A metallic rod $$PQ$$ of length $$l$$ is rotated with an angular velocity $$\omega$$ about an axis passing through its mid-point (O) and perpendicular to the plane of the paper, in uniform magnetic field $$\vec{B}$$, as shown in the figure. What is thee potential difference developed between the two ends of the rod, P and Q ?

Find the equation of current wave.

(a) A flat, circular coil does not actually produce a uniform magnetic field in the area it encloses. Nevertheless, estimate the inductance of a flat, compact, circular coil with radius $$R$$ and $$N$$ turns by assuming the field at its center is uniform over its area. (b) A circuit on a laboratory table consists of a $$1.50-volt$$ battery, a $$270-\Omega$$ resistor, a switch, and three $$30.0-cm$$-long patch cords connecting them. Suppose the circuit is arranged to be circular. Think of it as a flat coil with one turn. Compute the order of magnitude of its inductance and (c) of the time constant describing how fast the current increases when you close the switch.

Review. An AM radio station broadcasts isotropically (equally in all directions) with an average power of $$4.00 \,kW$$. A receiving antenna $$65.0 \,cm$$ long is at a location $$4.00 \,mi$$ from the transmitter. Compute the amplitude of the emf that is induced by this signal between the ends of the receiving antenna.

(a) The induced emf and

(b) induced current will be more and why?

(a) What is the instantaneous value of the emf induced in the wire?

(b) What is the direction of the emf?

(c) Which end of the wire is at the higher electrical potential?

What is the maximum emf produced when the armature completes $$1800$$ rotation ?

Consider this thesis: "Joseph Henry, America's first professional physicist, caused a basic change in the human view of the Universe when he discovered self-induction during a school vacation at the Albany Academy aboutBefore that time, one could think of the Universe as composed of only one thing: matter. The energy that temporarily maintains the current after a battery is removed from a coil, on the other hand, is not energy that belongs to any chunk of matter. It is energy in the massless magnetic field surrounding the coil. With Henry's discovery, Nature forced us to admit that the Universe consists of fields as well as matter."

(a) Argue for or against the statement.

(b) In your view, what makes up the Universe?

The type of electric current that changes its direction twice during one cycle of the dynamo is called _____________ .

(b) How does one understand this motional emf by invoking the Lorentz force acting on the free charge carriers of the conductor? Explain.

b) When the current in the primary is switched OFF. What happens to the magnetic field in the secondary coil? How will this change influence the current in the secondary and the glow in the electric bulb?

Take $$\pi=\sqrt {10}$$

Explain the shape of the graph.

Define mutual inductance.

material. (a) Sketch the field lines through and about the material

due to the magnet. What is the direction of (b) the loops net magnetic dipole moment $$\vec \mu$$, (c) the conventional current i in the loop

(clockwise or counterclockwise in the figure), and (d) the magnetic

force acting on the loop?

*$$t=0$$*, the current in the long straight wire is 5.0 A rightward.

Thereafter, the current changes according to $$i=5.0A-(2.0A/s^2)t^2$$. (The straight wire is insulated; so there is no electrical contact between it and the wire of the loop.) What is the magnitude of the current induced in the loop

at times $$t>0$$?

At a radial distance of 1.6 cm, what is the amplitude of the electric field induced by the variation?

Find the current produced in the rectangular loop of wire $$ABCD$$ if its resistance is $$R$$ (Fig.).

(i) fast seed,

(ii) slow speed.

In which case, is the induced emf and work done more?

[Self inductance of coil is $$ 0.25 H $$].

(a)Mximum induced volatage.

(b)Induced emf at $$ t=0.01s. $$

(c) Induced electric current at $$ t=0.005 s. $$

(if external resistance is $$100 \Omega $$)

Find out the frequency by drawing a time emf graph if the armature completes $$10$$ cycles in $$5$$ seconds.

Field magnet, Armature, Slip rings, Brush.

a. Explain the position of these parts in an AC generator.

b. Write down the functions of any two.

What is the specