length

$10^{-11} m = 0.1\overset {\circ}{A}$ belongs to gamma rays.

Name the electromagnetic radiations used for studying the crystal structure of solids.

X-rays is the electromagnetic radiations used for studying the crystal structure of solids.

Name the part of electromagnetic spectrum of wavelength $10^2\ m$ and mention its one application.

Wavelength

$10^2\ m$ belongs to radio-waves. This is used to broadcast radio programmes to long distances.

Special devices, like the klystron valve or the magnetro valve, are used for production of electromagnetic waves. Name the waves and also write one of their applications.

Name : Microwaves.

Use : For cooking in microwaves ovens.

Give a reason to show that microwaves are better carriers of signals for long range transmission than radio waves.

Microwaves are short wavelength waves, so they go straight in a specified direction without any bending.

Name the electromagnetic radiations used for viewing objects through haze and fog.

Infrared rays are used for viewing objects through haze and fog.

How are infrared waves produced?

Infrared waves are produced by hot bodies and molecules.

Professor C.V. Raman surprised his students by suspending freely a tiny light ball in a transparent vacuum chamber by shining a laser beam on it. Which property of em waves was he exhibiting? Give one more example of this property.

Electromagnetic waves exert radiation pressure. Tails of comets are due to solar radiation.

From the following, identify the electromagnetic waves having the (i) Maximum (ii) Minimum frequency.
(a) Radio waves
(b) Gamma-rays
(c) Visible light
(d) Microwaves
(e) Ultraviolet rays, and
(f) Infrared rays.

(i) The waves of maximum frequency are gamma rays.

(ii) The waves of minimum frequency are radio waves.

The following table gives the wavelength range of some constituents of the electromagnetic spectrum.
S.No. Wavelength Range
$1.$ $1\ mm$ to $700\ nm$
$2.$ $400\ nm$ to $1\ nm$
$3.$ $1\ nm$ to $10^{-3} nm$
$4.$ $< 10^{-3} nm$
Select the wavelength range and name the electromagnetic waves that are
(i) Widely used in the remote switches of household electronic devices.
(ii) Produced in nuclear reactions.

(i) Infrared waves (wavelength range

$1\ mm$ to

$700\ nm$ ).

(ii) Gamma rays (wavelength range

$< 10^{-3} nm$ ).

Name the part of electromagnetic spectrum which is used for taking photographs of earth under foggy conditions from great heights.

Infrared radiation is the part of electromagnetic spectrum which is used for taking photographs of earth under foggy conditions from great heights.

Name the electromagnetic waves that have frequencies greater than those of ultraviolet light but less than those of gamma rays.

X-ray are the electromagnetic waves that have frequencies greater than those of ultraviolet light but less than those of gamma rays.

Answer the following questions:
(i) Which segment of electromagnetic waves has highest frequency? How are these waves produced? Give one use of these waves.
(ii) Which $EM$ waves lie near the high frequency end of visible part of $EM$ spectrum? Give its one use. In what way this component of light has harmful effects on humans?

(i) Gamma rays have the highest frequency. These are produced during nuclear reactions and also emitted by radioactive nuclei. They are used in medicine to destroy cancer cells.

(ii) Ultraviolet rays lie near the high frequency end of visible part of EM spectrum. They are used to sterlize drinking water and surgical instruments. Exposure to

$UV$ radiation induces the production of more melanin, causing tanning of the skin.

Name the part of the electromagnetic spectrum whose wavelength lies in the range $10^{-10} m$ . Give its one use.

The electromagnetic waves having wavelength

10−10m10−10m are X-rays.

X-rays are used to study crystal structure.

Answer the following questions:
(i) How are electromagnetic waves produced by oscillating charges?
(ii) State clearly how a microwave oven works to heat up a food item containing water molecules.
(iii) Why are microwaves found useful for the radar systems in aircraft navigation?

(i) If a charge particle oscillates with some frequency, produces an oscillating electric field in space, which produces an oscillating magnetic field, which in turn, is a source of electric field, and so on. Thus oscillating electric fields and magnetic fields regenerate each other, and an electromagnetic wave propagates in the space.

(ii) In microwave oven, the frequency of the microwaves is selected to match the resonant frequency of water molecules so that energy from the waves get transferred efficiently to the kinetic energy of the molecules. This kinetic energy raises the temperature of any food containing water.

(iii) Microwaves are short wavelength radio waves, with frequency of order of few

$GHz$ . Due to short wavelength, they have high penetrating power with respect to atmosphere and less diffraction in the atmospheric layers. So these waves are suitable for the radar systems used in aircraft navigation.

To which regions of the electromagnetic spectrum, the following wavelengths belong? $2,000\overset {\circ}{A}, 5,000\overset {\circ}{A}, 10,000\overset {\circ}{A}$ and $1.0\overset {\circ}{A}$ .

$2,000\overset {\circ}{A}$ :- Ultraviolet radiation

$5,000\overset {\circ}{A}$ :- Visible light

$10,000\overset {\circ}{A}$ :- Infrared radiation

$1.0\overset {\circ}{A}$ :- X-rays.

Identify the electromagnetic waves whose wavelengths lie in the range
(a) $10^{-11} m < \lambda < 10^{-8} m$
(b) $10^{-4} m < \lambda < 10^{-1} m$
Write one use of each.

(a) X-rays/ Gamma rays

(b) Infrared/ Visible rays/ Microwaves

(i) X-rays are used as a diagnostic tool in medicine.

(ii) Gamma rays are used in medicine to destroy cancer cells.

(iv) Visible rays provide us information about the world.

(v) Microwaves are used in RADAR system for aircraft navigation.

Electromagnetic waves with wavelength
(i) $\lambda_{1}$ is used in satellite communication.
(ii) $\lambda_{2}$ is used to kill germs in water purifier,
(iii) $\lambda_{3}$ is used to detect leakage of oil in underground pipelines.
(iv) $\lambda_{4}$ is used to improve visibility in runways during fog and mist conditions.
(1) Identify and name the part of electromagnetic spectrum to which these radiations belong.
(2) Arrange these wavelengths in ascending order of their magnitude.
(3) Write one more application of each.

(1)

$\lambda_{1}\rightarrow Microwave, \lambda_{2} \rightarrow UV\ \lambda_{3} \rightarrow X\ rays, \lambda_{4} \rightarrow Infrared$

(2)

$\lambda_{3} < \lambda_{2} < \lambda_{4} < \lambda_{1}$

(3) Microwave - RADAR

$UV$ - LASIK eye surgery

X-ray - Bone fracture identification (bone scanning)

Infrared - Optical communication.

Identify the electromagnetic waves whose wavelengths vary as
(a) $10^{-12} m < \lambda < 10^{-8} m$
(b) $10^{-3} m < \lambda < 10^{-1} m$
Write one use for each.

(a) X-rays : Used as a diagnostic tool in medicine and as a treatment for certain forms of cancer.

(b) Microwaves : Used in radar systems for aircraft navigation.

Identify the following electromagnetic radiations as per the wavelengths given below.
(a) $10^{-3} nm$
(b) $10^{-3} m$
(c) $1\ nm$
Write one application of each.

(a)

$10^{-3}nm\rightarrow$ gamma radiation.

Application : Radio therapy or to initiate nuclear reactions.

(b)

$10^{-3} m\rightarrow microwaves$

Application : In RADAR for aircraft navigation.

(c)

$1\ nm \rightarrow X-ray$ .

Application : In medical science for detection of fractures, stones in kidney, gallbladder etc.

Answer the following questions:
Identify the part of the electromagnetic spectrum which is:
(i) Suitable for radar system used in aircraft navigation
(ii) Produced by bombarding a metal target by high speed electrons.
(iii) Why does a galvanometer show a momentary deflection at the time of charging or discharging a capacitor? Write the necessary expression to explain this observation.

(i) Microwaves

(ii)X-rays

(iii) Due to conduction current in the connecting wires and the production of displacement current between the plates of capacitor on account of changing electric field.

Current inside the capacitor is given by

$I_{d} = \epsilon_{0} d\varphi_{E}$ .

Write the following in descending order of wavelength:
Gamma rays, Hertzian waves, yellow light, blue light, infrared radiation, ultraviolet radiation, X-rays, $\gamma-rays$ .

Hertzian waves, infrared radiation, yellow light, blue light, ultraviolet radiation, X-rays,

$\gamma-rays$ .

Which part of Sun's energy is responsible for drying clothes and exposure to which part could be a health hazard?

Infra-red (IR) radiations are responsible for drying clothes and ultraviolet (UV) radiations could be a health hazard.

A variable frequency a.c source is connected to a capacitor. How will the displacement current change with decrease in frequency?

As we know that

${X}_{C}=\cfrac{1}{2\pi vC}$ and

$I=\cfrac {V}{{X}_{C}}$
So reactance of capacitor increases on decreasing frequency

${X}_{C}\propto \cfrac{1}{v}$
So

$I=2\pi vCV$
As reactance of capacitor increases, the current by Ohm's law will decrease

$[\because 1\propto \cfrac{1}{{X}_{C}}]$

Professor C.V.Raman surprised students by suspending freely a tiny light ball in a transparent vacuum chamber by shining a laser beam on it. Which property of EM waves was he exhibiting? Given one more example of this property.

We know the dual nature of radiation and matter, EM wave carries energy and momentum. Due to this change in momentum (by direction or velocity of wave), Em wave, exert pressure on the surface, by reflection and refraction. This property of EM wave helped professor CV Raman to surpise his students by suspending freely a tiny light ball in transparent vacuum chamber by shining a laser beam on it. The tails of the comets are also due to radiation pressure.
Electromagneitc radiations can pass even through vacuum and has particle nature.
Mobile phone placed in evacuated transparent chamber can ring up which can be seen through transparent chamber, but sound of ring tone cannot be herd, proves the propagation of electromagnetic wave in vacuum.

Why does microwave oven heats up a food item containing water molecules most effeciently?

In microwave oven, molecules of food item starts to vibrate by driven by driven force due to microwaves with the frequency of microwave. But the natural frequency of water molcules matches with microwave frequency which causes resonance (more amplitude) which further causes increase in temperature.

The charge on a parallel plate capacitor varies as $q={q}_{0}\cos{2\pi vt}$ . The plates are very large and close together (area $=h$ , separation $=d$ ). Neglecting the edge effects, find the displacement current through? the capacitor

The displacement current

${I}_{d}$ in capacitor is

${I}_{d}={I}_{c}=\cfrac{dq}{dt}$ where

$q={q}_{0}\cos{(2\pi vt)}$ (Given)

${I}_{d}={I}_{c}=\cfrac{d}{dt}{q}_{0}\cos {(2\pi vt)}$

${I}_{d}={q}_{0}2\pi vt$

${I}_{d}=2\pi v{q}_{0}\pi vt$

What is the range of wavelength of electromagnetic waves that constitute visible radiation?

The range of electromagnetic waves is about

$4000 A^{\circ}$ to

$7000 A^{\circ}$ , which constitute visible radiation.

Wavelength of radiation incident on a surface is $850 nm$ . Will the surface become visible when exposed to this radiation? Explain.

As we know, the range of wavelength of visible radiation is from

$400 nm$ to

$700 nm$ . The radiation having wavelength greater than

$700 nm$ is termed as infra red radiations which only produces warmth. So the wavelength of radiation

$850 nm$ cannot be visible.

Identify the following electromagnetic radiations as per the frequencies given below:
(a) $10^{20} Hz$
(b) $10^{9} Hz$
(c) $10^{11} Hz$
Write one application of each.

(a)

$10^{20}Hz \rightarrow \gamma - radiation$ .

Application : For treatment of cancer.

(b)

$10^{9} Hz \rightarrow Radio\ waves$

Application : For broadcasting radio-programmes to long distances.

(c)

$10^{11} Hz \rightarrow Microwaves$

Application : For cooking in microwave oven.

Experimental observations have shown that X-rays
(i) Travel in vacuum with a speed of $3\times 10^{8} ms^{-1}$
(ii) Exhibit the phenomenon of diffraction and can be polarised.
What conclusion can be drawn about the nature of X-rays from each of these observations?

(i) X-rays are electromagnetic waves.

(ii) X-rays are transverse in nature.

What is the range of the wavelength of the following electromagnetic wave : Gamma rays ?

Gamma rays have wavelength shorter than

$0.1$ Å or

$10^{-11}\ m$ .

What is the range of the wavelength of the following electromagnetic waves : Ultraviolet wave ?

Ultraviolet rays have wavelength range from

$100$ Å to

$4000$ Å .

What is the range of the wavelength of the following electromagnetic waves : X-rays ?

X-rays have wavelength range from

$0.1$ Å to

$100$ Å .

Electromagnetic waves with wavelength
(i) ${\lambda}_{1}$ is used in satellite communication.
(ii) ${\lambda}_{2}$ is used to kill germs in water purifiers
(iii) ${\lambda}_{3}$ is used to detect leakage of oil in underground pipelines
(iv) ${\lambda}_{4}$ is used to improve visibility in runways during fog and mist conditions
Arrange these wavelengths in ascending order of their magnitude

eletromagnetic waves used for detect leakage of oil in underground pipelines have lowest wavelength, followed by wavelength of wave used for kill germs in water purifiers,wavelength of wave used for improve visibility in runways during fog and mist conditions and then wavelength of wave used in satellite communication.

The arrangement of the wavelengths in ascending order are

${\lambda}_{3},{\lambda}_{2},{\lambda}_{4},{\lambda}_{1}$

(a) Give a list of at least five radiations , in order of their increasing frequencies , which make up the complete electromagnetic spectrum.
(b) Which of the radiations mentioned in answer part (a) has the highest penetrating power ?

(a) Five radiations , in the order of their increasing frequencies are :

$Infrared\ waves\ , Visible\ light \ , Ultraviolet\ rays\ , X-rays\ and\ Gamma\ rays$ .
(b)

$Gamma\ rays$ have the highest penetrating power .

What is the range of the wavelength of the following electromagnetic waves :
Visible Light ?

The range of wavelength of visible light is approximately

$4000$ Å to

$8000$ Å , with violet being at the lower end (3800Å−4500Å) and red at the higher end (6200Å − 7500Å) .

Electromagnetic waves with wavelength
(i) ${\lambda}_{1}$ is used in satellite communication.
(ii) ${\lambda}_{2}$ is used to kill germs in water purifiers
(iii) ${\lambda}_{3}$ is used to detect leakage of oil in underground pipelines
(iv) ${\lambda}_{4}$ is used to improve visibility in runways during fog and mist conditions
Write one more application of each

(i) Microwave is used in satellite communication so,

${\lambda}_{1}$ is the wavelength of microwave. It is used in microwave oven.
(ii) Ultraviolet rays are used to kill germs in water purifiers so,

${\lambda}_{2}$ is the wavelength of ultraviolet rays.
(iii) X rays are used to detect leakage of oil in underground pipelines so

${\lambda}_{3}$ is in X ray region. It is also used to detect cracks in machinery and to detect fracture in bones of body.
(iv) Infrared rays

${\lambda}_{4}$ are used to improve visibility due to larger wavelength of low scattering
Infrared rays are used in optical communication

Arrange the following electromagnetic waves in the order of their increasing wavelength:
(a) $\gamma-rays$
(b) Microwaves
(c) $X-rays$
(d) Radio waves
How are infra-red waves produced? What role does infra-red radiation play in (i) maintaining the Earth's warmth and (ii) physical therapy?

We have to arrange electromagnetic waves in order of increasing wavelength

Wavelength of

$\gamma$ rays

$=<{ 10 }^{ -3 }nm$

Wavelength of micro waves =

$0.1mm$ to

$1mm$

Wavelength of X rays

$=1nm$ to

${ 10 }^{ -3 }nm$

Wavelength of Radio waves

$=>0.1m$

Smaller wavelength wave

$=\gamma$ rays

Larger wavelength wave

$=$ Radio waves

$\gamma$ rays $<$ X rays $<$ Microwave rays $<$ Radio waves

$\Rightarrow$ Infrared waves are produced by hot bodies and molecules. This band lies adjacent to low frequency or long wavelength end of visible spectrum.Infrared waves are sometimes referred to as heat waves. This is because water molecules present in most of the materials readily absorb infered waves. After absorbtion, their thermalmotion increase, that is they heat up and heat their surroundings.

$\Rightarrow$ Infrared radiation maintains the earth's warmth through greenhouse effect. Incoming visible light (which passes relatively easily through atmosphere) is absorb by earth's surface and reradiated as infrared radiation. This radiation is trapped by green house gases such as carbon dioxide and water vapour.

$\Rightarrow$ Physical therapies are used to cure injuries, increase strength. Infrared radiation are penetrated into body to gencrak theocratic benefits via amplyfeed blood flow and tissue oxygenation.The quick increase of blood flow and tissue oxygenation can help encouraging the generation of energy needed for heating.

Answer the following
(a) Name the em waves which are used for the treatment of certain forms of cancer. Write their frequency range.
(b) Welders wear special glass goggles while working. Why? Explain
(c) Why are infrared waves often called as heat waves? Give their one application.

(a) Gamma rays are used for the treatment of certain forms of cancer. The frequency range is

$3 \times 10^{19} Hz$ to

$5 \times 10^{24} Hz$ .

(b) Welders wear special glass googles while working so that they can protect their eyes from harmful electromagnetic(UV) radiation.

(c) Infrared waves are often called as heat waves because they induced resonance in molecules and increase internal energy in a substance.
Infrared waves are used in burglar alarms, security lights and remote controls for television and DVD players.

Fill in the blanks with suitable words:
Electromagnetic waves are ____ waves.

Electromagnetic waves are non mechanical waves. They do not require any material medium for oscillation of electric and magnetic fields. They can travel in vacuum also. Oscillations of electric and magnetic field are self sustaining in free space or vacuum.

What is electromagnetic radiation?

Electromagnetic radiation is form of energy that is all around us and takes many forms, Such as

$X$ rays and gamma rays. Sunlight is also a form of

$M$ energy, but visible light is only a small portion of

$EM$ spectrum, which contains a broad range of electromagnetic wavelengths.

Fill in the blanks with suitable words
The rays used to show bone structure is __________.

The rays used to show bone structure is

$X$ ray.

Bone

$X$ rays are used small dose of ionizing radiation to produce pictures of any bone in the body. Commonly used to diagnose fractured bones or fount dislocation.

$X$ rays in the form of radiation pass through parts of body. Different parts of body absorb X rays in varying degrees. Dense bone absorbs much of the radiation while soft tissue, Sach as muscle, fat and organs as a result bones appear white on

$X$ ray, Soft tissue shows up in the shade of grey and air appears black.

Match the EM waves from list I with corresponding Inventors in list II:

Microwaves - Microwaves were first predicted by James Clerk Maxwell in 1864 by the use of his equations
Infrared radiation - Infrared was discovered in 1800 by astronomer Sir William Herschel, who discovered a type of invisible radiation in the spectrum lower in energy than red light, by means of its effect on a thermometer.
X - rays - X-rays were discovered in 1895 by Wilhelm Conrad Roentgen (1845-1923).
Gamma rays - Paul Villard, a French chemist and physicist, discovered gamma radiation in 1900 while studying radiation emitted by radium.
Ultraviolet radiation - Johann Wilhelm Ritter is best known for his discovery of ultraviolet light in 1801.

Fill in the blanks with suitable words
The range of wavelength of visible light is __________.

The range of wavelength of visible light is

$7000A°$ to

$4000A°$ .

Our eyes is sensitive to visible light. Visible light emitted or reflected from objects around us provides information about world. Visible light is produced by transition of electrons in an atom from one energy level to other.

To which regions of the electromagnetic spectrum do the following wavelengths belong :
(a) $250 nm$
(b) $1500 nm$

(a)

$250 nm$ lies in Visible spectrum
(b)

$1500 nm$ lies in Infrared spectrum

List the properties of electromagnetic waves.

Electromagnetic waves are composed oscillating electric and magnetic field at right angles to each other.

Properties

Electromagnetic waves are propagated by oscillating electric fields and magnetic field oscillation at right angles to each other.
These waves travel with speed $3\times { 10 }^{ 8 }m{ s }^{ -1 }$ in vacuum.
They are not deflected by electric or magnetic field.
They can show interference or diffraction.
They are transverse waves.
May be polarized.
Need no medium of propagation.
wavelength and frequency related as $c=v\lambda$ .

How are electric vector $\vec{(E)}$ , magnetic vector $\vec{(B)}$ velocity vector $\vec{(c)}$ oriented in an electromagnetic wave ?

According to the Fleming's right hand rule, the electric vector

$\vec{(E)}$ , the magnetic vector

$\vec{(B)}$ and the velocity vector

$\vec{c}$ are mutually perpendicular to each other.

Explain the electromagnetic spectrum with a diagram.

Electromagnetic Spectrum :

$\rightarrow$ The basic source of electromagnetic wave is accelerated charge. This produces the changing electric and magnetic field constitute and electromagnetic wave. An electromagnetic wave may be have its wavelength varying from zero to infinity all of them are not discovered. But some are known

The classification of electromagnetic waves according to frequency or wavelength is called ELECTROMAGNETIC SPECTRUM

electromagnetic spectrum

S.No. Type Wavelength Range Frequency Range

1 Radio waves

$>0.1 m$

$<3\times { 10 }^{ 9 }㎐$

2 Micro waves

$0.1 m - 1 ㎜$

$3\times { 10 }^{ 9 }$ to

$3\times { 10 }^{ 11 }㎐$

3 Infrared

$1㎜$ to

$7000A°$

$3\times { 10 }^{ 11 }$ to

$4.3\times { 10 }^{ 17 }㎐$

4 Visible light

$7000$ to

$4000A°$

$4.3\times { 10 }^{ 14 }㎐$ to

$7.5to{ 10 }^{ 14 }㎐$

5 Ultraviolet

$4000A°$ to

$10A°$

$7.5\times { 10 }^{ 17 }$ to

$3\times { 10 }^{ 17 }㎐$

6 X-Rays

$10A°$ to

$0.01A°$

$3\times { 10 }^{ 17 }$ to

$3\times { 10 }^{ 20 }㎐$

7 Gamma Rays

$<0.01A°$

$>3\times { 10 }^{ 20 }㎐$

Electromagnetic waves with wavelength
(i) ${\lambda}_{1}$ is used in satellite communication.
(ii) ${\lambda}_{2}$ is used to kill germs in water purifiers
(iii) ${\lambda}_{3}$ is used to detect leakage of oil in underground pipelines
(iv) ${\lambda}_{4}$ is used to improve visibility in runways during fog and mist conditions
Identify and name the part of electromagnetic spectrum to which these radiations belong.

(i) Microwave is used in satellite communication so,

${\lambda}_{1}$ is the wavelength of microwave. It is used in microwave oven.
(ii) Ultraviolet rays are used to kill germs in water purifiers so,

${\lambda}_{2}$ is the wavelength of ultraviolet rays.
(iii) X rays are used to detect leakage of oil in underground pipelines so

${\lambda}_{3}$ is in X ray region. It is also used to detect cracks in machinery and to detect fracture in bones of body.
(iv) Infrared rays

${\lambda}_{4}$ are used to improve visibility due to larger wavelength of low scattering
Infrared rays are used in optical communication

Even through an electric field $E$ exerts a force $qE$ on a charged particle yet the electric field of an EM wave does not contribute to the radiation pressure (but transfers energy). Explain.

In electromagnetic wave, the electric field is oscillating, so the resultant electric force on the particle will be zero, as the direction of electric force changes every half of time period. As the electric field vibrates, the radiation of energy will takes place only due to vibrating electric and magnetic field.

When an electron falls from a higher energy to a lower energy level, the difference in the energies appears in the form of electromagnetic radiation. Why cannot it be emitted as other forms of energy ?

When charge i.e., electron jumps from higher to lower energy level; there is acceleration in charge particle. The accelerated charge particle can produce electromagnetic wave only.

Give one use of ultraviolet radiations.

1.Ultraviolet radiations are used for detecting the purity of gems , eggs , ghee etc.

2.UV radiation is widely used in industrial processes and in medical and dental practices for a variety of purposes, such as killing bacteria, creating fluorescent effects, curing inks and resins, photo therapy and suntanning.

State the approximate range of wavelength associated with the visible light .

The range of wavelength of visible light is approximately

$4000$ Å to

$8000$ Å , with violet being at the lower end (3800Å−4500Å) and red at the higher end (6200Å − 7500Å) .

What is the range of the wavelength of the following electromagnetic waves : Micro waves ?

Microwaves have wavelength range from

$10^7$ Å to

$10^{11}$ Å .

Name two electromagnetic waves of frequency greater than that of violet light. State one use of each.

X-rays and ultraviolet rays are electromagnetic waves of frequency greater than that of violet light.
Uses :
1.X-rays are used for studying atomic arrangement in crystals.
2.Ultraviolet rays are used for detecting the purity of gems , eggs , ghee , etc.

State the approximate range of wavelength associated with the infrared rays.

Infrared radiations have wavelength range from

$8000$ Å to

$10^7$ Å .

Give one use of infrared radiations .

1.Infrared radiations are used in remote control of television and other gadgets.

2.Heat-sensitive thermal imaging cameras : These can be used to study human and animal body heat patterns, but more often, they are used as night-vision cameras.

3.Infrared is also widely used in astronomy.

Give one use of microwaves.

1.Microwaves are used for satellite communication.

2.They are used by mobile phones (produced from a transmitter chip and antenna) as well as WiFi.

3.They are also used in radar which is used by ships, aircraft and weather forecasters.

What is the range of the wavelength of the following electromagnetic waves : Infrared rays ?

Infrared radiations have wavelength range from

$8000$ Å to

$10^7$ Å .

State the approximate range of wavelength associated with the ultraviolet rays .

Ultraviolet rays have wavelength range from

$100$ Å to

$4000$ Å

What is the range of the wavelength of the following electromagnetic waves : Radio waves ?

Radio waves have wavelength range above

$10^{11}$ Å .

Give two such properties of infrared radiations which are not true for visible light.

Two properties of infrared radiations which are not true for visible light are :

(a) Infrared radiations are invisible.
(b) They do not affect the ordinary photographic film.

Name three properties of ultraviolet radiations which are similar to visible light.

(a) Ultraviolet radiations travel in a straight line with a speed of

$3 \times 10^8 \,m$ in air (or vacuum).
(b) They obey the laws of reflection and refraction.
(c) They affect the photographic plate.

What are infrared radiations ? How are they detected ? State one use of these radiations.

Infrared radiations are the electromagnetic waves of wavelength in the range of

$8000$ Å to

$10^7$ Å .

$Detection$ : If a thermometer with a blackened bulb is moved from the violet end towards the red end, it is observed that there is a slow rise in temperature , but when it is moved beyond the red region, a rapid rise in temperature is noticed. It means that the portion of spectrum beyond the red end has certain radiations which produce a strong heating effect , but they are not visible. These radiations are called the infrared radiations.

$Use$ : The infrared radiations are used for therapeutic purpose by doctors and in satellite communication ..

Two waves A and B have wavelength $0.01$ Å and $9000$ Å respectively. Compare the speeds of these when they travel in vacuum.

Ratio of speed's of these waves in vacuum is

$1 : 1$ as all electromagnetic waves travel with the same speed of light in vacuum.

What are ultraviolet radiations ? How they are detected ? State one use of these radiations.

The electromagnetic radiations of wavelength from

$100$ Å to

$4000$ Å are called the ultraviolet radiations.

$Detection$ : If the different radiations from the red part of the spectrum to the violet end and beyond it , are made incident on the silver -chloride solution , it is observed that from the red to the violet end , the solution remain unaffected . How ever just beyond the violet end, it first turns violet and finally it becomes dark brown. Thus there exist certain radiations beyond the violet end of the spectrum, which are chemically more active than visible light, called ultraviolet radiations.

$Use$ : Ultraviolet radiations are used for sterilizing purposes.

Give one use of gamma rays .

1.Gamma rays are used in medical science to kill cancer cells.

2.Gamma rays are used in medicine (radiotherapy), industry (sterilization and disinfection) and the nuclear industry.

Explain the following :
Infrared radiations are used for photography in fog.

Infrared radiations are used in photography in fog because they are not much scattered by the atmosphere , so they can penetrate appreciably through it.

Mention three properties of infrared radiations similar to the visible light.

(a) Infrared radiations travel in straight line as light does , with a speed equal to

$3 \times 10^8 \, m/s$ in vacuum.
(b) They obey the laws of reflection and refraction.
(c)They are unaffected by electric and magnetic fields.

Two waves A and B have wavelength $0.01$ Å and $9000$ Å respectively. Name the two waves

The 2 waves are : A -

$Gamma$ rays and B -

$Infrared$ radiations

Explain the following :
Infrared radiations are used as signals during war.

Infrared radiations are used as signals during the war as they are not visible and they are not absorbed much in the medium.

Explain the following :
A quartz is required for obtaining the spectrum of the ultraviolet light.

A quartz prism is used to obtain the spectrum of the ultraviolet radiations as they are not absorbed by quartz , where as ordinary glass absorbs the ultraviolet light.

Explain the following :
The photographic darkrooms are provided with infrared lamps.

Infrared lamps are used in dark rooms for developing photographs since they do not affect the photographic film chemically , but they provide some visibility.

Explain the following :
A rock salt prism is used instead of a glass prism to obtain the infrared spectrum.

Infrared spectrum can be obtained only with the help of a rock-salt prism since the rock salt prism does not absorb infrared radiations where as a glass prism absorbs them.

Explain the following : Ultraviolet bulbs have a quartz envelope instead of glass.

Ultraviolet bulbs have a quartz envelope instead of glass as they are not absorbed by quartz , where as ordinary glass absorbs the ultraviolet light.

Write the uses of infra-red rays.

Uses of Infrared waves

$\to$ Infrared waves/radiation plays an important role in maintaining the earth's warmth or average temperature through the green house effect

$\to$ Infrared lamps are used in physical therapy.

$\to$ Infrared detectors are used in earth satellites, both for military purposes and to observe growth of crops.

$\to$ Infrared waves are used in remotes and other electronic systems for signal transmitting

$\to$ Infrared waves are used in observation of changing blood flow in the skin, and to detect over heating of electrical apparatus. And for thermal imaging using thermal cameras

An electromagnetic wave has a frequency of $500$ MHz and a wavelength of $60$ cm .
(a) Calculate the velocity of the wave.
(b) Name the medium through which it is travelling

(a) Frequency

$= 500$ MHz

$= 500 \times 10^6$ Hz
Wavelength

$= 60 \,cm = 0.6\,m$
Velocity of wave = Frequency

$\times$ Wavelength

$= 500 \times 10^6 \times 0.6 = 3 \times 10^8 \, m/s$
(b) Electromagnetic wave is travelling through air .

Explain the inconsistency of Ampere's circuital law during charging of a capacitor. Define displacement current.

In classical electromagnetism, Ampere's circuital law relates the integrated magnetic field around a closed loop to the electric current passing through the loop.

Ampere's law is valid only when there is a steady flow of current or electrostatic flux through a closed surface remains conserved, but at time of charging or discharging the flux does not remain conserved or there is no steady state.

So ampere law fails there, when displacement current is also considered then the flux remains conserved or we get steady state condition.

(i) The conduction and displacement currents are individually discontinuous, but the currents together possess the property of continuity through any closed electric circuit.

(ii) The displacement current is precisely equal to the

conduction current when the two present in different parts of the circuit.

(iii) The displacement current arises due to the rate of change of electric flux (or electric field) between the two plates of the capacitor.

(iv) Just as the conduction current, the displacement current is also the source of magnetic field.

Name the rays of
1.Waves of highest frequency
2.Rays used for taking photographs in the dark
3.Rays of wavelength nearly $0.1\ nm$

(i)Gamma rays are of highest frequency.

(ii)Infrared rays are used for taking photographs in dark.

(iii)X-rays are of wavelength nearly 0.1nm.

Fill in the blanks with the proper words.
GMRT is used for .......... waves.

GMRT is used for radio waves.

Fill in the blanks with the proper words.
A certain X-ray telescope is named after scientist ............

A certain X-ray telescope is named after scientist Subramanian Chandrashekhar .

Fill in the blanks with the proper words.
The wavelength of visible light is between .......... and ...........

The wavelength of visible light is between

$400\,nm$ and

$800\,nm$

Answer in brief:
Can microwaves be used in the experiment on photoelectric effect?

No, The microwaves cannot be used in photoelectric effect experiments.

Explanation:

The photoelectric effect is totally a Quantum physics phenomenon. A single photon of light delivers it's a tiny bundle of energy to the metal and ejects a single electron with a very precise energy balance.

Electric sparks emitted from metal points/edges in a microwave oven are a macroscopic phenomenon that has no need for a quantum explanation. The microwave generator pumps hundreds of watts of electromagnetic energy into the oven cavity. The microwaves have a frequency of 2.4 gigahertz which gives them a wavelength of about 12 cm. (About 4 3/4 inches for those in the US).

These intense electric fields induce currents to flow in the metal. Sharp points/edges concentrate the buildup of the electrons which can locally increase the voltage enough to cause the arcing.

Name the components of electromagnetic spectrum in decreasing order of wavelength.

The electromagnetic spectrum is generally divided into seven regions, in order of decreasing wavelength:

1. Radiowaves (

$10^3$ m)

2. Microwaves (

$10^{-2}$ m)

3. Infrared rays (

$10^{-5}$ m)

4. Visible rays (

$0.5 \times 10^{-6}$ ) m

5. Ultraviolet rays (

$\sim 10^{-8}$ ) m

6. X-rays (

$\sim 10^{-10}$ )

7. Gamma rays (

$\sim 10^{-12}$ m)

Name the components of electromagetic spectrum in decreasing order of wavelenght

The electromagnetic spectrum is generally divided into seven regions in order of decreasing wavelenght

1.Radiowaves

$(10^3m)$

2.Microwaves

$10^{-2m}$

3.Infrared rays

$(10^{-5}m)$

4.Visible rays

$(0.5 \times 10^{-6}m)$

5.Ultra rays

$(\sim 10^{-8}m)$

6.X-rays

$(\sim10^{-10}m)$

7.Gamma rays

$(\sim10^{-12}m)$

Which type of wave is a light wave?

A light wave is a non-mechanical wave, i.e. it does not require a mechanical medium for its propagation. It can also travel in vacuum.

What physical quantity is the same for X -rays of wavelength $10^{-1}$ m , red light wavelength 6800 A and radio waves of wavelength 500 m,?

Both X - rays and red light are parts of the electromagnetic spectrum . They travel with the same speed in Vaccum .

Given below are some fomous numbers associated with electromagnetic radiation in different contexts in physics .State the part of the electromagnetic spectrum to which each belongs .
1057 MH z (frequency of radiation arising from two close energy levels in hydrogen : know as lamb shift ).

Radiation of frequency of 1,057 MH z : It also corresponds to radio waves of short oil.wavelength [or of high frequency ].

Given below are some fomous numbers associated with electromagnetic radiation in different contexts in physics .State the part of the electromagnetic spectrum to which each belongs .
5890 A - 5890 A (double lines of sodium )

Double lines of sodium [ 5 , 890 A - 5 , 869 A ] : These lines corresponds to visible light in yellow region .

Given below are some fomous numbers associated with electromagnetic radiation in different contexts in physics .State the part of the electromagnetic spectrum to which each belongs .
7 K (temperature mwcrited with the isotropic radiation fHifag nil space - thought to be a reMC of the 'Mg - baugtrigbi of the universe }

Temperature of 2.7 K : As obtained in above question this temperature corresponds to the emission of microwaves.

What is Maxwell's displacement current?

The displacement current is produced , when in an electric circuit (say across the plates of a charged ), the electric field changes with time . Mathematically ,

$l_{D}\epsilon _{o}\times \dfrac{d\phi _{E}}{dt}$

A radio can tune in to any station in the 7.5 MH z to 12 band . What is the corresponding wavelength band ?

Corresponding to v = 7.5 Mh z

$= 7.5 \times 10^{6} H z$

$\lambda = \dfrac{C}{v} = \dfrac{3 \times 10^{8}}{7.5 \times 10^{6}} = 40 m$
and corresponding to

$v 12 MH z = 12\times 10^{6} Hz$

$\lambda = \dfrac{C}{v} = \dfrac{3 \times 10^{8}}{12 \times 10^{6}} = 25 m$
Therefore , the corresponding wavelength band is 25 m and 40 m .

Given below are some fomous numbers associated with electromagnetic radiation in different contexts in physics .State the part of the electromagnetic spectrum to which each belongs .
21 cm (wavelength emitted by atomic hydrogen in interstellar space ).

Radiation of wavelength of 21 cm : It corresponding to radio waves of short wavelength.

Use the formula $\lambda _{m}T = 29 cm K$ Obtain the charcteristic temperature ranges for different part of the electromagnetic spectrum .What do the numbers that you obtain tell you ?

$b = 0 . 29 cm^{k} = 0.0029mK$
wavelength of a -ray photon,

$\lambda _{m} = 5 \times 10^{-12}$
Therefore , temperature required for the emission of a r -ray photon,

$T = \dfrac{b}{\lambda _{m}} = \dfrac{0 . 0029}{5 \times 10^{-12}} = 5.8 \times 10^{8}K$

Given below are some fomous numbers associated with electromagnetic radiation in different contexts in physics .State the part of the electromagnetic spectrum to which each belongs .
14.4 keV { energy of a particular transition in 57 Fe nucles associated with a famous highresolution spectroscopic method (Mossbauer spectrocopy )]

Energy of 14.4 ke V : As obtained in question above, this energy corresponds to X - ray of low energy (Or - X - rays),

Find the wavelength of the electromagnetic wave of frequency $5\times 10^{19}$ Hz in free space identify the wave.

$V = 5\times 10^{19}Hz$

$C= 3\times 10^{8}ms^{-1}$

$C=V\lambda$

$\Rightarrow \lambda =\dfrac{C}{V}=\dfrac{3\times 10^{8}}{5\times 10^{19}}$

$=6\times 10^{-12}m$

$\lambda =6\times 10^{-12}m$ Corresponding to y - rays

$\xi$ and $\partial\xi/\partial x$ as functions of $x$ at the moments $t=0$ and $t=T/2,$ where $T$ is the oscillation period;

We are given

$\xi =a\cos kx \omega t$
so

$\dfrac {\partial \xi}{\partial x}=-a k \sin kx \cos \omega t$ and

$\dfrac {\partial \xi}{\partial t}=-a\omega \cos kx \sin \omega t$
Thus

$( \xi)_{t=0}=a\cos kx, ( \xi)_{t=\tau/2}=-a\cos kx$

$\left( \dfrac {\partial \xi}{\partial x}\right)_{t=0}=ak\sin kx, \left( \dfrac {\partial \xi}{\partial x}\right)_{t=T/2}=-ak\sin kx$
The graph of

$( \xi)$ and

$\left( \dfrac {\partial \xi}{\partial x}\right)$ are as shown in figure of the book.

Analyse and describe the working of a microwave oven.

Microwave oven is a device which is used for heating effect of electric current. It produces heat without a heating coil. Eddy current is used in the working of microwave oven. The heat is generated as a result of microwave radiations. The water molecules are stimulated using 'magnet one' and thus attains high temperature. Metal utensils are avoided and the substances without water content are not heated by this.

The magnetic field around the current carrying conductor AB is depicted
Based on the Maxwell's Right Hand Cork Screw Rule find out the direction of current and record it.

If a right hand screw is rotated in such a wave that its tip advances along the direction of the current in the conductor, then the direction of rotation of the screw gives the direction of the magnetic field around the conductor. In figure the current flows from B to A.
1789544_1848978_ans_b23ffb2d6352416f9141762db4154f9a.png

1789544_1848978_ans_b23ffb2d6352416f9141762db4154f9a.png

The ground state energy of hydrogen atom is $-13.6$ eV. If an electron makes a transition from an energy level $-1.51$ eV to $-3.4$ eV, then calculate the wavelength of the spectral line emitted and name the series of hydrogen spectrum to which it belongs.

Given ground state energy of hydrogen

${E}_{n}$ =

$\dfrac{-13.6}{{n}^{2}}eV$

As per question there is only 1 hydrogen atom than

${E}_{1}$ =

$-13.6$ eV

Now during electron transition from from one energy level to another energy level

${E}_{2}=-1.51eV\quad and\quad{E}_{3}=-3.4eV$

So,

${E}_{1}={E}_{2}$

$-1.51=\dfrac{-13.6}{{{n}^{2}}_{1}}$

${n}_{2}= 3$ ,similarly solving for

${E}_{2}$ we get the value of

${n}_{3}$ =

$2$

Thus electron transition takes place from

$n=3$ to

$n=2$ which corresponds to Balmer series

Thus

$\dfrac { 1 }{ \lambda } =R\{ \dfrac { 1 }{ { n }_{ 2 }^{ 3 } } -\dfrac { 1 }{ { n }_{ 2 }^{ 2 } } \}$

Substituting the values in above equation we get

$\dfrac { 1 }{ \lambda } =1.097\times { 10 }^{ 7 }\{ \dfrac { 1 }{ 4 } -\dfrac { 1 }{ 9 } \}$

$\\ \lambda =6563\mathring { A }$

An electromagnetic wave is radiated by a $100$ W bulb. If efficiency of the bulb is $20%$ then the amplitude of magnetic field at a distance of $1$ m is (Consider bulb as a point source)

Given power of bulb

$P=100 W$ and efficiency

$\eta=20$ %

Now the surface area of the surrounding sphere considering bulb as a point source which radiates electromagnetic

wave

$A=4\pi{r}^{2}$ where r= distance between the bulb and magnetic filed

$= 1m$

$A=12.56 {m}^{2}$

Now intensity at a distance of 1 m

$I=\dfrac{Power}{Area}=\dfrac{100\times0.20}{12.56}=1.59$

Also we know

$\dfrac{1}{2}I=\dfrac{1}{2}({\epsilon}_{0}{E}_{rms}^{2}C)$

${E}_{rms}=\sqrt{\dfrac{I}{{\epsilon}_{0}C}}$ where C= speed of light in air

$=3\times{10}^{8}$ and

${\epsilon}_{0}$ =permeability

$=8.85\times{10}^{-12}$

${E}_{rms}=\sqrt{\dfrac{1.59\times{10}^{4}}{8.85\times3}}=24.48$

Again we know Amplitude

${A}^{2}=E$

$A=\sqrt{24.48}=4.98$

A parallel plate capacitor (fig.) made of circular plates each of radius $R=6.0\ cm$ has a capacitance $C= 100 \mu F$ . The capacitor is connected to a $230\ V$ ac supply with a (angular) frequency of $300$ rad $s^{-1}$ . Determine the amplitude of $B$ at a point $3.0\ cm$ from the axis between the plates.?

Given: A parallel plate capacitor made of circular plates each of radius R=6.0 cm has a capacitance

$C=100\mu F$ . The capacitor is connected to a 230 V ac supply with a (angular) frequency of

$300 rad s^{−1} .$

To find the amplitude of B at a point 3.0 cm from the axis between the plates

Solution:

Radius of plates,

$R=6cm=6\times10^{-2}m$

Capacitance of capacitor,

$C=100\mu F=100\times10^{-6}F=10^{-4}F$

Voltage of capacitor,

$V=230V$

Frequency of capacitance,

$\omega=300rad/s$

By definition of the displacement current,

$I_d=\varepsilon_0\dfrac{d\phi_E}{dt}\\\implies I_d=\varepsilon_0\dfrac d{dt}(EA)\\\implies I_d=\varepsilon A\dfrac {dE}{dt}$

But

$E=\dfrac {\sigma}{\varepsilon_0}=\dfrac {Q}{\varepsilon_0 A}$

Substituting this in the abve equation, we get

$I_d=\varepsilon_0 A\dfrac d{dt}\left(\dfrac Q{\varepsilon_0 A}\right)\\\implies I_d=\varepsilon_0A.\dfrac 1{\varepsilon_0 A}.\dfrac {dQ}{dt}\\\implies I_d=\dfrac {dQ}{dt}=I$

The distance of point from the axis between the plates

$r=3cm=0.03m$

Radius of the plates,

$R=6cm=0.06m$

The magnetic field at a point between the plates

$B=\dfrac {\mu_0}{2\pi R^2}.r.I_d\\\implies B=\dfrac {\mu_0rI}{2\pi R^2}$

$I=I_0$ , maximum value of the current then

$I=\sqrt 2I_rms$

and

The rms value of the current

$I_{rms}=\dfrac {V_{rms}}{X_C}...........(i)$

And

$X_C=\dfrac 1{\omega C}$

Substituting this in eqn(i), we get

$I_{rms}=\dfrac {V_{rms}}{\dfrac1{\omega C}}\\\implies I_{rms}=V{rms}\times\omega\times C\\\implies I_{rms}=230\times300\times10^{-4}\\\implies I_{rms}=69\times10^3\times10^{-4}=6.9A$

Therefore

$B=\dfrac {\mu_0r}{2\pi R^2}\sqrt2I_{rms}\\\implies B=\dfrac{4\pi\times10^{-7}\times0.03\times \sqrt 2\times 6.9}{2\pi\times0.06\times0.06}\\\implies B=1.63\times10^{-5}T$

is the amplitude of B at a point 3.0 cm from the axis between the plates.

A silver wire has resistivity $\rho = 1.62 \times 10^{-8}\,\Omega.m$ and
a cross-sectional area of $5.00\, mm^2$ . The current in the wire is uniform and changing at the rate of $2000 \, A/s$ when the current is $100$ A. (a) What is the magnitude of the (uniform) electric field in
the wire when the current in the wire is $100$ A ? (b) What is the
displacement current in the wire at that time? (c) What is the ratio
of the magnitude of the magnetic field due to the displacement
current to that due to the current at a distance r from the wire?

a) Using Eq. , we find

$E=\rho J=\dfrac{\rho i}{A}=\dfrac{(1.62 \times 10^{-8}\,\Omega.m)(100\,A)}{500 \times 10^{-6}\,m^2}=0.324\,V/m$

(b) The displacement current is

$i_d=\epsilon_0\dfrac{d\phi_E}{dt}=\epsilon_0A\dfrac{dE}{dt}=\epsilon_0A\dfrac{d}{dt}\Bigg(\dfrac{\rho i}{A}\Bigg)=\epsilon_0\rho\dfrac{di}{dt}=(8.85 \times 10^{-12}\,F/m)(1.62 \times 10^{-8}\,\Omega)(2000\,A/s)$

$=2.87\times10^{-16}\,A$

(c) The ratio of fields is

$\dfrac{B(due \,to\, i_d)}{B(due \,to\, i)}=\dfrac{\mu_0i_d/2\pi r}{\mu_0i/2\pi r}=\dfrac{i_d}{i}=\dfrac{2.87 \times 10^{-16} \,A}{100\,A}=2.87\times10^{-18}$

Uniform displacement current. The figure shows a circular
region of radius $R = 3.00$ cm in which a uniform displacement current $i_d = 0.500$ A is out of the page. What is the magnitude of the
magnetic field due to the displacement current at radial distances
(a) $2.00$ cm and (b) $5.00$ cm?

As we know,

(a) Equation gives

$B=\dfrac{\mu_0i_dr}{2\pi R^2}=2.22\,\mu T$

(b) Equation gives

$B=\dfrac{\mu_0i_d}{2\pi r}=2.00\,\mu T$

A parallel-plate capacitor having plate-area A and plate separation d is joined to a battery of emf $\varepsilon$ and internal resistance R at $t = 0$ . Consider a plane surface of area $A/2$ , parallel to the plates and situated symmetrically between them.If the displacement current through this surface as a function of time is given as:
Y = $\dfrac{\varepsilon }{nR}e^{-\dfrac{td}{\epsilon AR}}$
Then find the value of n.

$E = \dfrac{Q}{\epsilon _{0}A}$ (Electric field)

$\phi = E.A. = \dfrac{Q}{\epsilon _{0}A}\dfrac{A}{2} = \dfrac{Q}{\epsilon _{0}2}$

$i_{0} = \epsilon _{0} \dfrac{d\phi _{E}}{dt} = \epsilon _{0}\dfrac{d}{dt}\left ( \dfrac{Q}{\epsilon _{0}2} \right ) = \dfrac{1}{2}\left ( \dfrac{dq}{dt} \right )$

$= \dfrac{1}{2}\dfrac{d}{dt}(ECe^{-1/RC})$

$= \dfrac{1}{2}EC-\dfrac{1}{RC}e^{-t/RC}$

$=\dfrac{-E}{2R}e^{\dfrac{-td}{RE_{0}2}}$

Uniform displacement-current density. The figure shows a
circular region of radius $R = 3.00$ cm in which a displacement current is directed out of the page. The displacement current has a
uniform density of magnitude $J_d = 6.00 \,A/m^2$ . What is the magnitude of the magnetic field due to the displacement current at radial
distances (a) $2.00$ cm and (b) $5.00$ cm?

(a) Equation gives, with

$A = πR^2$ ,

$B=\dfrac{\mu_0i_dr}{2\pi R^2}=\dfrac{\mu_0J_dAr}{2\pi R^2}=\dfrac{\mu_0J_d(\pi R^2)r}{2\pi R^2}=\dfrac{1}{2}\mu_0J_dr$

$=\dfrac{1}{2}(4 \times 10^{-7}\,T.m/A)(6.00\, A/m^2 )(0.0200\, m)= 75.4\, nT .$

(b) Similarly, Eq. 32-17 gives

$B=\dfrac{\mu_0i_d}{2\pi R}=\dfrac{\mu_0J_d\pi R^2}{2\pi R}=67.9\,nT$

Sea water at frequency $v=4\times {10}^{8}Hz$ has permittivity $\varepsilon =80{ \varepsilon }_{ 0 }$ permeability $\mu ={\mu}_{0}$ and resistivity $\rho =0.25\Omega-m$ . Imagine a parallel plate capacitor immersed in sea water an driven by an alternating voltage source $V(t)={V}_{0}\sin {(2\pi vt)}$ . What fraction of the conduction current density is the displacement current density?

Suppose distance between the parallel plates of capacitor is

$d$ and the applied voltage

$V(t)={ V }_{ 0 }\sin { \left( 2\pi vt \right) }$

$\therefore$

$E=\cfrac{V(t)}{d}=\cfrac{{ V }_{ 0 }\sin { \left( 2\pi vt \right) } }{d}$
By ohm's conduction current density

${ \vec { J } }_{ C }=\cfrac { 1 }{ \rho } \vec { E } =\cfrac { 1 }{ \rho } \cfrac { { V }_{ 0 }\sin { \left( 2\pi vt \right) } }{ d } \quad$
Let

${J}_{0}^{C}=\cfrac{{V}_{0}}{\rho d}$

$\therefore$

${J}_{C}={J}_{0}^{C}\sin { \left( 2\pi vt \right) }$
The displacement current

${J}_{d}=\varepsilon \cfrac { dE }{ dt } =\varepsilon \cfrac { d }{ dt } \cfrac { { V }_{ 0 } }{ d } \sin { \left( 2\pi vt \right) } =\cfrac { { eV }_{ 0 } }{ d } \cos { \left( 2\pi vt \right) } \left( 2\pi v \right) =\cfrac { 2\pi v\varepsilon { V }_{ 0 } }{ d } \cos { \left( 2\pi vt \right) }$

Let

$\quad { J }_{ 0 }^{ d }=\cfrac { 2\pi v\varepsilon { V }_{ 0 } }{ d }$

Then

${ J }_{ d }={ J }_{ 0 }^{ d }\cos { \left( 2\pi vt \right) }$

$\cfrac { { J }_{ 0 }^{ d } }{ { J }_{ 0 }^{ c } } =\cfrac { \cfrac { 2\pi v\varepsilon { V }_{ 0 } }{ d } }{ \cfrac { { V }_{ 0 } }{ \rho d } } =2\pi v{ \varepsilon }_{ 0 }\rho$

$\cfrac { { J }_{ 0 }^{ d } }{ { J }_{ 0 }^{ c } } =2\pi v{ \varepsilon }_{ 0 }\rho =2\pi \times 4\times { 10 }^{ 8 }\times 80{ \varepsilon }_{ 0 }\times 0.25=4\pi { \varepsilon }_{ 0 }\times 2\times 80\times 0.25\times { 10 }^{ 8 }=\cfrac { 2\times 80\times 0.25\times { 10 }^{ 8 } }{ 9\times { 10 }^{ 9 } } =\cfrac { 4 }{ 9 }$

In Figure, a uniform
electric field collapses. The vertical axis scale is set by $E_s = 6.0 \times 10^5\, N/C$ , and the horizontal axis scale is
set by $t_s = 12.0\, \mu s$ . Calculate the
magnitude of the displacement current through a $1.6 \,m^2$ area perpendicular to the field during each of
the time intervals a, b, and c shown
on the graph. (Ignore the behavior
at the ends of the intervals.)

(a) In region

$a$ of the graph,

$|i_d|=\epsilon_0\Bigg|\dfrac{d\phi_E}{dt}\Bigg|=\epsilon_0A\Bigg|\dfrac{dE}{dt}\Bigg|=(8.85 \times 10^{-12}\,F/m)(1.6\,m^2)\Bigg|\dfrac{4.5 \times 10^5\,N/C- 6.0 \times 10^5\, N/C}{4.0 \times 10^{-6}\, s}\Bigg|=0.71\,A$

(b)

$\, i_d ∝ dE/dt = 0$ .

$|i_d|=\epsilon_0\Bigg|\dfrac{d\phi_E}{dt}\Bigg|=\epsilon_0A\Bigg|\dfrac{dE}{dt}\Bigg|=(8.85 \times 10^{-12}\,F/m)(1.6\,m^2)\Bigg|\dfrac{-4.0 \times 10^5\,N/C}{2.0 \times 10^{-6}\, s}\Bigg|=2.8\,A$

There is a vacuum photocell whose one electrode is made of cesium and the other of copper. Find the maximum velocity of photoelectrons approaching the copper electrode when the cesium electrode is subjected to electromagnetic radiation of wavelength $0.22 \mu \mathrm{m}$ and the electrodes are shorted outside the cell.

A simple application of Einstein's equation

$\dfrac{1}{2} mv_{max}^{2} = hv - hv_{0} = \dfrac{2\pi hc}{\lambda} - A_{cs}$

gives incorrect result in this case because the photoelectrons emitted by the Cesium electrode are retarded by a small electrical field that exists between the Cesium electrode and the Copper electrode even in the absence of external emf. This small electrical field is caused by the contact potential difference whose magnitude equals the difference of work functions

$\dfrac{1}{e} (A_{cu} - A_{cs})$ volts.

Its physical origin is explained below.

The maximum velocity of the photoelectron reaching the copper electrode is then

$\dfrac{1}{2} mv_{m}^{2} = \dfrac{1}{2}mv_{0}^{2} - (A_{cu} - A_{cs}) = \dfrac{2\pi hc}{\lambda} - A_{cu}$

Here

$v_{0}$ id the maximum velocity of the photoelectrons immediately after emission. Putting the values we get, on using

$A_{cu} = 4 \cdot 47 eV, \lambda = 0 \cdot 22 \mu m,$

$v_{m} = 6 \cdot 41 \times 10^{5} m/s$

The origin of contact potential difference is the following. Inside the metal free electrons can be thought of as a Fermi gas which occupy energy levels up to a maximum called the Fermi energy

$E_{F}$ . The work function

$A$ measures the depth of the Fermi level.

When two metals 1 & 2 are in contact, electrons flow from one to the other till their Fermi levels are the same. This requires the appearance of contact potential difference of

$A_{1} - A_{2}$ between the two metals externally.

1952578_1854944_ans_cc3bbf3e6f88459ca97499b5a1cadf26.png

Demonstrate that the law of electric charge conservation, i.e. $\bigtriangledown \cdot j = -\partial \rho/ \partial t$ , follow from Maxwell's equations.

From the equation Curl

$\vec {H} - \dfrac {\partial \vec {D}}{\partial t} = \vec {j}$
We get on taking divergence of both sides

$-\dfrac {\partial}{\partial t} div \vec {D} = \div \vec {j}$
But div

$\vec {D} = \rho$ and hence

$div \hat {j} + \dfrac {\partial \rho}{\partial t} = 0$ .

Proceeding from Maxwell's equation show that in the case of a plane electromagnetic wave (Fig $4.38$ ) propagating in vacuum the following
$\dfrac{\partial E}{\partial t}=-c^{2}\dfrac{\partial B}{\partial x}=\dfrac{\partial B}{\partial t}=-\dfrac{\partial E}{\partial x}$ .

$\vec E=\hat j E ( t, x)$

$\vec B=\hat k B (t_1x)$
and Curl

$\vec E =\hat k \dfrac{\partial E}{\partial x}=-\dfrac{\partial \vec B}{\partial t}=-\hat k \dfrac{\partial B}{\partial t}$
so

$-\dfrac{\partial E}{\partial x}=\dfrac{\partial B}{\partial t}$
Also Curl

$\vec B=\varepsilon_0 \mu_0 \dfrac{\partial \vec E }{\partial t}=\dfrac {1}{c^2}\dfrac {\partial \vec E}{\partial t}$
and Curl

$\vec B=-\hat j \dfrac{\partial B}{\partial x}$ so

$\dfrac {\partial B}{\partial x}=-\dfrac{1}{c^2}\dfrac{\partial E}{\partial t}$ .

Demonstrate that a closed system of charged non-relativistic particles with identical specific charges emits no dipole radiation.

$P. \alpha \dot{| p|^2}$ when

$\vec p=\sum e_i \vec r_i =\sum \dfrac {e_i}{m_i}m_i \vec r_1=\dfrac {e}{m}\sum m_i \vec r_i$
if

$\dfrac {e_i }{m_i}=\dfrac em=fixed$
But

$\dfrac {d^2}{dt^2}\sum m_i \vec r_i=0$ for a closed system
Hence

$P=0$ .

Find the free electron concentration in ionosphere if its refractive index is equal to $n = 0.09$ for radio waves of frequency $v = 100 MHz.$

From the previous problem

$n^2 = 1 - \dfrac{n_0e^2}{\varepsilon_0 m \omega^2}$

$= 1 - \dfrac{n_0e^2}{4\pi^2\varepsilon _0mv^2}$

Thus

$n_0 = (4\pi^2 v^2 m\varepsilon_0/e^2) (1-n^2)=2.36\times 10^7 cm^{-3}$

How fast should a car move for the driver to perceive a red traffic light ( $\lambda \approx 0.70 \mu m$ ) as a green one ( $\lambda' \approx 0.55 \mu m$ )

1915545_1854677_ans_259c65a87c2e41f2a32502d6bc7986a3.PNG

A plane electromagnetic wave propagates in a medium moving with constant velocity $V \ll c$ relative to an intertial frame K. Find the velocity of that wave in the frame K if the refractive of the wave coincides with that of the medium.

The velocity of light in the frame in which the medium is moving is then by the law of addition of velocities is

$\frac{\frac{c}{n}+v}{1+\frac{c}{n}.v/c^2} = (\frac{c}{n}+v)(1-\frac{v}{cn}+.....)$

$\frac{c}{n}+v-\frac{v}{n^2}+.... = \frac{c}{n}+v(1-\frac{1}{n^2})$

This is the velocity of light in the medium in a frame in which the medium is moving with velocity v<<c.

Conceptual Questions
Radio stations often advertise "instant news." If that means you can hear the news the instant the radio announcer speaks it, is the claim true? What approximate time interval is required for a message to travel from Maine to California by radio waves? (Assume the waves can be detected at this range.)

No. Radio waves travel at a finite speed, the speed of light. Radio waves can travel around the curved surface of the Earth, bouncing between the ground and the ionosphere, which has an altitude that is small when compared to the radius of the Earth.

The distance across the lower forty-eight states is approximately

$5000 \,km$ , requiring a transit time of

$\dfrac{5\times10^6 \,m}{3 \times 10^8 \,m/s}\sim 10^{-2}s$ .

Conceptual Questions
Is Ampere’s law valid for all closed paths surrounding a conductor? Why is it not useful for calculating $\overrightarrow{B}$ for all such paths?

Ampere's law is valid for all closed paths surrounding a conductor, but not always convenient. There are many paths along which the integral is cumbersome to calculate, although not impossible. Consider a circular path around but not coaxial with a long, straight current-carrying wire. Ampere's law is useful in calculating

$\overrightarrow{B}$ if the current in a conductor has sufficient symmetry that the line integral can be reduced to the magnitude of

$\overrightarrow{B}$ times an integral.

Demonstrate that Maxwell's equations $\bigtriangledown \times E = -\partial B/\partial t$ and $\bigtriangledown \cdot B = 0$ are compatible, i.e. the first one does not contradict the second one.

From

$\vec {\bigtriangledown}\times \vec {E} = -\dfrac {\partial \vec {B}}{\partial t}$
we get on taking divergence

$0 = -\dfrac {\partial}{\partial t} div \vec {B}$
This is compatible with

$div \vec {B} = 0$ .

Conceptual Questions
Suppose a creature from another planet has eyes that are sensitive to infrared radiation. Describe what the alien would see if it looked around your library. In particular, what would appear bright and what would appear dim?

The entire room and its contents have a soft glow. Incandescent light bulbs shine brightly in the infrared, but fluorescent lights do not. The top of a computer monitor glows brighter than the screen, which glows faintly. Windowpanes appear dark if they are cool, and a patch of wall where sunlight falls glows brighter than where the sunlight does not fall. Heating resistors or warm air outlets shine, and the air near to them has a faint glow, but cold air outlets are dark, and the nearby air has no glow.

What does a radio wave do to the charges in the receiving antenna to provide a signal for your car radio?

Consider a typical metal rod antenna for a car radio. Charges in the rod respond to the electric field portion of the carrier wave. Variations in the amplitude of the incoming radio wave cause the electrons in the rod to vibrate with amplitudes emulating those of the carrier wave. Likewise, for frequency modulation, the variations of the frequency of the carrier wave cause constant-amplitude vibrations of the electrons in the rod but at frequencies that imitate those of the carrier.

An electromagnetic radiation is used for photography in fog.
Why is this radiation mentioned by you, ideal for this purpose?

An electromagnetic radiation is used for photography in fog.
This radiation is ideal for this purpose because it can penetrate fog.

An empty plastic or glass dish being removed from a microwave oven can be cool to the touch, even when food on an adjoining dish is hot. How is this phenomenon possible?

The frequency of EM waves in a microwave oven, typically

$2.45 \,GHz$ , is chosen to be in a band of frequencies absorbed by water molecules. The plastic and the glass contain no water molecules. Plastic and glass have very different absorption frequencies from water, so they may not absorb any significant microwave energy and remain cool to the touch.

Why should an infrared photograph of a person look different from a photograph taken with visible light?

An infrared photograph records the infrared light reflected, but also emitted by a person's face. When a person blushes or exercises or becomes excited, warmer areas glow brighter in the infrared. A person's nostrils and the openings of the ear canals are bright; brighter still are just the pupils of the eyes.

Describe the path of $\gamma$ -rays in a magnetic field.

Magnetic field exert force on charge particles

$\gamma$ rays are neutral in nature so they are not deflected by magnetic fields and travel straight.

What new concept did Maxwell’s generalized form of Ampere’s law include?

Maxwell included a term in Ampere's law to account for the contributions to the magnetic field by changing electric fields, by treating those changing electric fields as "displacement currents".

An electromagnetic radiation is used for photography in fog.
Identify the radiation.

The electromagnetic radiation which is used for photography in fog is Infrared radiation.

Do Maxwells equations allow for the existence of magnetic monopoles? Explain.

No, they do not. Specifically, Gauss's law in magnetism prohibits magnetic monopoles. If magnetic monopoles existed, then the magnetic field lines would not have to be closed loops, but could begin or terminate on a magnetic monopole, as they can in Gauss's law in electrostatics.

Figure represents the electromagnetic spectrum.
Fill in the blank spaces between visible light and radio waves by adding the names of the radiations.

Order of electromagnetic spectrum is :

$\gamma$ rays

$X-$ rays

Ultra violet

Visible light

Infra red

Microwaves

Radio waves

Figure represents the electromagnetic spectrum.
State the radiation that has the shortest wavelength.

1897622_1913525_ans_808c68a45767486f83fffa66765a3901.jpeg

the plots of $\xi,\partial\xi/\partial t,$ and $\partial \xi/\partial x$ vs $x;$

The given equation is,

$\xi =a\cos ( \omega t -kx)$
So at

$t=0$ ,

$\xi =a\cos kx$
Now,

$\dfrac{d\xi}{dt}=-a \omega \sin ( \omega t -kx)$
and

$\dfrac{d \xi}{dt}=a\omega \sin kx$ , at

$t=0$ .
Also,

$\dfrac{d\xi }{dx}=+ak \sin ( \omega t -kx)$
and at

$t=0$ ,

$\dfrac{d\xi}{dx}=-a k \sin kx$ .
Hence all the graphs are similar having different amplitudes.
1792264_1853354_ans_32624b21e5b64bd7aed7206ebccc4c6a.jpg

1792264_1853354_ans_32624b21e5b64bd7aed7206ebccc4c6a.jpg

Fig. 5.40 shows the plot of the function $y(x)$ representing a fraction of the total power of thermal radiation falling within
the spectral interval from 0 to $x .$ Here $x=\lambda / \lambda_{m}\left(\lambda_{m}\right.$ is the wavelength corresponding to the maximum of spectral radiation density). Using this plot, find:
(c) how many times the power radiated at wavelengths exceeding $0.76 \mu \mathrm{m}$ will increase if the temperature rises from 3000 to $5000 \mathrm{K}$

The value of x corresponding to 0.76 are

$x_1= 0.76$

$\frac{0.29}{0.3} = 0.786$ at 3000 K

$x_2 = 0.76$

$\frac{0.29}{0.5} = 1.31$ at 5000 K

A gas consists of atoms of mass m being in thermodyamic equilibrium at temperature T. Suppose $\omega_o$ is the natural frequency of light emitted by the atoms.
(a) Demosntrate that the spectral distribution of the emitted light is defined by the formula
$I_{\omega} = I_o e^{-a(1 - \omega/\omega_o)^2}$ ,
( $I_o$ is the spectral intensity sorresponding to the frequency $\omega_o, a = mc^2/2kT)$ .
(b) Find the relative width $\Delta \omega/ \omega_o$ of a given spectral line, i.e. the width of the line between the frequencies at which $I_omega = I_o /2$ .

1918135_1854744_ans_bd04eaf841674da68f9aa838671d5c81.png

Fig. 5.40 shows the plot of the function $y(x)$ representing a fraction of the total power of thermal radiation falling within
the spectral interval from 0 to $x .$ Here $x=\lambda / \lambda_{m}\left(\lambda_{m}\right.$ is the wavelength corresponding to the maximum of spectral radiation density). Using this plot, find:
(b) the fraction of the total radiation power falling within the visible range of the spectrum $(0.40-0.76 \mu \mathrm{m})$ at the temperature $5000 \mathrm{K}$

At 5000 K

$\lambda = \frac{0.29}{0.5}*10^-6m = 0.58 \mu m$

From the visible range 0.40 to 0.70 corresponds to the range 0.69 to 1.31 of x

From the curve, y(0.69) = 0.07

y(1.31) = 0.44

A sounding of dilute plasma by radio waves of various frequencies reveals that radio waves with wavelengths exceeding $\lambda_{0} = 0.75m$ experience total internal reflection. find the free electron concentration in that plasma.

1918125_1853942_ans_229c81e48465483b99b5d431c9c07731.PNG

A source of velocity relative to a receiver. Demonstrate that for $v \gg c$ the fractional variation of frequency of light is defined by

1915491_1854551_ans_d98c10131cd04a379bb55864e11a219a.PNG

Maxwells Equations and Hertzs Discoveries(6)
A very long, thin rod carries electric charge with the linear density $35.0 \,nC/m$ . It lies along the $x$ axis and moves in the $x$ direction at a speed of $1.50 \times 10^7 \,m/s$ . (a) Find the electric field the rod creates at the point $(x = 0, \,y = 20.0 \,cm, \,z = 0)$ . (b) Find the magnetic field it creates at the same point. (c) Find the force exerted on an electron at this point, moving with a velocity of $(2.40 \times 10^8)\hat{i} \,m/s$ .

1915607_1881056_ans_464297ef486646f59ddcb5a5efd77b8f.jpeg

Maxwells Equations and Hertzs Discoveries(17)
Review. A microwave oven is powered by a magnetron,an electronic device that generates electromagnetic waves of frequency $2.45 \,GHz$ . The microwaves enter the oven and are reflected by the walls. The standing-wave pattern produced in the oven can cook food unevenly,with hot spots in the food at antinodes and cool spots at nodes, so a turntable is often used to rotate the food and distribute the energy. If a microwave oven intended for use with a turntable is instead used with a cooking dish in a fixed position, the antinodes can appear as burn marks on foods such as carrot strips or cheese. The separation distance between the burns is measured to be $6 \,cm \pm 5\%$ . From these data, calculate the speed of the microwaves.

1915617_1881067_ans_e0af5c599e5b4763b45006a9d442fd8d.jpeg

Maxwells Equations and Hertzs Discoveries(14)
A radar pulse returns to the transmitter-receiver after a total travel time of $4.00 \times 10^{-4} \,s$ . How far away is the object that reflected the wave?

1915384_1881064_ans_74ff0ee9ac7f4d818bb165d74365fa60.jpeg

Figure represents the electromagnetic spectrum.
(i) Describe a common uses of X-rays.
(ii) State a precaution taken by those who work with X-rays.

1897624_1913527_ans_199fcdd2defe43b8864043040a33d8c3.jpeg

What are electromagnetic waves? Write its nature.

Electromagnetic waves: According to Maxwell "electromagnetic waves are those waves in which there are sinusoidal vibration of electric field and magnetic field vectors at right angles to each other as well as right angles to the direction of wave propagation."

$E_y=E_0sin\omega\left(t-\displaystyle\frac{x}{c}\right)$

$B_x=B_0sin\left(t-\displaystyle\frac{x}{c}\right)$
Where,

$E_0$ and

$B_0$ are the peak values of

$\vec{E}$ and

$\vec{B}$ ,

$E_y$ and

$B_x$ are instantaneous value of

$\vec{E}$ and

$\vec{B}$ distance x along X-axis and c is the velocity of electromagnetic waves.
The frequencies of both the fields are equal.
From eq. (1) and (2) it is clear that both the fields a re same phase.
i.e., at the instant where

$\vec{E}$ is maximum, then $$\vec{B} is also maximum.

In electromagnetic spectra, the wave length and frequencies are inversely related. A radio can tune in to any station in the $7.5 MHz$ to $12 MHz$ band. Determine the corresponding wave length band.

Speed of an EM wave

$c = 3\times10^8 m/s$

Wavelength of an EM wave

$\lambda = \dfrac{c}{\nu}$

Corresponding wavelength for the frequency

$7.5 MHz$ ,

$\lambda_1 = \dfrac{3\times 10^8}{7.5\times 10^6}$

$\implies$

$\lambda_1 = 40$ m

Corresponding wavelength for the frequency

$12 MHz$ ,

$\lambda_1 = \dfrac{3\times 10^8}{12\times 10^6}$

$\implies$

$\lambda_2 = 25$ m

Thus wavelength band is

$25$ m to

$40$ m.

The sound waves are the longitudinal waves. The electromagnetic waves are ________.

The sound waves are the longitudinal waves (a wave in which the medium vibrates along the direction of its propagation) whereas electromagnetic waves are transverse wave (a wave in which the medium vibrates at right angles to the direction of its propagation).

The ultraviolet radiant bulbs are made of quartz. Not of glass. Why?

The ultraviolet radiant bulbs are made of quartz and not of glass because glass absorbs ultra violet rays while the quartz does not.

Arrange the following electromagnetic waves in increasing order of their frequencies (i.e., begin with the lowest frequency): Visible light, $\gamma$ rays, X rays, micro waves, radio waves, infrared radiations and ultraviolet radiations.

electromagnetic waves in increasing order of their frequency :

Radio waves, micro waves, infrared waves, visible light, ultraviolet radiations,

$X$ rays,

$\gamma$ rays.

Identify the electromagnetic waves whose wavelengths lie in the range
1) $10^{11}\,m < \lambda < 10^{-11}m$
2) $10^{-4}\,m < \lambda < 10^{-6}m$
Write one use of each.

${ 10 }^{ 11 }m<\lambda { 10 }^{ -11 }m$ - Radio waves

They help in contacting the signals from satellite far from the earth. They have high frequency therefore dont scatter.

${ 10 }^{ -4 }m<\lambda { 10 }^{ -6 }m$ -Visible light

They help us to see the world in different colors.They give our eyes the color.

Write any three uses of infrared radiations.

$Infrared$

$radiation$

Spectrum of infrared radiations extend from $700$ nanometers to $1$ millimeter.
most of thermal radiation emitted by objects near room temperature is infrared.
Uses

It is used in heat sensitive thermal imaging cameras
It is used to send signals through fibre optic cables
Most remote controls operate by sending pulses of infrared

Write the following radiations in an ascending order in respect of their frequencies : X- rays, microwaves, UV (ultra - violet) rays and radio waves.

Referring to the electromagnetic spectrum shown in the figure, the radiations in an ascending order of frequencies are :

Radio Waves
Microwaves
Ultra Violet Rays
X rays

State Maxwell's theory of electromagnetic wave related to light. Write down four characteristics of electromagnetic waves.

According to Maxwell, light waves are associated with changing electric and magnetic fields.

Changing electric field produces a time and space varying magnetic field and a changing magnetic field produces a time and space varying electric field. The changing electric and magnetic fields result in the propagation of electromagnetic waves (or light waves) even in vacuum.

Characteristics of electromagnetic waves :

1)EM waves always travel at speed of light =

$3 \times 10^8 m/s$

2)EM waves can travel through vacuum.

3)EM waves consists of mutually perpendicular time varying electric and magnetic fields.

4)EM waves do have characteristics like wavelength , amplitude and frequency.

The smoke from a fire looks white.
Which of the following statements is true?
$1$ . Molecules of the smoke are bigger than the wavelength of light.
$2$ . Molecules of the smoke are smaller than the wavelength of light.

The smoke from fire looks white. This is because molecules of smoke are bigger than the wavelength of light. This is why smoke looks white because of scattering of white light to the same extent if the smoke molecules were smaller then the scattering of the light would be different and we would see a bond of Cobus, but all wavelengths are scattered same. Therefore white light is visible.

Name an electromagnetic wave which is used in the radar system used in aircraft navigation. Give another use of the wave.

Microwaves are less energetic electromagnetic waves which are used in radar system for aircraft navigation.

What do you mean by electromagnetic waves? Write the names of all electromagnetic waves from gamma rays to radio waves in order of their increasing wavelengths.

Electromagnetic waves are the waves or radiations having sinosuidal electric field and magnetic field varying perpendicular to each other and the electromagnetic waves propagates in the direction mutually perpendicular to both the fields.
Electromagnetic waves in the increasing order of wavelengths are given as :
Gamma rays < X-rays < Ultraviolet (UV) < Visible light < Infrared radiations < Microwaves < Radio waves.

What is the ratio of the speed of gamma rays to that of radio waves in vacuum?

Since both gamma rays and radio waves are electromagnetic waves and all electromagnetic waves travel with same speed in vacuum.
Thus speed of gamma rays is equal to that of radio waves in vacuum.
Thus ratio of their speed is

$1$ .

(a) Why are infra-red waves often called heat waves? Explain.
(b) What do you understand by the statement, "Electromagnetic waves transport momentum"?

(a) Infrared waves whenever encounter any object, they cause entire atoms and molecules to vibrate.

And due to these vibrations, the internal energy and temperature of the object increases.

Due to this infra red waves are often called as heat waves.

(b) Electromagnetic waves carry energy. It means that they also carry momentum and exerts radiation pressure.

The energy and momentum transported are not continuously distributed over the wave front. Energy and momentum are transported by photons in discrete packages.

Define displacement current.

In electromagnetism, displacement current is a quantity appearing in Maxwell's equations that is defined in terms of the rate of change of electric displacement field. Displacement current has the units of electric current density, and it has an associated magnetic field just as actual currents do.

It is mathematically represented as

$I_{d} = \epsilon_{0} \dfrac {d\phi_{E}}{dt}$ .

In a cylindrical space uniform electric field varies with respect to time with rate $(dE/dt)$ . $P$ is a point at a distance $r$ from the axis of the space. Deduce the expression for the magnetic field at $P$ .

Applying Maxwell's Equation

$\oint B.dt = \mu_{0}\epsilon_{0} \dfrac {d\phi_{6}}{dt}$

$\oint B . dt = \mu_{0}\epsilon_{0} . \dfrac {d(EA)}{dt}$

$\oint B . dt = \mu_{0}\epsilon_{0}A \dfrac {dE}{dt}$

$B . 2\pi r = \mu_{0}\epsilon_{0}A \dfrac {dE}{dt}$

$B = \dfrac {\mu_{0}\epsilon_{0}A}{2\pi r} \cdot \dfrac {dE}{dt}$

$B = \dfrac {\mu_{0}\epsilon_{0}2\pi r l}{2\pi r} \cdot \dfrac {dE}{dt}$

$\dfrac {B}{l} = \mu_{0}\epsilon_{0} \dfrac {dE}{dt}$

$B = \mu_{0}\epsilon_{0} \dfrac {de}{dt}$ .

A capacitor has been charged by a DC source. What are the magnitude of conduction and displacement current, when it is fully charged?

When the capacitor is fully charged, no current will pass through the capacitor. so there will be no conduction current as well as no displacement current. The circuit will act like an open circuit. The value of conduction current= displacement current=0.

The frequency of oscillation of the electric field vector of a certain e.m. wave is $5 \times 10^{14}\ Hz$ . What is the frequency of oscillation of the corresponding magnetic field vector and to which part of the electromagnetic spectrum does it belong?

Given: The frequency of oscillation of the electric field vector of a certain e.m. wave is

$5\times 10^4 Hz$ .

To find the frequency of oscillation of the corresponding magnetic field vector and to which part of the electromagnetic spectrum does it belong

The frequency of the electric field vector

$f=5\times10^{4}Hz$

The frequency of the magnetic field vector is also =

$5\times10^4Hz$

And we know,

$c=\lambda f\\\implies \lambda=\dfrac cf\\\implies \lambda=\dfrac {3\times10^8}{5\times10^4}\\\implies \lambda=0.6\times10^4=6\times10^3m$

Electromagnetic waves with longer wavelengths and lower frequencies include infrared light, microwaves, and radio and television waves lie in visible region.

Plane electromagnetic wave of intensity S are incident normally on a flat surface.Only a fraction $f$ of the incident energy is absorbed.What is the radiation pressure?

Given,

Radiation intensity= $S$

Reflected radiation $=S(1-f)$

Speed of light is $C=3\times {{10}^{8}}\,m{{s}^{-1}}$

Radiation pressure, $P=\dfrac{S}{c}+\dfrac{S(1-f)}{c}=\dfrac{2S}{c}-\dfrac{Sf}{c}$

Hence, radiation pressure, $\dfrac{S(2-f)}{c}$ $N{{m}^{-2}}$

A wave travels out in all directions from a point source. Justify the expression $y=(a_0/r)\sin k(r-vt)$ , at a distance r from the source. Find the speed, periodicity and intensity of the wave.

If P be the power of the point source then
Intensity,

$I=\dfrac{P}{4\pi r^2}$
or

$I\propto \dfrac{1}{r^2}$
But I

$\propto (amplitude)^2$
So

$A\propto 1/r$ or

$A=a_0/r$
Here

$a_0$ is constant.
The equation in standard form is

$y=a\sin k(r-vt)$
Therefore above equation is written as

$y=\dfrac{a_0}{r}\sin k(r-vt)$
Now comparing this equation with

$y=A\sin (kr-\omega t)$
We have

$\omega =kv$ , or

$n=\dfrac{kv}{2\pi}$ and

$k=\dfrac{2\pi}{\lambda}$
or

$\lambda =\dfrac{2\pi}{k}$ ; speed

$c=n\lambda =\dfrac{kv}{2\pi}\times \left(\dfrac{2\pi}{k}\right)$

$c=v$ and

$T=\dfrac{1}{n}=\dfrac{2\pi}{kv}$
Thus intensity is given by

$I=\dfrac{1}{2}\rho a^2\omega^2c$

$\Rightarrow I=\dfrac{1}{2}\rho \dfrac{a^2_o}{r^2}k^2v^2.v=\dfrac{1}{2}\dfrac{\rho a^2_ok^2v^3}{r^2}$ .

The subjective property of light related to its wavelength is ..........(colour, refractive index).

Different wavelength in the visible light is perceived as a different colors to human eye. Visible light is divided into seven bands- VIBGYOR each having a different range of wavelength.

What physical quantity is the same for X-rays of wavelength $10^{-10}m$ , red light of wavelength 6800 $\mathring A$ and radiowaves of wavelength 500m?

The speed in vacuum is the same for all,

$c=3 \times 10^{8}m/s$

Name the parts of the electromagnetic spectrum which is
(i) Suitable for radar systems used in aircraft navigation.
(ii) Used to treat muscular strain.
(iii) Used as a diagnostic tool in medicine.
Write in brief, how these waves can be produced.

(a) Microwaves are used for radar system in air craft navigation. Source of their production is oscillating currents in special vacuum tubes like klytrons, magnetrons, & gunn diodes.

(b) Infrared rays are used to treat muscular strain.

Source of the rays are vibrations of atoms & molecules in hot bodies.

Source of the rays are fast moving electrons striking a metal target with high atomic mass in X ray tubes.

Name the parts of the electromagnetic spectrum which is
(a) suitable for radar systems used in aircraft navigation
(b) used to treat muscular strain
(c) used as a diagnostic tool in medicine
Write in brief, how these waves can be produced

a. Microwaves are suitable for radar systems that are used in aircraft navigation.
These rays are produced by special vacuum tubes, namely Klystrons, magnetrons and Gunn diodes.
b. Infrared waves are used to treat muscular strain.
These rays are produced by hot bodies and molecules.
c. X rays are used as a diagnostic tool in medicine.
These rays are produced when high energy electrons are stopped suddenly on a metal of high atomic number.

To which part of the electromagnetic spectrum does a wave of frequency $5 \times 10^{11} Hz$ belong?

A wave of frequency

$5 \times 10^{11} Hz$ will belong to the microwaves of electromagnetic spectrum.

Welders wear special goggles or face masks with glass windows to protect their eyes from electromagnetic radiations. Names the radiations and write the range of their frequency

Welders wear special goggles with glass windows to protect the eyes from Ultra Violet rays also known as UV rays.

Goggles provide them a degree of eye protection from heat, optical radiation and sparks produced by the welding. Welding produces UV and IR radiations which cannot be seen by naked eye and can produce eye injury If special goggles are not wear.

UV blocking protective welding goggles are considered primary protection, with this eyes are still protected even when the face shield or helmet is lifted up.

Ultraviolet rays UV rays have frequency range 400nm to 0.6nm. Where nm denotes Nanometers.

To which part of the electromagnetic spectrum does a wave of frequency $3 \times 10^{13} Hz$ belong?

Infrared radiation frequency lies between frequency

${ 10 }^{ 14 }\quad to\quad { 10 }^{ 12 }$ Hz

thus frequency

$3\times { 10 }^{ 13 }Hz$ belong to category of infrared radiation

Why food placed in a microwave oven cooks more quickly than in a normal oven?

Food placed in a microwave oven cooks more quickly than in a normal oven. This is because water molecules in the food absorb the microwaves and become very hot.

Why welders generally wear mask during welding ?

To protect them self from the harmful radiations and gases releases during welding, they wear mask .The ultra - violet light coming out of the welding arc is harmful to eyes. The mask has a filter that absorbs the ultra-violet light.

The electromagnetic spectrum that has least wave length is .......................

Gamma ray has the shortest wavelength and ultraviolet has the third shortest wavelength in EM spectrum.

Name the radiations :
(i) That are used for photography at night.
(ii) Used for detection of fraction in bones.
(iii) Whose wavelength range is from $100\mathring { A }$ to $4000 \mathring { A }$ (or $10 nm$ to $400 nm$ ).

(i) Infrared radiations are used for photography at night.
(ii) X-rays are used for detection of fraction in bones.
(iii) Ultraviolet radiations are having the wavelength range from

$100\mathring { A }$ to

$4000 \mathring { A }$ (or

$10 nm$ to

$400 nm$ ).

Which electromagnetic radiation has wavelength greater than that of X rays and smaller than that of visible light?

Ultraviolet radiation has wavelength shorter than visible light and longer than X-rays as it lies in the wavelength range

$10nm$ to

$400nm$ .

A type of electromagnetic wave has wavelength $50\overset {\circ}{A}$ .
What is the speed of the wave in vacuum?

Electromagnetic waves have same speed as that of light in vacuum i.e,

$3\times 10^{8}m/s$ , even though these waves possess different wavelengths.

A type of electromagnetic wave has wavelength $50\overset {\circ}{A}$ .
State one use of this type of wave.

X-rays are having the wavelength range

$0.1\overset {\circ}{A}$ to

$100\overset {\circ}{A}$ .

X-rays are used for detection of fracture in bones.

$(i)$ Name the high energetic invisible electromagnetic waves which help in the study of the structure of crystals.
$(ii)$ State an additional use of the waves mentioned in part $(i)$ .

$\large\underline{\textbf{Concept applied:}}$

$\bullet$ X-rays have wavelength in the range of

$0.1\ \buildrel_{\circ} \over A$ to

$100\ \buildrel_{\circ} \over A$

$\bullet$ X-rays strongly affect the photographic plate. They cause fluorescence in certain materials such as zinc sulphide.

$\bullet$ X-rays can penetrate through human flesh, but they are stopped by bones.

$\large\underline{\textbf{Explanation:}}$

$\textbf{Part a:}$

X-rays are used for studying atomic arrangement in crystals.

$\textbf{Part b:}$

X-rays are used for the detection of fractures in bones, teeth, etc.(i.e. radiography) and for diagnostic purposes such as CAT scan in medical science.

A type of electromagnetic wave has wavelength $50\overset {\circ}{A}$ .
(i) Name the wave.
(ii) What is the speed of the wave in vacuum ?
(iii) State one use of this type of wave.

(i) X-Ray has wavelength

$50\overset {\circ}{A}$ .

(ii) The speed of the wave in vacuum is

$3 \times 10^8 m/s$ .

(iii) X-Rays are used for detection of fracture in bones.

The electromagnetic radiations that are used to take photographs of objects in darkness ...................

The electromagnetic radiation that is used in cameras to take photograph in darkness is infrared radiation whose wavelength is

$10^{-5} \ m$ .All heat waves mostly consist of infrared waves which are not visible to human eye.

Which electromagnetic waves are used in remote controller (switches)?

Remote controller usually use radio waves to control distance switches. A radio remote control system commonly has two parts: transmit and receive. The transmitter part is divided into two types, namely, RF remote control and transmitter module, by the way of using, the RF remote control can be used independently as a whole while the transmitter module is used as a component in the circuit.

Give the uses of ultraviolet radiation.

(i) They are used to destroy the bacteria and for sterilizing surgical instruments.
(ii) These radiations are used in detection of forged documents, finger-prints in forensic Laboratories.
(iii) They are used to preserve the food items.
(iv) They help to find structure of atoms.

i) If $force = mass \times acceleration$ , then $momentum =$ __
ii) If liquid hydrogen is for rocket, then _ is for MRI

If force = mass $\times$ acceleration, then momentum = mass $\times$ velocity
If liquid hydrogen is for rocket than liquid helium for MRI.

Helium is the preferred coolant to make the coils superconductive. It is colder than liquid Hydrogen

Write the name of the radiations of shortest and longest wavelength in the electromagnetic spectrum.

Shortest wave length: Gamma rays.
Longest wave length: Radio waves.

What are the applications of microwaves?

Applications of Microwave:

To cook food as it cause water and fat molecules to vibrate, which makes the substances hot.
Mobile phones use microwaves, as they can be generated by a small antenna.
Wifi also uses microwaves.
Fixed traffic speed cameras
For radar, which is used by aircraft, ships and weather forecasters.

Which waves are used as signal through fog and why?

At the time of fog, infrared light is used, because its wavelength is greater and it is not scattered, hence its penetrating power become more and they can travel more in fog.

Mention two applications of infrared radiation.

The following are the two applications of infrared radiation : -

1. It is used for night vision and security cameras as Infrared Radiation is visible in daytime or night-time.

2. Police use it to catch criminals, army use it to detect enemy.

How are Microwaves produced?

Microwaves are produced by vacuum tubes devices that operate on the ballistic motion of electron controlled by magnetic or electric fields. They work in the density modulated mode, instead of current modulated mode, meaning that they work on the basis of clumps of electrons flying ballistically through them, instead of using a constant flow of electrons. Lower power microwaves can me produced by some solid state devices such as the FET (field effect transistor), the tunnel diode, the gunn diode, and the IMPATT diode.

The frequency of optical waves is of the order of ________.

The highest energy wavelength detectable by the human eye is generally determined to be

$3.80 \times 10^{-7}$ m. Rewriting the formula c = λ f as f = c / λ yields (

$3.00 \times 10^8$ m/s /

$3.80 \times 10^{-7}$ m) =

$7.9 \times 10^{14}$ Hz for a frequency of the wave.

So, the answer is

$10^{14}$ Hz.

A radiation X is focused by a particular device on the bulb of a thermometer and mercury in the thermometer shows a rapid increase. Name the radiation X.

Infrared radiation is focused on the bulb of thermometer so that the mercury in the thermometer rises rapidly.

Give any two applications of X-rays.

$X-rays$ are used

$\to$ as a diagnostic tool in medicine to detect fracture of bones, foreign bodies like bullets and stones in body.

$\to$ in the treatment of certain cancer.

$\to$ for detecting faults, cracks and flaws in metal casting

$\to$ in the investigation of structure of crystals

$\to$ to cause photoelectric effect.

Is the colour of 620 nm light and 780 nm light same? Is the colour of 620 nm light and 621 nm light same? How many colours are there in white light?

No, colour of 620 nm light and 780 nm will not be light same.

Colour of 620 nm is orange and colour of 780 nm will be red.

yes,620 and 621 is same.

There are seven colours in white light.

Violet

Blue

Green

Yellow

Orange

Red

Do electromagnetic waves carry energy and momentum?

Yes, EM waves carry energy E and momentum P. As electromagnetic waves contain both electric and magnetic fields, there is a non-zero energy density associated with it.

Who unified electricity and magnetism?

Michael Faradyay and James clerk Maxwell unified electricity and magnetism in classical field theory.

Write the names of waves in electromagnetic spectrum having smallest and largest wavelength.

Electromagnetic spectrum in an increasing order of wavelength is given as :
Gamma rays < X-rays < UV < Visible < IR < Microwaves < Radio waves
Thus gamma rays have the smallest wavelength and radio waves have the largest wavelength in the electromagnetic spectrum.

The charging current for a capacitor is $0.25\ A$ . What is the displacement current across its plates?

The displacement current us equal to the charging elvocent. So, in the case the displacement elvocent is also

$0.25A$ . As of the charging current.

Is the ratio of frequencies of ultraviolet rays and infrared rays in glass more than, less than or equal to $1$ ?

Ultraviolet rays have more frequency than infrared rays hence ratio is:

$\dfrac {v_{ultraviolet}}{v_{infrared}} > 1$ .

Which out of the following are electromagnetic waves: X-rays, sound waves and radio waves?

X-rays and radio waves are electromagnetic waves.

If phase Difference between E and 1 is $\dfrac{\pi}{4}$ and f = 50 Hz then calculate time difference.

$\omega t = \displaystyle {\pi \over 4}$

$2\pi ft = \displaystyle {\pi \over 4}$

$t =\displaystyle {1 \over {8 \times 50}}\,\sec .$

$= 2.5\,m\sec .$

Answer the following questions .
Long - distance radio brodcasts use shorts -wave bands ,Why ?

The shortwaves (wavelength less than 200m or frequency greater than 1,500 kHz) are absorbed by the earth due to their high frequency but are effectively reflected by Flayer in the ionophere .

Considering the case of a parallel plate capacitor being charged, show how one is required to generalize Ampere's circuital law to include the term due to displacement current.

The space between the capacitor consists of an insulator. Hence, no actual transfer of charge occurs in this region. Current flows in the circuit during the charging of a capacitor. This demands the need of the presence of a displacement current in the capacitor resulting in a magnetic field.

$\int B.dl =\mu_o I$

Here

$I$ is the sum of conduction and displacement currents.

An electron beam passes through a transverse magnetic field of $2\times 10^{-3}$ tesla and electric field $E$ of $3.4\times 10^{4}V/m$ acting simultaneously. If the path of the electrons remain undeviated, calculate the speed of the electrons

Data:
Strength of magnetic field

$(B) = 2\times 10^{-3} Tesla$
Strength of electric field

$(E) = 3.4\times 10^{4} V/m$
Speed of electron

$V = \dfrac {E}{B}$

$= \dfrac {3.4\times 10^{4}}{2\times 10^{-3}} = 1.7\times 10^{7} ms^{-1}$ .

Write the relation for the speed of electromagnetic waves in terms of the amplitudes of electric and magnetic fields.

Consider following harmonic electromagnetic wave,
Assume that the electric and magnetic fields are constrained to the y and z directions, respectfully, and that they are both functions of only

$x$ and

$t$

$E=E_m\cos(kx-\omega t)$

$B=B_m\cos(kx-\omega t)$
E and B are electric and magnetic fields with amplitudes

$E_m$ and

$B_m$ respectively. k is the wave number and

$\omega$ is the frequency.
Now Maxwell's equation gives us

$\nabla\times E= -\frac{\partial B}{\partial t}$
The curl of electric field yields

$\frac{\partial E}{\partial x}\hat k$

$\therefore$

$\frac{\partial E}{\partial x}=-\frac{\partial B}{\partial t}$
Partially differentiating the Electric and Magnetic field equations above.

$kE_m\sin(kx-\omega t)=-(-B_m\omega \sin(kx-\omega t))$

$c=\frac{\omega}{k}=\frac{E_m}{B_m}$
where c is phase speed of electro-magnetic waves

Why are microwaves used in radars?

Microwaves have longer wavelengths and low frequencies. So they can be focussed along a straight line without much deviation and thus do not bend around corners of any obstacle coming in their path.

Who predicted the existence of electromagnetic waves? Give the wavelength range of electromagnetic spectrum.

James Clerk Maxwell predict the existence of electromagnetic waves undulations in intertwined electric and magnetic fields, traveling with the velocity of light.

Draw and label the diagram showing various regions of Electro-magnetic spectrum and their wavelength ranges.

The given diagram shows the electromagnetic spectrum.

You have learned that the temperature of stars can be guessed from their colour.
Rewrite the following list in the ascending order (lower to higher) of temperature.
(a) Orange star
(b) Blue star
(c) Red star

Stars according to their temperature in ascending order (lower to higher) are:

(a) Red star

(b) Orange star

Fill in the blanks in the following passage(s) from the words given inside the box.

magnet, carrying magnetic effect, electricity, the magnitude of current deflection increases, eastwards, southwards.

Oersted was the first to put forth the direct relation between ___ and magnetism. He conducted several experiments to determine the _ of a current _ wire. The following describes the Oersted experiment conducted to establish that a current carrying wire acts as a _.
A long straight wire is connected to an external battery and an electric current is passed through it. When a magnetic needle is placed below the wire such that the wire is parallel to the axis of the magnetic needle and the current flows in the south to north direction, a deflection in the needle is observed. It is observed that the north pole of the needle is deflected westwards and as the _ is increased, the deflection, _ till the north pole of the needle turns towards exact west. It is also observed that if instead of placing the magnetic needle below the wire, if it was placed above the wire, the north pole of the magnetic needle is deflected _____ .

Oersted was the first to put forth the direct relation between electricity and magnetism. He conducted several experiments to determine the magnetic effect of a current carrying wire. The following describes the Oersted experiment conducted to establish that a current carrying wire acts as a magnet. A long straight wire is connected to an external battery and an electric current is passed through it. When a magnetic needle is placed below the wire such that the wire is parallel to the axis of the magnetic needle and the current flows in the south to north direction, a deflection in the needle is observed. It is observed that the north pole of the needle is deflected westwards and as the magnitude of current is increased, the deflection increases till the north pole of the needle turns towards exact west. It is also observed that if instead of placing the magnetic needle below the wire, if it was placed above the wire, the north pole of the magnetic needle is deflected eastwards.

How are microwaves produced ? Why is it necessary in microwave ovens to select the frequency of microwaves to match the resonant frequency of water molecules ?

Microwaves are produced by vacuum tubes devices that operate on the ballistic motion of electron controlled by magnetic or electric fields. Some different kinds of microwave emitters are the cavity magnetron, the klystron, the traveling-wave tube(TWT), the gyrotron and all stars. These devices work in the density modulated mode, instead of current modulated mode, meaning that they work on the basis of clumps of electrons flying ballistically through them, instead of using a constant flow of electrons. Lower power microwaves can me produced by some solid state devices such as the FET (field effect transistor), the tunnel diode, the gunn diode, and the IMPATT diode.

Microwaves are used in microwave ovens for cooking and keeping the food fresh. In such ovens the frequency of microwave is selected to match the resonant frequency of water molecules so that energy from these waves is transferred efficiently as kinetic energy of water molecules which is shared by the entire food without any waste of energy

Write two important uses of infra-red waves.

(1) Infrared is used in night vision equipment when there is insufficient visible light.
(2) Infrared radiation can be used to remotely determine the temperature of objects (if the emissivity is known). This is termed thermography, or in the case of very hot objects in the NIR or visible it is termed pyrometry.

A radio can tune in to any station in the 7.5 MHz to 12 MHz band. What is the corresponding wavelength band?

$f_1=7.5\times 10^6\ Hz$

$f_2=12\times 10^6\ Hz$

$\lambda_1=c/f_1=40\ m$

$\lambda_2=c/f_2=25\ m$

So the range is 40m to 25m

Find the
(a) maximum frequency
(b) Minimum wavelength of X-rays produced by 30 kV electrons.

(a). Potential of the electrons,

$V = 30 kV = 3 × 10^4 V$

Hence, energy of the electrons,

$E = 3 × 104 eV$

Where,

e = Charge on an electron =

$1.6 × 10^{−19} C$

Maximum frequency produced by the X-rays is

$\nu$

The energy of the electrons is given by the relation is

$E=h\nu$

Where,

h = Planck’s constant =

$6.626 × 10^{−34}Js$

$\nu=E/h=7.24\times 10^{18}Hz$

(b). Energy of a electron,

$E=30\times 10^3eV$

Let Maximum frequency produced by the X-rays be

$\nu$

$\nu=E/h=1.6\times 10^{-19}\times 3\times 10^4/6.626\times 10^{-34}=7.24\times 10^{18}Hz$ where

$h$ is the planck's constant.

The minimum wavelength produced by the X-rays is given as-

$\lambda=c/\nu=0.0414nm$

A charged particle oscillates about its mean (equilibrium) position with a frequency of $10^{9} Hz$ . What is the frequency of the electromagnetic waves produced by the oscillator?

The frequency of an electromagnetic wave produced by the oscillator is same as that of charged particle oscillating about its mean position i.e.,

$10^9Hz$ .

Given below are some famous numbers associated with electromagnetic radiations in different contexts in physics. State the part of the electromagnetic spectrum to which each belongs.
(a) 21 cm (wavelength emitted by atomic hydrogen in interstellar space).

(b) 1057 MHz (frequency of radiation arising from two close energy levels in hydrogen; known as Lamb shift).

(c) 2.7 K [temperature associated with the isotropic radiation filling all space thought to be a relic of the big-bang origin of the universe].

(d) $5890 \mathring A- 5896 \mathring A$ [double lines of sodium]

(e) 14.4 ke V [energy of a particular transition in $^{57}$ Fe nucleus associated with a famous high resolution spectroscopic method ( $\text{M}\ddot o \text{ssbauer spectroscopy}$ )].

(a)

Radio waves have wavelengths of 1mm to 100km. Hence, 21cm lies at short wavelength end of radio waves.

(b)

Radio waves belong to the shortest wavelength in the electromagnetic spectrum.

(c)

$\lambda_m=0.29/T=0.11cm$

This wavelength corresponds to the microwaves.

(d)

Lines from 400nm to 700nm lies in visible range. The range of 589nm lies in Yellow part of visible spectrum.

(e)

$E=h\nu$

$\nu=3.4\times 10^{18}Hz$

This corresponds to the X-rays.

Write the expression for the generalized form of Ampere's circuital law. Discuss its significance and describe briefly how the concept of displacement current is explained through charging/discharging of a capacitor in an electric circuit

Ampere's Circuital Law states that the line integral of magnetic field induction equals the current enclosed times the permeability.

$\oint \vec B . \vec {dl} = \mu_o I_{enclosed}$

A capacitor is separated by a region of insulator. During charging/discharging of capacitor, electric current flows in the circuit. However, no actual charge flows in the insulator region of the capacitor. This demands the needs to incorporate a new fictitious displacement current

$I_D$ in the region which gives rise to a magnetic field in the region.

Write the uses of the following:
a. Radio waves
b. Microwaves
c. Ultraviolet radiation
d. X-rays
e. Infrared radiation
f. Gamma rays

Uses :

$\rightarrow$

1) Radio waves :

$\rightarrow$

They are used in radio and television communication systems.

2) Micro waves :

$\rightarrow$

Microwave oven are used in kitchen.

3) UV radiation :

$\rightarrow$

Important role in production of vitmin O.

4) X rays :

$\rightarrow$

X rays are used as diagnostic tool in medicine and as treatment for varrious forms of cancer.

5) Infrared Radiation :

$\rightarrow$

$\rightarrow$ used in detection of tumours.

$\rightarrow$ observe growth of crops.

6) Gamma rays :

$\rightarrow$

$\rightarrow$ used in medicine to destroy cancer cells.

Draw the diagram of electromagnetic wave.

Electromagnetic wave

When electromagnetic waves propagate in space then electric and magnetic field oscillate in mutually perpendicular direction.

Further they are perpendicular to the direction of propagation of electromagnetic.

Write the name of electromagnetic wave produced by vacuum tube magnetron.

The cavity magnetron is a high-powered vacuum tube that generates "microwaves" using the interaction of a stream of electrons with a magnetic field while moving past a series of open metal cavities (cavity resonators). Electrons pass by the openings to these cavities and cause radio waves to oscillate within. The magnetron serves solely as an oscillator, generating a microwave signal from direct current electricity supplied to the vacuum tube.

Hence microwaves are produced by vacuum tube magnetron.

How long would gamma radiation take to travel from sun to earth, a distance of $1.5\times 10^{11}m$ ?

We know

$S = \dfrac {d}{t}$

$t = \dfrac {1.5\times 10^{11}}{3\times 10^{8}}$

$= 500\ seconds$ .

What is displacement current? Obtain an expression of displacement current for a charged capacitor. Write Ampere-Maxwell's law.

When a capacitor is charging (or discharging), current flows in the circuit. However, there is no actual charge transfer in the insulated region between capacitor which is contradictory to the flow of current. Hence, displacement current is the current in the insulated region due to the changing electric flux.

For a charged capacitor, electric field between the plates is given by:

$E = \cfrac{Q}{\varepsilon_o A}$

$Q = \varepsilon_o \phi_E$

Displacement current is given by:

$i_d = \cfrac{dQ}{dt} = \varepsilon_o \cfrac{d\phi_E}{dt}$

According to Maxwell's Ampere circuital Law, the line integral of magnetic field along a closed path is equal to

$\mu_o$ times the total current.

$\oint \vec B . \vec {dl} = \mu_o (i_c + i_d)$

where

$i_c:$ Conduction current

$i_d:$ Displacement current

$\oint \vec B . \vec {dl} = \mu_o (i_c + \varepsilon_o\cfrac{d\phi}{dt})$

Identify the constituent radiations of electromagnetic spectrum which
(a) is obsorbed by ozone layer in the atmosphere
(b) i produced by bombarding a metal target by high speed electrons
(c) is used in satellite communication
(d) has wavelength range between 400 nm to 700 nm.

(a) Ultraviolet radiation is obsorbed by ozone layer in the atmosphere
(b) X-ray is produced by bombarding a metal target by high speed electrons
(c) Radio waves are used in satellite communication
(d) Visible spectrum has wavelength range between 400 nm to 700 nm.

(a) In free space at a point magnitude of electric field vector $\left( \overrightarrow { E } \right)$ is $9.3V/m$ . Find the magnitude of magnetic field vector $\left( \overrightarrow { B } \right)$ at the point.
(b) Out of ultraviolet, infrared and X-rays whose wavelength is maximum?

(a)

Ratio of magnitudes of electric field to magnetic field in an electromagnetic wave equals the speed of light.

$\cfrac{E}{B} = 3 \times 10^8$

$B = \cfrac{9.3}{3 \times 10^8}$

$B = 3.1 \times 10^{-8}\ T$

(b)

From the attached figure, frequency of X-rays > UV > Infrared

Write the mathematical equation of 'Ampere-Maxwell law'.

$\nabla\times B=\mu_0 J+\mu_0\epsilon_0\dfrac{\partial E}{\partial t}$

where

$J$ is the magnetization current density as well as conduction and polarization current densities.

$B$ is the magnetic field

$E$ is the electric field.

Write an expression for the displacement current.

By integral form of modified Maxwell's equations, we have:

$\oint _{ \partial S } { B }\cdot d{ \ell }=\mu _{ 0 }\int _{ S } ({ J }+\epsilon _{ 0 }\dfrac { \partial { E } }{ \partial t } )\cdot d{ S }\,$

Where the displacement current density is given by:

${ J }_{ D }={ \epsilon }_{ 0 }\dfrac { \partial E }{ \partial t }$

The above integral states that, the line integral of magnetic field around any loop is equal to

${ \mu }_{ 0 }$ times the surface integral of the total current density.

Give two uses of Infrared Rays.

Infrared rays have a variety of applications. Two of them are-

A typical television remote control uses infrared energy at a wavelength around 940 nanometers.
Weather forecasting makes use of the infrared radiation emitted by cloud formations, which can be captured and transmitted by weather satellites as images to meteorologists.

Screen S is illuminated by two point sources A and B. Another source C sends a parallel beam of light towards point P on the screen. Line AP is normal to the screen and the lines AP, BP and CP are 6, 3 and 3m respectively. The radiant powers of sources A and B are 45 and 90 W respectively. The beam from C is of intensity 0.4 $W/m^2$ . The total incident intensity at P is

Given: Screen S is illuminated by two point sources A and B. Another source C sends a parallel beam of light towards point P on the screen. Line AP is normal to the screen and the lines AP, BP and CP are 6, 3 and 3m respectively. The radiant powers of sources A and B are 45 and 90 W respectively. The beam from C is of intensity is

$0.4W/m^2$

To find the total intensity at P

Solution:

The total intensity at point P will be

$I_P=I_A+I_B+I_C$

And

Intensity at point P due to source A is

$I_A=\dfrac {\text{Illumination power}\times \cos\theta}{4\pi r^2}\\\implies I_A=\dfrac {45\times\cos 0}{4\pi 6^2}\\\implies I_A=\dfrac 5{16\pi}W/m^2$

Similarly,

Intensity at P due to source B is

$I_B=\dfrac {90\times\cos(45^\circ)}{4\pi 3^2}\\\implies I_B=\dfrac {7}{4\pi}$

And

Intensity at P due to beam C of intensity

$0.4W/m^2$ along the direction CP is

$I_C=0.4\times\cos(45^\circ)=0.28$

Hence,

$I_P=\dfrac 5{16\pi}+\dfrac7{4\pi}+0.28=0.94W/m^2$

is the intensity at point P.

Write the name of any four waves (radiations) produced in electromagnetic spectrum.

The four waves produced in EM spectrum are-
1) X-rays
2) Radio-wave
3) Infrared
4) Microwave

The monoenergetic beams of electronics moving along + y direction enters a region of uniform electric and magnetic fields. If the beam goes straight through, then ithese simultaneously field $\vec{B}$ and $\vec{E}$ are directed ?

Force of monoenergetic beam of electrons due to magnetic field

$=\vec { V } \times \vec { B }$

B = magnetic field

V = velocity of electrons

and force is perpendicular to magnetic field direction

Force due to electric field

$=q\vec { \epsilon }$

$q=$ magnitude of charge

$\vec { \epsilon }$ = electric field

direction of force due to electric field is parallel to velocity of beam.

If beam of electrons pass straight it means no force due to magnetic field that implies magnetic field and velocity are parallel and electric field also parallel to electrons.

Direction of magnetic field = y axis

Direction of electric field = y axis

Only then it is possible when beam of electrons went straight.

What are electromagnetic waves? Describe Maxwell's electromagnetic theory in brief.

We know that stationary charge produce electric field. Charges in uniform motion produce both electric and magnetic field. ACCELERATED CHARGE RADIATE ELECTROMAGNETIC WAVES. It is an important result of Maxwell's theory. Thus an electron produces all three electric field,magnetic field and electromagnetic waves.

Maxwell theory :

When electromagnetic waves propagate in space than electric and magnetic field oscillate in mutual perpendicular direction.

We know that time varying magnetic field produces electric field.

Maxwell explained that time varying electric field also produces magnetic field Maxwell formulated a set of equations (Maxwell questions) involving electric and magnetic field.

Ampere law

$\oint { Bdl } ={ \mu }_{ 0 }i$

Maxwell formed the relation of time varying electric and magnetic field.

$\oint { B.dl }= { \mu }_{ 0 }{ \varepsilon }_{ 0 }\cfrac { d{ \phi }_{ \varepsilon } }{ dt }$

So combination of ampere law

$\oint { B.dl }= { \mu }_{ 0 }{ \varepsilon }_{ 0 }\cfrac { d{ \phi }_{ \varepsilon } }{ dt } +\quad { \mu }_{ 0 }i$

${ \mu }_{ 0 }(id+i )$

$id=$ displacement current

$i=$ conduction current

$id={ \varepsilon }_{ 0 }\cfrac { d{ \phi }_{ \varepsilon } }{ dt }$

${ \varepsilon }_{ 0 }=$ permittivity

Time dependent electric field and magnetic field give rise to each other.

Name the phenomenon which shows the quantum nature of electromagnetic radiation.

Photoelectric effect shows the quantum nature of electromagnetic radiation.

This effect was discovered by Hertz in

$1887$ .

When light of appropriate frequency is incident on metallic surface,electrons are liberated from that surface.The observation is known as photoelectric effect.

For photo-electrons emission, energy of incident light photon should be greater than equal to work function of metal

$E\ge W$

$E=$ energy of incident light

$W=$ work function of metal

Write any three medical applications of X-rays.

Three medical applications of X-rays are :
(1) : Projectional radiography is the practice of producing 2-D images using X-rays radiations. These are helpful in detection of some disease process in soft tissue.
(2) : The use of X-rays as a treatment, known as radiation therapy, is used for management of cancer.
(3) : CT scanning is a medical imaging modality where where tomography images of specific areas of body are obtained from a large series of 2-D X-ray images taken in different directions.

What is displacement current? Why was this concept introduced? Explain. Also obtain the Ampere-Maxwell equation.

Displacement current is a quantity appearing in Maxwell’s Equation. It is defined in terms of the rate of change of electric displacement field. The units of displacement current are same as that of electric current density. Displacement current is not an electric current caused due to moving of charges(called conventional current), but it is caused by a time varying electric field.

If we consider a capacitive circuit, we can see there is current flowing through the circuit. But if you look at the capacitor plates, there is a small empty region in between them.

Then how the circuit is completed?

The circuit is completed despite the small space because there is displacement in that region which is developed as a consequence of the electric field in between the plates.

So according to Ampere circuital law,

$\oint \vec B. \vec dl = {\mu}_0 (I_c + I_D)$

where Ic is conduction current, and Id is displacement current.

Displacement current caused by varing electric field therefore has

${I}{}_{D} = \epsilon _o \dfrac{d {\phi}_E}{dt}$

Substituting the value in Ampere circuital law. We get

$\oint \vec B. \vec dl = {\mu}_o(I_C + {\epsilon}_o \dfrac{d {\phi}_E}{dt})$

Hence the ampere Circutal law is modified to Ampere-Maxwell Law.

A parallel plate capacitor (Fig.) made of circular plates each of radius R = 6.0 cm has a capacitance C = 100 pF. The capacitor is connected to a 230 V ac supply with a (angular) frequency of 300 rad $s^{-1}$ .
(a) What is the rms value of the conduction current?

(b) Is the conduction current equal to the displacement current?

(c) Determine the amplitude of B at a point 3.0 cm from the axis between the plates.

$(a)$ RMS value of the conduction current,

$I=\dfrac{V}{X_c}$

$X_c=\dfrac{1}{\omega C}$

$\Rightarrow I= V\omega C$

$\Rightarrow I= 230\times300\times100\times10^{-12}$

$\Rightarrow I=6.9\mu A$

$(b)$ Yes. Conduction current is equal to the displacement current.

$(c)$ $B=\dfrac{\mu_o rI_o}{2\pi R^2}$

$I_o=\sqrt 2 I$

r is distance between plates from the axis, $r=0.03 m$

putting values

$B = \dfrac{4\pi\times10^{-7}\times0.03\times\sqrt 2\times6.9\times10^{-6}}{2\pi\times0.06^{2}}$

$\Rightarrow B=1.63\times 10^{-11}\ T$

When the voltage applied to an $X-$ ray tube increased emitted from ${ V }_{ 1 }=10\ KV$ to ${ V }_{ 2 }=20\ KV,$ the wavelength interval between the ${ K }_{ \alpha }$ -line and the short wavelength cut-off of the continuous $X-$ ray spectrum increases by a factor of $3$ . Find the atomic number of the element of the target

1321421_1014098_ans_84a9340235174358bd970d792637182c.jpg

A plane electromagnetic wave of frequency $25\ MHz$ travels in free space along the x-direction. At a particular point in space and time, $\vec { E } =6.3\hat { j } { V }/{ m }$ . What is $\vec {B}$ at this point?

The magnitude of B is

B =

$\frac{E}{C}$

$\frac{6.3}{3\times10^8}$

$2.1 \times 10^{-8}T$

To find the direction, we note that E is along y - direction and the wave propagates along x - axis.

Therefore, B should be in a direction perpendicular to both x - and y - axes.

Using vector algebra, E

$\times$ B should be along x - direction.

since, ( + j )

$\times ( + k ) = i$ ,

so, B is along + k

or the z - direction

$\vec B=2.1\times 10^{-8} k$

An electron gun with its collector at a potential of $100V$ fires out electrons in a spherical bulb containing hydrogen gas at low pressure ( $\sim {10}^{-2}mm$ of Hg). A magnetic field of $2.83\times {10}^{4}T$ curves the path of the electrons in a circular orbit of radius $12.0cm$ . (The path can be viewed because the gas ions in the path focus the beam by attracting electrons, and emitting light by electron capture, this method is known as the fine beam tube method. Determine $e/m$ from the data.

Here,

Potential at the collector, V =100V

Magnetic field B is

$2.83 \times {10^{ - 4}}T$

Radius of the circular orbit

$r = 12cm = 12 \times {10^{ - 2}}m$

When electrons are accelerated through a potential of V volts the gain in the kinetic energy K.E. of the electron is given by:

$\begin{array}{l} \dfrac { 1 }{ 2 } m{ v^{ 2 } }=eV \\ { v^{ 2 } }=\dfrac { { 2eV } }{ m } \end{array}$

Since the electron moves in a circular orbit under the magnetic field,therefore, force on the electron due to magnetic field provides the centripetal force to the electron.

$\begin{array}{l} evB=\dfrac { { m{ v^{ 2 } } } }{ r } \\ eB=\dfrac { { mv } }{ r } \\ From\, above\, equations, \\ { v^{ 2 } }=\dfrac { { { e^{ 2 } }{ B^{ 2 } }{ r^{ 2 } } } }{ { { m^{ 2 } } } } \\ \dfrac { e }{ m } =\dfrac { { 2V } }{ { { r^{ 2 } }{ B^{ 2 } } } } =\dfrac { { 2\times 100 } }{ { { { \left( { 12\times { { 10 }^{ -2 } } } \right) }^{ 2 } }\times { { \left( { 2.83\times { { 10 }^{ -4 } } } \right) }^{ 2 } } } } =1.73\times { 10^{ 11 } }Ck{ g^{ -1 } } \end{array}$

A message signal of frequency 20 KHz and peak voltage of 20 volts is used to modulate a carrier signal of frequency 2 MHz and peak voltage of 40 volts. Determine (i) modulation index, (ii) the side bands produced. Draw the corresponding frequency spectrum of amplitude modulated signal.

Given

For message signal

Frequency,

$f_m=20\ kHz$

Peak voltage,

$A_m=20\ V$

For carrier frequency

Frequency,

$f_c=2MHz=2000\ kHz$

Peak voltage,

$A_c=40\ V$

(i) Modulation frequency is given by

$\mu=\dfrac{A_m}{A_c}=\dfrac{20}{40}=0.5$

(ii) The side band will be at

$(f_c\pm f_m)=(2000\pm20)\ kHz=2020\ kHz\ and\ 1980kHz$

The electromagnetic waves of frequency range $100$ to $300$ GHz are used in

Radio waves have many uses—the category is divided into many subcategories, including microwaves and electromagnetic waves used for AM and FM radio, cellular telephones and TV.

The lowest commonly encountered radio frequencies are produced by high-voltage AC power transmission lines at frequencies of 50 or 60 Hz. These extremely long wavelength electromagnetic waves (about 6000 km) are one means of energy loss in long-distance power transmission.

Extremely low frequency (ELF) radio waves of about 1 kHz are used to communicate with submerged submarines. The ability of radio waves to penetrate salt water is related to their wavelength (much like ultrasound penetrating tissue)—the longer the wavelength, the farther they penetrate. Since salt water is a good conductor, radio waves are strongly absorbed by it; very long wavelengths are needed to reach a submarine under the surface.

Which part of electromagnetic spectrum has largest penetrating power?

Gamma rays have maximum energy and hence, maximum penetration power.

A parallel plate capacitor (fig.) made of circular plates each of radius $R=6.0\ cm$ has a capacitance $C= 100 \mu F$ . The capacitor is connected to a $230\ V$ ac supply with a (angular) frequency of $300$ rad $s^{-1}$ . What is the $rms$ value of the conduction current?

Given: A parallel plate capacitor made of circular plates each of radius R=6.0 cm has a capacitance

$C=100\mu F$ . The capacitor is connected to a 230 V ac supply with a (angular) frequency of

$300 rad s^{−1} .$

To find the rms value of the conduction current

Solution:

Radius of plates,

$R=6cm=6\times10^{-2}m$

Capacitance of capacitor,

$C=100\mu F=100\times10^{-6}F=10^{-4}F$

Voltage of capacitor,

$V=230V$

Frequency of capacitance,

$\omega=300rad/s$

The rms value of the current

$I_{rms}=\dfrac {V_{rms}}{X_C}...........(i)$

And

$X_C=\dfrac 1{\omega C}$

Substituting this in eqn(i), we get

$I_{rms}=\dfrac {V_{rms}}{\dfrac1{\omega C}}\\\implies I_{rms}=V{rms}\times\omega\times C\\\implies I_{rms}=230\times300\times10^{-4}\\\implies I_{rms}=69\times10^3\times10^{-4}=6.9A$

is the rms value of the conduction current

An observer is moving with half the speed of light towards a stationary microwave source emitting waves at frequency 10 GHz. What is the frequency of the microwave measured by the observer? $\left( speed\quad of\quad light=3\times { 10 }^{ 8 }{ ms }^{ -1 } \right)$

2048997_1398305_ans_3dff149e4d7d4a33836354c048738578.jpg

Which part of electromagnetic spectrum is used in
(i)Treating mascular pains
(ii) Detecting flaws in crystallography
(iii)RADAR communication

1448652_1364853_ans_807116160fd64eb4a6d9c06393d9ad35.jpeg

Nonuniform displacement-current density. The figure shows a circular region of radius $R=3.00$ cm in which a displacement current is directed out of the page. The magnitude of the density of this displacement current is $J_d = (4.00 \, A/m^2 )(1 - r/R)$ ,
where r is the radial distance ( $r \leq R$ ). What is the magnitude of the
magnetic field due to the displacement current at (a) $r = 2.00$ cm
and (b) $r = 5.00$ cm?

(a) The equation applies (though the last term is zero) but we must be careful with

$i_{d,enc}$ . It is the enclosed portion of the displacement current, and if we related this to the
displacement current density

$J_d$ , then

$i_{d,enc}=\int^r_0J_d\,2\pi r\,dr=(4.00\, A/m^2 )(2\pi)\int(1-r/R)r\,dr=8\pi\Bigg(\dfrac{1}{2}r^2-\dfrac{r^3}{3R}\Bigg)$

with SI units understood. Now, we apply (with

$i_d$ replaced with

$i_{d, enc}$ ) or start
from scratch with, to get

$B=\dfrac{\mu_0i_{d,enc}}{2\pi r}=27.9\, nT$

(b) The integral shown above will no longer (since now

$r > R$ ) have r as the upper limit;
the upper limit is now R. Thus,

$i_{d\,enc}=i_d=8\pi\Bigg(\dfrac{1}{2}r^2-\dfrac{r^3}{3R}\Bigg)=\dfrac{4}{3}\pi R^2$

Now Eq. gives

$B=\dfrac{\mu_0i_d}{2\pi r}=15.1\, nT$

The Sun is approximately an ideal blackbody radiator with a surface temperature of $5800 \mathrm{K}$ . (a) Find the wavelength at which its spectral radiancy is maximum and (b) identify the type of electromagnetic wave corresponding to that wavelength. (See Fig. 33-1.)(c) As we shall discuss in Chapter 44, the universe is approximately an ideal blackbody radiator with radiation emitted when atoms first formed. Today the spectral radiancy of that radiation peaks at a wavelength of $1.06 \mathrm{mm}$ (in the microwave region). What is the corresponding temperature of the universe?

(a) Using the value

$h c=1240 \mathrm{eV} \cdot \mathrm{nm}$ , we obtain

$\lambda=\dfrac{h}{p}=\dfrac{h}{\sqrt{2 m_{e} K}}=\dfrac{h c}{\sqrt{2 m_{e} c^{2} K}}=\dfrac{1240 \mathrm{eV} \cdot \mathrm{nm}}{\sqrt{2(511000 \mathrm{eV})(1000 \mathrm{eV})}}=0.0388 \mathrm{nm}\\$

(b) A photon's de Broglie wavelength is equal to its familiar wave-relationship value. Using the value

$h c=1240 \mathrm{eV} \cdot \mathrm{nm}$

$\lambda=\dfrac{h c}{E}=\dfrac{1240 \mathrm{eV} \cdot \mathrm{nm}}{1.00 \mathrm{keV}}=1.24 \mathrm{nm}\\$

$1.675 \times 10^{-27} kg$ . Using the conversion from electronvolts to Joules, we obtain

$\lambda=\dfrac{h}{\sqrt{2 m_{n} K}}=\dfrac{6.63 \times 10^{-34} \mathrm{J} \cdot \mathrm{s}}{\sqrt{2\left(1.675 \times 10^{-27} \mathrm{kg}\right)\left(1.6 \times 10^{-16} \mathrm{J}\right)}}=9.06 \times 10^{-13} \mathrm{m}\\$

Just after detonation, the fireball in a nuclear blast is approximately an ideal blackbody radiator with a surface temperature of about $1.0 \times 10^{7} \mathrm{K} .$ (a) Find the wavelength at which the thermal radiation is maximum and(b) identify the type of electromagnetic wave corresponding to that wavelength. (See Fig. 33-1.) This radiation is almost immediately absorbed by the surrounding air molecules, which produces another ideal blackbody radiator with a surface temperature of about $1.0 \times 10^{5} \mathrm{K} .$ (c) Find the wavelength at which the thermal radiation is maximum and (d) identify the type of electromagnetic wave corresponding to that wavelength.

The de Broglie wavelength of the electron is

$\lambda=\dfrac{h}{p}=\dfrac{h}{\sqrt{2 m_{e} K}}=\dfrac{h}{\sqrt{2 m_{e} e V}}\\$

where

$V$ is the accelerating potential and

$e$ is the fundamental charge. This gives

$\begin{aligned}\lambda &=\dfrac{h}{\sqrt{2 m_{e} e V}}=\dfrac{6.626 \times 10^{-34} \mathrm{J} \cdot \mathrm{s}}{\sqrt{2\left(9.109 \times 10^{-31} \mathrm{kg}\right)\left(1.602 \times 10^{-19} \mathrm{C}\right)\left(25.0 \times 10^{3} \mathrm{V}\right)}} \\&=7.75 \times 10^{-12} \mathrm{m}=7.75 \mathrm{pm}\end{aligned}\\$

In Figure, a capacitor with
circular plates of radius $R= 18.0$ cm is connected to a source of emf $E = E_m sin \omega t$ , where $E_m = 220$ V
and $\omega = 130\, rad/s$ . The maximum value of the displacement current is $i_d = 7.60 \mu A$ . Neglect fringing of the electric field at the
edges of the plates. (a) What is the maximum value of the current i
in the circuit? (b) What is the maximum value of $d\phi_E/dt$ , where $\phi_E$ is the electric flux through the region between the plates? (c) What
is the separation d between the plates? (d) Find the maximum
value of the magnitude $\vec B$ of between the plates at a distance of $r = 11.0$ cm from the center.

(a) At any instant, the displacement current id in the gap between the plates equals the
conduction current i in the wires. Thus

$i_{max} = i_{d\, max} = 7.60 \,μA$ .

(b) Since

$i_d = ε_0 (dΦ_E/dt)$ ,

$\Bigg(\dfrac{d\phi_E}{dt}\Bigg)_{max}=\dfrac{i_{d\,max}}{\epsilon_0}=\dfrac{7.60 \times 10^{-6}\,A}{8.85 \times 10^{-12}\,F/m}=8.59\times10^5\,V.m/s$

(c) Let the area plate be A and the plate separation be d. The displacement current is

$i_d=\epsilon_0\dfrac{d\phi_E}{dt}=\epsilon_0\dfrac{d}{dt}(AE)=\epsilon_0A\dfrac{d}{dt}\Bigg(\dfrac{V}{d}\Bigg)=\dfrac{\epsilon_0A}{d}\Bigg(\dfrac{dV}{dt}\Bigg)$

Now the potential difference across the capacitor is the same in magnitude as the emf of
the generator, so

$V = ε_m\, \sin ωt$ and

$dV/dt = ωε_m \cos ωt$ . Thus,

$i_d=(ε_0Aωε_m/d)\cos \omega t$ and

$i_{d\,max}=ε_0Aωε_m/d$ . This means

$d=\dfrac{ε_0Aωε_m}{i_{d\,max}}=\dfrac{(8.85 \times10^{-12}\,F/m)(0.180\, m)(130\,rad/s)(220 \,V)}{7.60 \times 10^{-6}\, A}=3.39\times10^{-3}\,m$

where

$A = πR^2$ was used.

(d) We use the Ampere-Maxwell law in the form

$\oint \vec B.d\vec s=\mu_oi_d$ , where the path of
integration is a circle of radius r between the plates and parallel to them.

$I_d$ is the
displacement current through the area bounded by the path of integration. Since the
displacement current density is uniform between the plates, $$Id = (r^2/R^2
)i_d

$, where$ i_d$$ is the
total displacement current between the plates and

$R$ is the plate radius. The field lines are circles centered on the axis of the plates, so

$\vec B$ is parallel to

$d\vec s$ . The field has constant
magnitude around the circular path, so

$\oint \vec B.d\vec s =2πrB$ . Thus,

$2πrB=\mu_0\Bigg(\dfrac{r^2}{R^2}\Bigg)i_d\,\Rightarrow\,B=\dfrac{\mu_0i_dr}{2\pi R^2}$

The maximum magnetic field is given by

$B_{max}=\dfrac{\mu_0i_{d\,max}r}{2\pi R^2}=\dfrac{(4\pi \times 10^{-7}\, T.m/A)(7.6 \times 10^{-6}\, A) (0.110\,m)}{2\pi(0.180\,m)^2}=5.16 \times 10^{-12}\, T$

Answer the following questions:
Which one of the following electromagnetic radiations has least frequency:
(i) $UV$ radiations, X-rays, Microwaves?
(ii) How do you show that electromagnetic waves carry energy and momentum?
(iii) Write the expression for the energy density of an electromagnetic wave propagating in free space.

(i) Microwave

(ii) When a charge oscillates with some frequency. It produces an oscillating electric field and magnetic field in space. So, an electromagnetic wave is produced.

The frequency of the em wave is equal to the frequency of oscillation of the charge.

Hence energy associated with the em wave comes at the expenses of the energy of the source.

If the em wave of energy

$U$ strikes on a surface and gets completely absorbed, total momentum delivery to the surface is

$p = \dfrac {U}{E}$ .

(iii) The em wave consists of oscillating electric and magnetic fields, so net energy density of em wave is

$U = U_{E} + U_{B}$

$U = \dfrac {1}{2} \epsilon_{0} E^{2} + \dfrac {1}{2} \epsilon_{0} E^{2} + \dfrac {1}{2} \dfrac {B^{2}}{\mu_{0}}$ .

$(a)$ What maximum light wavelength will excite an electron in the valence band of diamond to the conduction band? The energy gap is $5.50 eV$ . $(b)$ In what part of the electromagnetic spectrum does this wavelength lie?

(a) Since the electron jumps from the conduction band to the valence band, the energy
of the photon equals the energy gap between those two bands. The photon energy is given by

$hf = hc/\lambda$ , where

$f$ is the frequency of the electromagnetic wave and

$\lambda$ is its wavelength. Thus,

$Eg = hc/\lambda$ and

$\lambda =\frac{hc}{E_g}=\frac{(6.63\times 10^{-34}J.s)(2.998\times 10^8 m/s)}{(5.5eV)(1.60\times 10^{-19}J/eV)}=2.26\times 10^{-7}m=226nm$
Photons from other transitions have a greater energy, so their waves have shorter
wavelengths.
(b) These photons are in the ultraviolet portion of the electromagnetic spectrum.

What happens to the intensity of light from a bulb if the distance from the bulb is doubled? As a lesser beam travels across the length of a room, its intensity essentially remains constant.
What geometrical characteristic of LASER beam is responsible for the constant intensity which is missing in the case of light from the bulb?

Bulb spreads its light in all ground spherically and symmetrically. So, if the distance from the bulb is doubled, the surface area covered by radiations change from

$4\pi {r}^{2}$ to

$4\pi {(2r)}^{2}$ ie.,

${2}^{2}$ or four times decreased in straight laser. But in a bulb it decreased by

$4(4\pi)$ ie.,

$16\pi$ decreased. So, the intensity becomes one-fourth the initial value in straight line. Since

$(I\propto \cfrac{1}{{r}^{2}})$ and for spherical source

$(I \propto \dfrac{1}{4\pi {r}^2})$
In case of laser, it does not spread in all directions. It passes only along a straight line. So, its intensity remains same almost.
Geometrical characteristics of LASER beam which is responsible for the constant intensity are:
(i) Monochromatic (ii) Coherent (iii) Highly collimated from all around source, (iv) Unidirectional
these characteristics are missing in the case of light from the bulb.

Assume that in the SternGerlach experiment as described for neutral silver atoms, the magnetic field $overrightarrow B$ has a magnitude of 0.50 T. (a) What is the energy difference between the magnetic moment ori-entations of the silver atoms in the two subbeams? (b) What is the frequency of the radiation that would induce a transition between these two states? (c) What is the wavelength of this radiation, and (d) to what part of the electromagnetic spectrum does it belong?

1754105_1778303_ans_23269dc018cc48009638087b35814eef.jpg

Figure 8.6 shows a capacitor made of two circular plates each of the radius 12 cm , and separated by 5.0 cm .The capacitor is being charged by an external source (not shown in the figure ) .The charging current is constant and equal to 0.15 A .
Obtained the displacement current cross the plates .

Here ,

$1 = 0.15 A ; d = 5.0 cm = 5.0 \times 10^{-2}m$

$R = 12 cm = 12 \times 10^{-2}m$

Therefore , area of each plate,

$A = \pi R^{2} = \pi \times \left [ 12 \times 10^{-2} \right ]^{2} = 1 .44\pi \times 10^{-2} m^{2}$

we know that

$\varepsilon _{0} = 8.85 \times 10^{-12} C ^{2} N^{-1}m^{-2}$

The capacitance of the parallel plate capacitor is given by

$C = \varepsilon _{0}\dfrac{A}{d} = \dfrac{8.85 \times 10^{-12}\times 1.44\pi \times 10^{-2}}{5.0 \times 10^{-2}}$

$= 8.01 \times 10^{-12}F$

Now , q = C v

$\therefore I = \dfrac{dq}{dt} = \dfrac{d}{dt} (CV) = C\dfrac{dv}{dt}$

$\dfrac{dv}{dt} = \dfrac{1}{C} = \dfrac{0.15}{8.01 \times 10^{-12}} = 1.873 \times 10^{10} Vs^{-1}$

The displacement current is equal to the conduction current i.e 0.15 A

In Figure, a parallel-plate
capacitor has square plates of edge length $L =1.0$ m. A current of $2.0$ A charges the capacitor, producing a uniform electric field
between the plates, with $\vec E$ perpendicular to
the plates. (a) What is the displacement current $i_d$ through the region between the
plates? (b) What is $dE/dt$ in this region?
(c) What is the displacement current encircled by the square dashed path of edge
length $d = 0.50$ m? (d) What is the value of
$\oint \vec B.d\vec s$ around this square dashed path?

The electric field between the plates in a parallel-plate capacitor is changing, so there
is a nonzero displacement current

$i_d=\epsilon_0(d\phi_E/dt)$ between the plates.

Let A be the area of a plate and E be the magnitude of the electric field between the plates.
The field between the plates is uniform, so

$E = V/d$ , where V is the potential difference
across the plates, and d is the plate separation. The current into the positive plate of the
capacitor is

$i=\dfrac{dq}{dt}=\dfrac{d}{dt}(CV)=C\dfrac{dV}{dt}=\dfrac{\epsilon_0A}{d}\,\dfrac{d(Ed)}{dt}=\epsilon_0A\dfrac{dE}{dt}=\epsilon_0\dfrac{d\phi_E}{dt}$

which is the same as the displacement current.

(a) At any instant, the displacement current

$i_d$ in the gap between the plates equals the
conduction current i in the wires. Thus

$i_d = i = 2.0$ A.
(b) The rate of change of the electric field is

$\dfrac{dE}{dt}=\dfrac{1}{\epsilon_0A}\Bigg(\epsilon_0\dfrac{d\phi_E}{dt}\Bigg)=\dfrac{i_d}{\epsilon_0A}=\dfrac{i_d}{\epsilon_0A}=\dfrac{2.0\,A}{(8.85\times10^{-12}\,F/m)(1.0\,m)^2}=2.3\times10^{11}\,\dfrac{V}{m.s}$

$i'_d=i_d\Bigg(\dfrac{d^2}{L^2}\Bigg)=(2.0\,A)\Bigg(\dfrac{0.50\,m}{1.0\,m}\Bigg)^2=0.50\,A$

(d) The integral of the field around the indicated path is

$\oint \vec B.d\vec s=\mu_0i'_d=(1.26 \times 10^{-16}\,H/m) (0.50\,A)=6 3 \times 10^{-7}\,T.m$

Martian $CO_2$ laser. Wheresunlight shines on the atmosphere of Mars, carbon dioxide molecules at an altitude of about 75km undergo natural laser action. The energy levels involved in the
action are shown in the above figure; population inversion occurs between energy levels E2 and E1.
(a) What wavelength of sunlight excites the molecules in the lasing action? (b) At what wave-length does lasing occur? (c) In what region of the electromagnetic spectrum do the excitation and lasing wavelengths lie?

1974228_1778629_ans_fcea9036a02a4b64bf17584d149b8472.jpg

Nonuniform displacement current. The figure shows a
circular region of radius $R=3.00$ cm in which a displacement
current id is directed out of the figure. The magnitude of the
displacement current is $i_d = (3.00 A)(r/R)$ ,
where r is the radial distance ( $r \leq R$ ) from the
center. What is the magnitude of the magnetic field due to id at radial distances (a) $2.00$ cm and (b) $5.00$ cm?

(a) The equation applies (though the last term is zero) but we must be careful with

$i_{d,enc}$ .
It is the enclosed portion of the displacement current. Thus Equation (which derives
from Eq. 32-11) becomes, with id replaced with

$i_{d, enc}$ ,

$B=\dfrac{\mu_0i_{d\,enc}}{2\pi r}=\dfrac{\mu_0(3.00 A)( r/R)}{2\pi r}$

which yields (after canceling r, and setting

$R = 0.0300$ m)

$B = 20.0 \,μT$ .

(b) Here

$i_d = 3.00$ A, and we get

$B=\dfrac{\mu_0i_d}{2\pi r}=12.0\,\mu T$

the efficient value of the displacement current density;

$E=E_m \cos ( 2\pi vt -kx)$

$j_{dis}=\dfrac{\partial D}{\partial t}=-2\pi \varepsilon_0 vE_m \sin ( \omega t-kx)$
Thus

$(j_{dis})_{rms}= < j_{dis}^2 >^{1/2}$

$=\sqrt 2 \pi \varepsilon_0 v E_m=0.20\ mA/m^2$ .

A conductor in the shape of a square frame with side $a$ suspended by an elastic thread is located in a uniform horizontal magnetic field with induction $B$ . In equilibrium the plane of the frame is parallel to the vector $B$ Fig. Having been displaced from the equilibrium position, the frame performs small oscillations about a vertical axis passing through its centre. The moment of inertia of the frame relative to that axis is equal to $I$ , its electric resistance is $R$ . Neglecting the inductance of the frame, find the time interval after which the amplitude of the frame's deviation angle decreases e-fold.

$\phi=$ angle of deviation of the frame from its norm,al position, then an e.m.f.

$\varepsilon =B a^2 \dot \phi$
is induced in the frame in the dispalced position and a current

$\dfrac{\varepsilon }{R}=\dfrac{B a^2 \dot \phi}{R}$ flows in it .A couple

$\dfrac{B a^2 \dot \phi}{R}.B.a.a=\dfrac{B a^4 }{R} \dot \phi$
then acts on the fram ein addition to any elastic energy couple

$c \phi$ . We write teh equatin of the frame as

$I \ddot \phi +\dfrac{B a^4 }{R} \dot \phi +c \phi=0$
Thuis

$\beta \dfrac{B a^4 }{2 I R}$ where

$\beta$ is defined in th book.
Amplitude of oscillation die out acoording to

$e^{ \beta t}$ so time required for the oscillations to decreses to

$\dfrac{1}{e}$ of its value is

$\dfrac{1}{\beta}=\dfrac{2 I R}{B^2 a^4}$

the ratio of electromagnetic radiation flow densities $S_{1}/S_{2}$ at the point $P$ at the moments of time when the particle moves, from the standpoint of the observer $P$ , toward him and away from him as shown in the figure.

Energy flow density of

$EM$ radiation

$S$ is proportional to the square of the

$y-$ projection of the observed acceleration of the particle

$\left( i.e.\dfrac{d^2y^1}{d{t^1}^2}\right)$ .
Thus

$\dfrac{S_1}{S_2}=\left[ \dfrac{\left( \dfrac vc -1 \right)}{\left( 1-\dfrac vc \right)^3}/ \dfrac{\left( \dfrac vc +1 \right)}{\left( 1+\dfrac vc \right)^3}\right]^2=\dfrac{\left( 1+\dfrac vc \right)^4}{\left( 1-\dfrac vc \right)^4}$ .

A parallel capacitor (Fig . 8.7) made of circular plates of radius R = 6.0 cm has a capacitance C = 100 pF . The capacitor is connected to a 230 Y ac supply with an (angular)frequency of 300 rad $s^{1}$
Is the conduction current equal to the displacement current ?

Here ,

$C = 100 pF = 100 \times 10^{-12} F :$

$E_{v} = 230 V ;$

$\omega = 300 rads^{-1} and R = 6 cm = 6 \times 10^{-2}m$
The e.m.s value of the conduction current is given by

$I_{c} = \dfrac{E_{v}}{X_{c}} = \dfrac{E_{v}}{\dfrac{1}{\omega C}}$

$= 230 \times 300 \times 100 \times 10^{-12} = 6.9 \times 10^{-6} A$ Yes the conduction current and the displacement current will be equal . It is true , even if the conduction current is oscillating.

A charged particle moves along the $y$ axis according to the law $y=a\cos \omega t$ , and the point of observation $P$ is located on the $x$ axis at a distance $l$ from the particle $(l\gg a)$ . Find the ratio of electromagnetic radiation flow densities $S_{1}/S_{2}$ at the point $P$ at the moments when the coordinate of the particle $y_{1}=0$ and $y_{2}=a$ . Calculate that ratio if $\omega =3.3 . 10^{6}\ s^{-1}$ and $l=190\ m$ .

$P$ is a fixed point at a distance

$l$ from the equilibrium position of the particle. Because

$l >> a$ , to first order in

$\dfrac al$ the distance between

$P$ and the instantaneous position of the particle is still

$l$ . For the fist case

$y=0$ so

$t=T/4$
The corresponding retarded time is

$t'=\dfrac T4-\dfrac lc$
Now

$\dot y (t')=-\omega^2 a\cos \omega \left( \dfrac I4 -\dfrac Ic\right) =-\omega^2 a \sin \dfrac {\omega l}{c}$
For the second case

$y=a$ at

$t=0$ so at the retarded time

$t'=-\dfrac{\omega l}{c}$
Thus

$\dot y( t')=-\omega^2 a\cos \dfrac{\omega l}{c}$
The radiation fluxed in the two cases are proportional to

$( \dot y ( t'))^2$ so

$\dfrac {S_1}{S_2}=\tan^2 \dfrac {\omega l}{c}=3.06$ on substitution.

A plane electromagnetic wave $E=E_{m}\cos (\omega t-kx)$ propagating in vacuum induces the emf $\xi_{ind}$ in a square frame with side $l$ . The orientation of the frame is shown in Fig $4.37$ . Find the amplitude value $\varepsilon_{ind}$ , if $E_{m}=0.50\ mV/m$ , the frequency $v=5.0\ MHz$ and $l=50\ cm$

$\xi_{ind}=\oint{\vec E. \vec dl}=E_m l(\cos \omega t-\cos ( \omega t-kl)$

$=-2E_m l \sin \dfrac{\omega l}{2c}\sin \left(\omega t-\dfrac{\omega l}{2c}\right)$
Putting the values

$E_m=50\ m\ V/m, l=\dfrac 12\ metre$

$\dfrac{\omega l}{c}=\dfrac {2\pi vl}{c}=\dfrac{\pi \times 10^8}{3\times 10^8}=\dfrac{\pi}{3}$

$\xi_{ind}=50\ mV \left( -\sin \dfrac{\pi}{6}\right) \sin \left( \omega t-\dfrac {\pi}{6}\right)$

$=-25\sin \left(\omega t +\dfrac {\pi}{6}-\dfrac {\pi}{2}\right)=25\cos \left( \omega t -\dfrac {\pi}{3}\right)\ mV$

A long straight cable of length $l$ is placed symmetrically along z-axis and has radius $a(<< l)$ . The cable consists of a thin wire and a co-axial conducting tube. An alternating current $I(t)={I}_{0}\sin { \left( 2\pi vt \right) }$ flows down the central thin wire and returns along the co-axial conducting tube. The induced electric field at a distance $s$ from the wire inside the cable is
$\vec { E } (s,t)={ \mu }_{ 0 }{ I }_{ 0 }v\cos { \left( 2\pi vt \right) } \log _{ e }{ \left( \cfrac { s }{ a } \right) } \hat { k }$
(i) Calculate the displacement current density inside the cable
(ii) Integrate the displacement current density across the cross-section of the cable to find the total displacement current ${I}_{d}$
(iii) Compare the conduction current ${I}_{0}$ with the displacement current ${I}_{0}^{d}$ .

(i) Induced electric field

$E(s,t)$ at distance

$s(s<$ radius of co-axial cable) is given as

$E(s,t)={E}_{0}{I}_{0}v\cos 2\pi vt \log _{ e }{ \left( \cfrac { s }{ a } \right) } \hat { k }$ . Displacement current density

${I}_{d}$ is given by

${ J }_{ d }={ \varepsilon }_{ 0 }\cfrac { dE }{ dt } ={ \varepsilon }_{ 0 }{ \mu }_{ 0 }{ I }_{ 0 }v\cfrac { d }{ dt } \left[ \cos { 2\pi vt } .\log _{ e }{ \left( \cfrac { s }{ a } \right) } \right] \hat { k }$

${ J }_{ d }={ \varepsilon }_{ 0 }{ \mu }_{ 0 }{ I }_{ 0 }v\left[ \left( -\sin { 2\pi vt } \right) .2\pi v.\log _{ e }{ \left( \cfrac { s }{ a } \right) } \right] \hat { k }$

$\because$

$s$ and

$a$ are constant

${ J }_{ d }=-{ \varepsilon }_{ 0 }{ \mu }_{ 0 }{ I }_{ 0 }2\pi { v }^{ 2 }\log _{ e }{ \left( \cfrac { s }{ a } \right) } \left( \sin { 2\pi vt } \right) \hat { k } =-\cfrac { 1 }{ C } _{ 0 }{ I }_{ 0 }2\pi { v }^{ 2 }\log _{ e }{ \left( \cfrac { a }{ s } \right) } \left( \sin { 2\pi vt } \right) \hat { k } \left[ \because C=\cfrac { 1 }{ \sqrt { { \mu }_{ 0 }{ \varepsilon }_{ 0 } } } \right]$

$=+\cfrac { 2\pi { v }^{ 2 } }{ { C }^{ 2 } } { I }_{ 0 }\log _{ e }{ \left( \cfrac { a }{ s } \right) } \left( \sin { 2\pi vt } \right) \hat { k } =\cfrac { 2\pi { v }^{ 2 } }{ { v }^{ 2 }{ \lambda }^{ 2 } } { I }_{ 0 }\log _{ e }{ \left( \cfrac { a }{ s } \right) } \left( \sin { 2\pi vt } \right) \hat { k }$

${ J }_{ d }=\cfrac { 2\pi }{ { \lambda }^{ 2 } } { I }_{ 0 }\log _{ e }{ \left( \cfrac { a }{ s } \right) } \left( \sin { 2\pi vt } \right) \hat { k }$
(ii)

${ I }_{ d }=\int { { J }_{ d }s } dsd\theta =\int _{ s=0 }^{ a }{ { J }_{ d }sds } \int _{ 0 }^{ 2\pi }{ d\theta } =\int _{ s=0 }^{ a }{ { J }_{ d }sds } \left[ 2\pi \right] =2\pi \int _{ s=0 }^{ a }{ \cfrac { 2\pi }{ { \lambda }^{ 2 } } { I }_{ 0 }\left[ \log _{ e }{ \left( \cfrac { a }{ s } \right) } \left( \sin { 2\pi vt } \right) \hat { k } \right] ds }$

${ I }_{ d }={ \left( \cfrac { 2\pi }{ { \lambda }^{ } } \right) }^{ 2 }{ I }_{ 0 }\left( \sin { 2\pi vt } \right) \hat { k }$

$\int _{ s=0 }^{ a }{ \log _{ }{ \left( \cfrac { a }{ s } \right) } } sds={ \left[ \log _{ }{ \left( \cfrac { a }{ s } \right) } \int _{ 0 }^{ a }{ sds } \right] }_{ 0 }^{ a }-\int _{ s=0 }^{ a }{ \left[ \cfrac { d }{ ds } \left[ \log _{ }{ \left( \cfrac { a }{ s } \right) } \right] .\int { sds } \right] ds }$

$={ \left[ \log _{ }{ \left( \cfrac { a }{ s } \right) } \cfrac { { s }^{ 2 } }{ 2 } \right] }_{ 0 }^{ a }-\int _{ s=0 }^{ a }{ \left( \cfrac { s }{ a } \right) . } \cfrac { { s }^{ 2 } }{ 2 } ds=\left[ \log _{ }{ \left( \cfrac { a }{ a } \right) \cfrac { { a }^{ 2 } }{ 2 } -0 } \right] -\cfrac { 1 }{ 2a } \int _{ s=0 }^{ a }{ { s }^{ 3 }ds } =0-\cfrac { 1 }{ 2a } { \left[ \cfrac { { s }^{ 4 } }{ 4 } \right] }_{ 0 }^{ a }=-\cfrac { { a }^{ 3 } }{ 8 } \left[ \because \log _{ e }{ 1 } =0 \right]$

$\therefore { I }_{ d }=-\cfrac { { a }^{ 3 } }{ 8 } { \left( \cfrac { 2\pi }{ { \lambda }^{ } } \right) }^{ }{ I }_{ 0 }\left( \sin { 2\pi vt } \right) \hat { k } =-\cfrac { a }{ 2 } \cfrac { { a }^{ 2 } }{ 4 } { \left( \cfrac { 2\pi }{ { \lambda }^{ } } \right) }^{ 2 }{ I }_{ 0 }\left( \sin { 2\pi vt } \right) \hat { k }$
Integration of

$\int _{ s=0 }^{ a }{ \log _{ }{ \left( \cfrac { a }{ s } \right) } } sds$
The negative sign shows that the displacement current

${I}_{d}$ is opposite to the conduction current

${I}_{C}$

${ I }_{ d }=\cfrac { a }{ 2 } { \left( \cfrac { 2\pi a }{ { 2\lambda }^{ } } \right) }^{ 2 }{ I }_{ 0 }\left( \sin { 2\pi vt } \right) (-\hat { k } )$
(iii)

${ I }_{ d }=\cfrac { a }{ 2 } { \left( \cfrac { \pi a }{ { \lambda }^{ } } \right) }^{ 2 }{ I }_{ 0 }\left( \sin { 2\pi vt } \right) (-\hat { k } )$

${I}_{d}={I}_{0}^{d}\sin (2\pi vt)$
where

${I}_{0}^{d}=\cfrac { a }{ 2 } { \left( \cfrac { 2\pi a }{ { 2\lambda }^{ } } \right) }^{ 2 }{ I }_{ 0 }$
required ratio

$\cfrac{{I}_{0}^{d}}{{I}_{0}}=\cfrac{\cfrac { a }{ 2 } { \left( \cfrac { \pi a }{ { \lambda }^{ } } \right) }^{ 2 }{ I }_{ 0 }}{{I}_{0}}=\cfrac { a }{ 2 } { \left( \cfrac { \pi a }{ { \lambda }^{ } } \right) }^{ 2 }$

$\cfrac{{I}_{0}^{d}}{{I}_{0}}=\cfrac{{\pi}^{2}{a}^{3}}{2{\lambda}^{2}}$

An electron experiences a quasi-elastic force $kx$ and a "friction force" $\dot{yx}$ in the field of electromagnetic radiation. The E-component of the field varies as $E = E_{0} \;cos \;\omega \;t.$ Neglecting the action of the magnetic component of the field, find:
(a) the motion equation of the electron;
(b) the mean power absorbed by the electron; the frequency at which that power is maximum and the expression for the maximum mean power.

1918368_1853906_ans_4e193d3bc9964eeda67466a6d1d0f0e6.jpg

An isotropic point source emits light with wavelength $\lambda=589 \mathrm{nm} .$ The radiation power of the source is $P=10 \mathrm{W} .$ Find:
(b) the distance between the source and the point at which the mean concentration of photons is equal to $n=100 \mathrm{cm}^{-3}$ .

1919012_1854911_ans_0ebabc3802214ad6b032ddd4d0ab7a4b.png

AN electromagnetic wave of frequency $\omega$ propagates in dilute plasma. The free electron concentration in plasma is equal to $n_{0}$ . Neglecting the interaction of the wave and plasma ions, find:
(a) the frequency dependence of plasma permittivity;
(b) hows the phase velocity of the electromagnetic wave depends on its wave lengthy $\lambda$ in plasma.

1914868_1853841_ans_1cf8f0a671904f21886b0c1a66881cfe.png

In a certain medium, the relationship between the group and phase velocities of an electromagnetic wave has the form $uv = c^{2},$ where $c$ is the velocity of light in vacuum. Find the dependence of permittivity of that medium on wave frequency, $\varepsilon (\omega)$ .

1918382_1854000_ans_548238aa17d34b2db10e180108aaf3db.jpg

A light filter is a plate of thickness $d$ whose absorption coefficient depends on wavelength $\lambda$ as
$x(\lambda) = \alpha(1 - \lambda/\lambda_{0})^{2} cm^{-1},$
where $\alpha \;and\lambda$ are constant. Find the bass band $\Delta \lambda$ of this light filter, that is the band at whose edges the attenuation o lights is $\eta$ the surface of the light filter is assumed to be the same at all wavelengths.

$T_0 = (transmissitivity at \lambda= \lambda_0) = (1-\rho)^2$

$T= transmissivity at \lambda = (1-\rho)^2e^(-x(\lambda)d)$

$\frac{T}{T_0} = e^(\alpha d(\frac{\Delta\lambda}{2\lambda_0}))^2$ =

$\eta$

$\frac{\Delta\lambda}{2\lambda_0} = \sqrt{(ln\frac{1}{\eta})/\alpha d}$

$\Delta\lambda = 2\lambda_0 \sqrt{\frac{1}{\alpha d}(ln\frac{1}{\eta}}$

The space between two concentric metallic spheres is filled up with a uniform poorly conducting medium of resistivity $\rho$ and permittivity $\epsilon$ . At the moment $t = 0$ the inside sphere obtains a certain charge. Find:
(a) the relation between the vectors of displacement current density and conduction current density at an arbitrary point of the medium at the same moment of time;
(b) the displacement current across an arbitrary closed surface wholly located in the medium and enclosing the internal sphere, if at the given moment of time the charge of that sphere is equal to $q$ .

(a) There is a radial outward conduction current. Let

$Q$ be the instantaneous charge on the inner sphere, then,

$j\times 4\pi r^{2} = -\dfrac {dQ}{dt}$ or,

$\vec {j} = -\dfrac {1}{4\pi r^{2}} \dfrac {dQ}{dt} \hat {r}$ .
On the other hand

$\vec {j}_{d} = \dfrac {\partial \vec {D}}{\partial t} = \dfrac {d}{dt} \left (\dfrac {Q}{4\pi r^{2}}\hat {r}\right ) = -\vec {j}$
(b) At the given moment,

$\vec {E} = \dfrac {q}{4\pi \epsilon_{0}\epsilon r^{2}}\hat {r}$
and by Ohm's law,

$\vec {j} = \dfrac {vec {E}}{\rho} = \dfrac {q}{4\pi \epsilon_{0}\epsilon \rho r^{2}}\hat {r}$
Then,

$\vec {j_{d}} = -\dfrac {q}{4\pi \epsilon_{0} \epsilon \rho r^{2}} \hat {r}$
and

$\oint \vec {j_{d}} \cdot d\vec {S} = -\dfrac {q}{4\pi \epsilon_{0}\epsilon \rho} \int \dfrac {dS\cos \theta}{r^{2}} = -\dfrac {q}{\epsilon_{0}\epsilon \rho}$ .

Using Maxwell's equations, show that
(a) a time-dependent magnetic field cannot exist without an electric field;
(b) a uniform electric field cannot exist in the presence of a time-dependent magnetic field;
(c) inside an empty cavity a uniform electric (or magnetic) field can be time-dependent.

(a) If

$\vec {B} = \vec {B}(t)$ , then,
Curl

$\vec {E} = \dfrac {-\partial \vec {B}}{\partial t} \neq 0$ .
So,

$\vec {E}$ cannot vanish.
(b) Here also, curl

$\vec {E} \neq 0$ , so

$\vec {E}$ cannot be uniform.
(c) Suppose for instance,

$\vec {E} = \vec {a}f(t)$
where

$\vec {a}$ is spatially and temporally fixed vector. Then

$-\dfrac {\partial \vec {B}}{dt} = curl\ \vec {E} = 0$ . Generally speaking this contradicts the other equation curl

$\vec {H} = \dfrac {\partial \vec {D}}{\partial t}\neq 0$ for in this case the left hand side is time independent but RHS. depends on time. The only exception is when

$f(t)$ is linear function. Then a uniform field

$\vec {E}$ can be time dependent.

The same spectral line undergoing anomalous Zeeman splitting is observed in direction $1$ and, after reflection from the mirror M (Fig. 6.9), in direction $2$ . How many Zeeman components are observed in both directions if the spectral line is caused by the transition
(a) $^{2}P_{3/2} \rightarrow ^{2}S_{1/2}$ ; (b) $^{3}P_{2} \rightarrow ^{3}S_{1}$ ?

1918669_1855587_ans_8a53d7629144497a81e1f86844fd599b.jpg

Maxwells Equations and Hertzs Discoveries(5)
A proton moves through a region containing a uniform electric field given by $\overrightarrow{E}=50.0\hat{j} \,V/m$ and a uniform magnetic field $\overrightarrow{B}=(0.200\hat{i}+0.300\hat{j}+0.400\hat{k}) \,T$ . Determine the acceleration of the proton when it has a velocity $\vec{v}=200\hat{i} \,m/s$ .

1915380_1881055_ans_02d1d6c627db4a15a3859dd95b2e3507.jpeg

Maxwells Equations and Hertzs Discoveries(9)
The distance to the North Star, Polaris, is approximately $6.44 \times 10^18 \,m$ . (a) If Polaris were to burn out today, how many years from now would we see it disappear? (b) What time interval is required for sunlight to reach the Earth? (c) What time interval is required for a microwave signal to travel from the Earth to the Moon and back?

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Maxwells Equations and Hertzs Discoveries(13)
The speed of an electromagnetic wave traveling in a transparent nonmagnetic substance is $v = 1/\sqrt{k\mu_0 \epsilon_0}$ , where $k$ is the dielectric constant of the substance. Determine the speed of light in water, which has a dielectric constant of $1.78$ at optical frequencies.

1915387_1881063_ans_b9434c63962b4911b08694afe034d4b6.jpeg

Maxwell’s Equations and Hertz’s Discoveries(7)
Suppose you are located $180 \ m$ from a radio transmitter. (a) How many wavelengths are you from the transmitter if the station calls itself $1150 \ AM$ ? (The AM band frequencies are in kilohertz.) (b) What if this station is
$98.1\ FM$ ? (The FM band frequencies are in megahertz.)

1915608_1881057_ans_4e558414670649f1a3769e72349c6183.jpeg

Maxwells Equations and Hertzs Discoveries(4)
An electron moves through a uniform electric field $\overrightarrow{E}=(2.50\hat{i}+5.00\hat{j}) \,V/m$ and a uniform magnetic field $\overrightarrow{B}=0.400\hat{k} \,T$ . Determine the acceleration of the electron when it has a velocity $\vec{v}=10.0\hat{i} \,m/s$ .

1915376_1881054_ans_0911c90a8659485dbb3c20639eb9fb65.jpeg

A small ideal mirror of mass $m=10 \mathrm{mg}$ is suspended by a weightless thread of length $l=10$ cm. Find the angle through which the thread will be deflected when a short laser pulse with energy $E=13 \mathrm{J}$ is shot in the horizontal direction at right angles to the mirror. Where does the mirror get its kinetic energy?

1922028_1854923_ans_6c20bb0fc7bb422f9bf70a5135999113.png

Figure represents the electromagnetic spectrum.
Identify one feature that is the same for all radiations that form the electromagnetic spectrum.

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Maxwells Equations and Hertzs Discoveries(16)
Verify by substitution that the following equations are $B=B_{max}\cos(kx-\omega t)$

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	wavelength / m	wavelength / m	wavelength / m	wavelength / m
	microwaves	infra-red	ultraviolet	X-rays
A	$10^{-6}$	$10^{-10}$	$10^{-12}$	$10^{-14}$
B	$10^{-4}$	$10^{-8}$	$10^{-10}$	$10^{-12}$
C	$10^{-2}$	$10^{-6}$	$10^{-8}$	$10^{-10}$
D	$10^{2}$	$10^{-4}$	$10^{-6}$	$10^{-8}$

S.No.	Wavelength Range
$1.$	$1\ mm$ to $700\ nm$
$2.$	$400\ nm$ to $1\ nm$
$3.$	$1\ nm$ to $10^{-3} nm$
$4.$	$< 10^{-3} nm$

Electromagnetic Waves - Class 12 Medical Physics - Extra Questions

A parallel plate capacitor (fig.) made of circular plates each of radius R=6.0 cmR=6.0\ cm has a capacitance C=100μFC= 100 \mu F. The capacitor is connected to a 230 V230\ V ac supply with a (angular) frequency of 300300 rad s−1s^{-1}. Is the conduction current equal to the displacement current?

A parallel plate capacitor of plate separation 2 mm2\ mm is connected in an electric circuit having source voltage 400 V400\ V. What is the value of the displacement current for 10−610^{-6} second if the plate area is 60 cm260\ cm^{2}.?

How electromagnetic waves are produced ?

In which situation is there a displacement current but no conduction current?

What is ratio of electric field and magnetic field in EMEM wave?

(i) What is main difference between electromagnetic waves theory and Planck's quantum theory.(ii) Which rule is violated in the following orbital diagram:

Answer the following questions:(i) How are infrared waves produced? Write their one important use.(ii) The thin Ozone layer on top of the stratosphere is crucial for human survival.

State two properties of ultra violet radiations which differs from visible light.

What is meant displacement current?

Analyse the diagram of solar spectrum and write answer.a. Which radiation has a wavelength greater than visible light in this spectrum ? b. Which color has the highest frequency in the visible part of the solar spectrum ? c. Write one merit and demerit of infrared and ultraviolet radiations.

Write any two Maxwell's equation.

Name the characteristics of electromagnetic waves that(i) increases(ii) remains constant.In the electromagnetic spectrum as one moves from radio wave region towards ultraviolet region.

______ was the first scientist who produced electromagnetic waves in a laboratory.

Write a short note on sky wave propagation.

Which of thee following electromagnetic waves has (a) minimum wavelength, and (b) minimum frequency? Write one use of each of these two waves.Infrared waves, Microwaves, y-rays and X-rays

Name the type of waves which are used by astronauts to communicate with one another on moon.

What is Maxwell's corkscrew rule ? For what purpose is it used ?

Using B=μ0HB = \mu _{0}H find the ratio E0/H0E_{0}/H_{0} for a plane electromagnetic wave propagating through vacuum. This ratio is a universal constant called the impedance of free space.

The figure gives the variationof an electric field that is perpendicular to a circular area of 2.0m22.0\, m^2.During the time period shown, whatis the greatest displacement currentthrough the area?

Why are infra-red radiations referred to as heat waves? Name the radiations which are next to these radiations in the electromagnetic spectrum having (i) shorter wavelength (ii) longer wavelength.

Arrange the following electromagnetic waves in order of increasing frequency:γ−rays\gamma-rays, microwaves, infrared rays and ultraviolet rays.

Which part of the electromagnetic spectrum is absorbed from sunlight by ozone layer?

Which part of the electromagnetic spectrum is used in operating a RADAR?

Arrange the following electromagnetic waves in order of decreasing frequency:γ−rays\gamma-rays, infrared rays, X-rays and microwaves.

Assume that lasers are available whose wavelengths can be precisely tuned to anywhere in the visible rangethat is, in the range 450nm<λ<650nm 450 nm < \lambda < 650 nm. If every television channel occupies a bandwidth of 10 MHz, how many channels can be accommodated within this wavelength range?

Name the electromagnetic waves, which (i) maintain the Earth's warmth and (ii) are used in aircraft nagivation.

Identify the part of the electromagnetic spectrum to which the following wavelengths belong:(i) 10−1m10^{-1} m(ii) 10−12m10^{-12} m.

Which of the following radiations are (i) heat radiation and (ii) used for long distance transmission? Infrared rays, gamma rays, ultraviolet rays, microwaves.

Which part of electromagnetic spectrum does the wavelength 10−10m10^{-10}m correspond to?

Identify the type of waves which are produced by the following way and write one application for each:(i) Radioactive decay of the nucleus(ii) Rapid acceleration and decelerations of electrons in aerials(iii) Bombarding a metal target by high energy electrons.

Which of the following has the minimum wavelength and which has the maximum wavelength?Blue light, infrared rays, gamma rays, green light.

Which of the following has the least wavelength? Gamma rays, blue light, infrared radiation and ultraviolet, radiation.

How are X−raysX-rays produced?

Name the part of the electromagnetic spectrum of wavelength 10−2m10^{-2}m and mention its one application.

Identify the part of the electromagnetic spectrum to which the following wavelengths belong:(i) 1 mm1\ mm(ii) 10−11m10^{-11} m.

Name the electromagnetic radiations used for studying the crystal structure of solids.

Name the part of electromagnetic spectrum of wavelength 102 m10^2\ m and mention its one application.

Special devices, like the klystron valve or the magnetro valve, are used for production of electromagnetic waves. Name the waves and also write one of their applications.

Give a reason to show that microwaves are better carriers of signals for long range transmission than radio waves.

Name the electromagnetic radiations used for viewing objects through haze and fog.

How are infrared waves produced?

Professor C.V. Raman surprised his students by suspending freely a tiny light ball in a transparent vacuum chamber by shining a laser beam on it. Which property of em waves was he exhibiting? Give one more example of this property.

From the following, identify the electromagnetic waves having the (i) Maximum (ii) Minimum frequency.(a) Radio waves(b) Gamma-rays(c) Visible light(d) Microwaves(e) Ultraviolet rays, and(f) Infrared rays.

Name the part of electromagnetic spectrum which is used for taking photographs of earth under foggy conditions from great heights.

Name the electromagnetic waves that have frequencies greater than those of ultraviolet light but less than those of gamma rays.

Name the part of the electromagnetic spectrum whose wavelength lies in the range 10−10m10^{-10} m. Give its one use.

Answer the following questions:(i) How are electromagnetic waves produced by oscillating charges?(ii) State clearly how a microwave oven works to heat up a food item containing water molecules.(iii) Why are microwaves found useful for the radar systems in aircraft navigation?

To which regions of the electromagnetic spectrum, the following wavelengths belong? 2,000∘A,5,000∘A,10,000∘A2,000\overset {\circ}{A}, 5,000\overset {\circ}{A}, 10,000\overset {\circ}{A} and 1.0∘A1.0\overset {\circ}{A}.

Identify the electromagnetic waves whose wavelengths lie in the range(a) 10−11m<λ<10−8m10^{-11} m < \lambda < 10^{-8} m(b) 10−4m<λ<10−1m10^{-4} m < \lambda < 10^{-1} mWrite one use of each.

Identify the electromagnetic waves whose wavelengths vary as(a) 10−12m<λ<10−8m10^{-12} m < \lambda < 10^{-8} m(b) 10−3m<λ<10−1m10^{-3} m < \lambda < 10^{-1} mWrite one use for each.

Identify the following electromagnetic radiations as per the wavelengths given below.(a) 10−3nm10^{-3} nm(b) 10−3m10^{-3} m(c) 1 nm1\ nmWrite one application of each.

Write the following in descending order of wavelength:Gamma rays, Hertzian waves, yellow light, blue light, infrared radiation, ultraviolet radiation, X-rays, γ−rays\gamma-rays.

Which part of Sun's energy is responsible for drying clothes and exposure to which part could be a health hazard?

A variable frequency a.c source is connected to a capacitor. How will the displacement current change with decrease in frequency?

Professor C.V.Raman surprised students by suspending freely a tiny light ball in a transparent vacuum chamber by shining a laser beam on it. Which property of EM waves was he exhibiting? Given one more example of this property.

Why does microwave oven heats up a food item containing water molecules most effeciently?

The charge on a parallel plate capacitor varies as q=q0cos2πvtq={q}_{0}\cos{2\pi vt}. The plates are very large and close together (area =h=h, separation=d=d). Neglecting the edge effects, find the displacement current through? the capacitor

What is the range of wavelength of electromagnetic waves that constitute visible radiation?

Wavelength of radiation incident on a surface is 850nm850 nm. Will the surface become visible when exposed to this radiation? Explain.

Identify the following electromagnetic radiations as per the frequencies given below:(a) 1020Hz10^{20} Hz(b) 109Hz10^{9} Hz(c) 1011Hz10^{11} HzWrite one application of each.

Experimental observations have shown that X-rays(i) Travel in vacuum with a speed of 3×108ms−13\times 10^{8} ms^{-1}(ii) Exhibit the phenomenon of diffraction and can be polarised.What conclusion can be drawn about the nature of X-rays from each of these observations?

What is the range of the wavelength of the following electromagnetic wave : Gamma rays ?

What is the range of the wavelength of the following electromagnetic waves : Ultraviolet wave ?

What is the range of the wavelength of the following electromagnetic waves : X-rays ?

(a) Give a list of at least five radiations , in order of their increasing frequencies , which make up the complete electromagnetic spectrum.(b) Which of the radiations mentioned in answer part (a) has the highest penetrating power ?

What is the range of the wavelength of the following electromagnetic waves :Visible Light ?

Arrange the following electromagnetic waves in the order of their increasing wavelength:(a) γ−rays\gamma-rays(b) Microwaves(c) X−raysX-rays(d) Radio wavesHow are infra-red waves produced? What role does infra-red radiation play in (i) maintaining the Earth's warmth and (ii) physical therapy?

Answer the following(a) Name the em waves which are used for the treatment of certain forms of cancer. Write their frequency range.(b) Welders wear special glass goggles while working. Why? Explain(c) Why are infrared waves often called as heat waves? Give their one application.

Fill in the blanks with suitable words:Electromagnetic waves are ____ waves.

What is electromagnetic radiation?

Fill in the blanks with suitable wordsThe rays used to show bone structure is __________.

Match the EM waves from list I with corresponding Inventors in list II:

Fill in the blanks with suitable wordsThe range of wavelength of visible light is __________.

To which regions of the electromagnetic spectrum do the following wavelengths belong :(a) 250 nm250 nm(b) 1500 nm1500 nm

List the properties of electromagnetic waves.

How are electric vector \vec{(E)}\vec{(E)}, magnetic vector \vec{(B)}\vec{(B)} velocity vector \vec{(c)}\vec{(c)} oriented in an electromagnetic wave ?

Explain the electromagnetic spectrum with a diagram.

Even through an electric field EE exerts a force qEqE on a charged particle yet the electric field of an EM wave does not contribute to the radiation pressure (but transfers energy). Explain.

When an electron falls from a higher energy to a lower energy level, the difference in the energies appears in the form of electromagnetic radiation. Why cannot it be emitted as other forms of energy ?

A parallel plate capacitor (fig.) made of circular plates each of radius $R=6.0\ cm$ has a capacitance $C= 100 \mu F$ . The capacitor is connected to a $230\ V$ ac supply with a (angular) frequency of $300$ rad $s^{-1}$ .
Is the conduction current equal to the displacement current?

A parallel plate capacitor of plate separation $2\ mm$ is connected in an electric circuit having source voltage $400\ V$ . What is the value of the displacement current for $10^{-6}$ second if the plate area is $60\ cm^{2}$ .?

What is ratio of electric field and magnetic field in $EM$ wave?

(i) What is main difference between electromagnetic waves theory and Planck's quantum theory.
(ii) Which rule is violated in the following orbital diagram:

Answer the following questions:
(i) How are infrared waves produced? Write their one important use.
(ii) The thin Ozone layer on top of the stratosphere is crucial for human survival.

Analyse the diagram of solar spectrum and write answer.
a. Which radiation has a wavelength greater than visible light in this spectrum ?
b. Which color has the highest frequency in the visible part of the solar spectrum ?
c. Write one merit and demerit of infrared and ultraviolet radiations.

Name the characteristics of electromagnetic waves that
(i) increases
(ii) remains constant.
In the electromagnetic spectrum as one moves from radio wave region towards ultraviolet region.

Which of thee following electromagnetic waves has (a) minimum wavelength, and (b) minimum frequency? Write one use of each of these two waves.
Infrared waves, Microwaves, y-rays and X-rays

Using $B = \mu _{0}H$ find the ratio $E_{0}/H_{0}$ for a plane electromagnetic wave propagating through vacuum. This ratio is a universal constant called the impedance of free space.

The figure gives the variation
of an electric field that is perpendicular to a circular area of $2.0\, m^2$ .
During the time period shown, what
is the greatest displacement current
through the area?

Arrange the following electromagnetic waves in order of increasing frequency:
$\gamma-rays$ , microwaves, infrared rays and ultraviolet rays.

Arrange the following electromagnetic waves in order of decreasing frequency:
$\gamma-rays$ , infrared rays, X-rays and microwaves.

Assume that lasers are available whose wavelengths can be precisely tuned to anywhere in the visible rangethat is, in the range $450 nm < \lambda < 650 nm$ . If every television channel occupies a bandwidth of 10 MHz, how many channels can be accommodated within this wavelength range?

Identify the part of the electromagnetic spectrum to which the following wavelengths belong:
(i) $10^{-1} m$
(ii) $10^{-12} m$ .

Which part of electromagnetic spectrum does the wavelength $10^{-10}m$ correspond to?

Identify the type of waves which are produced by the following way and write one application for each:
(i) Radioactive decay of the nucleus
(ii) Rapid acceleration and decelerations of electrons in aerials
(iii) Bombarding a metal target by high energy electrons.

Which of the following has the minimum wavelength and which has the maximum wavelength?
Blue light, infrared rays, gamma rays, green light.

How are $X-rays$ produced?

Name the part of the electromagnetic spectrum of wavelength $10^{-2}m$ and mention its one application.

Identify the part of the electromagnetic spectrum to which the following wavelengths belong:
(i) $1\ mm$
(ii) $10^{-11} m$ .

Name the part of electromagnetic spectrum of wavelength $10^2\ m$ and mention its one application.

From the following, identify the electromagnetic waves having the (i) Maximum (ii) Minimum frequency.
(a) Radio waves
(b) Gamma-rays
(c) Visible light
(d) Microwaves
(e) Ultraviolet rays, and
(f) Infrared rays.

Name the part of the electromagnetic spectrum whose wavelength lies in the range $10^{-10} m$ . Give its one use.

Answer the following questions:
(i) How are electromagnetic waves produced by oscillating charges?
(ii) State clearly how a microwave oven works to heat up a food item containing water molecules.
(iii) Why are microwaves found useful for the radar systems in aircraft navigation?

To which regions of the electromagnetic spectrum, the following wavelengths belong? $2,000\overset {\circ}{A}, 5,000\overset {\circ}{A}, 10,000\overset {\circ}{A}$ and $1.0\overset {\circ}{A}$ .

Identify the electromagnetic waves whose wavelengths lie in the range
(a) $10^{-11} m < \lambda < 10^{-8} m$
(b) $10^{-4} m < \lambda < 10^{-1} m$
Write one use of each.

Identify the electromagnetic waves whose wavelengths vary as
(a) $10^{-12} m < \lambda < 10^{-8} m$
(b) $10^{-3} m < \lambda < 10^{-1} m$
Write one use for each.

Identify the following electromagnetic radiations as per the wavelengths given below.
(a) $10^{-3} nm$
(b) $10^{-3} m$
(c) $1\ nm$
Write one application of each.

Write the following in descending order of wavelength:
Gamma rays, Hertzian waves, yellow light, blue light, infrared radiation, ultraviolet radiation, X-rays, $\gamma-rays$ .

The charge on a parallel plate capacitor varies as $q={q}_{0}\cos{2\pi vt}$ . The plates are very large and close together (area $=h$ , separation $=d$ ). Neglecting the edge effects, find the displacement current through? the capacitor

Wavelength of radiation incident on a surface is $850 nm$ . Will the surface become visible when exposed to this radiation? Explain.

Identify the following electromagnetic radiations as per the frequencies given below:
(a) $10^{20} Hz$
(b) $10^{9} Hz$
(c) $10^{11} Hz$
Write one application of each.

Experimental observations have shown that X-rays
(i) Travel in vacuum with a speed of $3\times 10^{8} ms^{-1}$
(ii) Exhibit the phenomenon of diffraction and can be polarised.
What conclusion can be drawn about the nature of X-rays from each of these observations?

(a) Give a list of at least five radiations , in order of their increasing frequencies , which make up the complete electromagnetic spectrum.
(b) Which of the radiations mentioned in answer part (a) has the highest penetrating power ?

What is the range of the wavelength of the following electromagnetic waves :
Visible Light ?

Arrange the following electromagnetic waves in the order of their increasing wavelength:
(a) $\gamma-rays$
(b) Microwaves
(c) $X-rays$
(d) Radio waves
How are infra-red waves produced? What role does infra-red radiation play in (i) maintaining the Earth's warmth and (ii) physical therapy?

Answer the following
(a) Name the em waves which are used for the treatment of certain forms of cancer. Write their frequency range.
(b) Welders wear special glass goggles while working. Why? Explain
(c) Why are infrared waves often called as heat waves? Give their one application.

Fill in the blanks with suitable words:
Electromagnetic waves are ____ waves.

Fill in the blanks with suitable words
The rays used to show bone structure is __________.

Fill in the blanks with suitable words
The range of wavelength of visible light is __________.

To which regions of the electromagnetic spectrum do the following wavelengths belong :
(a) $250 nm$
(b) $1500 nm$

How are electric vector $\vec{(E)}$ , magnetic vector $\vec{(B)}$ velocity vector $\vec{(c)}$ oriented in an electromagnetic wave ?

Even through an electric field $E$ exerts a force $qE$ on a charged particle yet the electric field of an EM wave does not contribute to the radiation pressure (but transfers energy). Explain.

Two waves A and B have wavelength $0.01$ Å and $9000$ Å respectively. Compare the speeds of these when they travel in vacuum.

Explain the following :
Infrared radiations are used for photography in fog.

Two waves A and B have wavelength $0.01$ Å and $9000$ Å respectively. Name the two waves

Explain the following :
Infrared radiations are used as signals during war.

Explain the following :
A quartz is required for obtaining the spectrum of the ultraviolet light.

Explain the following :
The photographic darkrooms are provided with infrared lamps.

Explain the following :
A rock salt prism is used instead of a glass prism to obtain the infrared spectrum.

An electromagnetic wave has a frequency of $500$ MHz and a wavelength of $60$ cm .
(a) Calculate the velocity of the wave.
(b) Name the medium through which it is travelling

Name the rays of
1.Waves of highest frequency
2.Rays used for taking photographs in the dark
3.Rays of wavelength nearly $0.1\ nm$

Fill in the blanks with the proper words.
GMRT is used for .......... waves.

Fill in the blanks with the proper words.
A certain X-ray telescope is named after scientist ............

Fill in the blanks with the proper words.
The wavelength of visible light is between .......... and ...........

Answer in brief:
Can microwaves be used in the experiment on photoelectric effect?

What physical quantity is the same for X -rays of wavelength $10^{-1}$ m , red light wavelength 6800 A and radio waves of wavelength 500 m,?

Given below are some fomous numbers associated with electromagnetic radiation in different contexts in physics .State the part of the electromagnetic spectrum to which each belongs .
1057 MH z (frequency of radiation arising from two close energy levels in hydrogen : know as lamb shift ).

Given below are some fomous numbers associated with electromagnetic radiation in different contexts in physics .State the part of the electromagnetic spectrum to which each belongs .
5890 A - 5890 A (double lines of sodium )

Given below are some fomous numbers associated with electromagnetic radiation in different contexts in physics .State the part of the electromagnetic spectrum to which each belongs .
21 cm (wavelength emitted by atomic hydrogen in interstellar space ).

Use the formula $\lambda _{m}T = 29 cm K$ Obtain the charcteristic temperature ranges for different part of the electromagnetic spectrum .What do the numbers that you obtain tell you ?

Find the wavelength of the electromagnetic wave of frequency $5\times 10^{19}$ Hz in free space identify the wave.

$\xi$ and $\partial\xi/\partial x$ as functions of $x$ at the moments $t=0$ and $t=T/2,$ where $T$ is the oscillation period;

The magnetic field around the current carrying conductor AB is depicted
Based on the Maxwell's Right Hand Cork Screw Rule find out the direction of current and record it.

The ground state energy of hydrogen atom is $-13.6$ eV. If an electron makes a transition from an energy level $-1.51$ eV to $-3.4$ eV, then calculate the wavelength of the spectral line emitted and name the series of hydrogen spectrum to which it belongs.

An electromagnetic wave is radiated by a $100$ W bulb. If efficiency of the bulb is $20%$ then the amplitude of magnetic field at a distance of $1$ m is (Consider bulb as a point source)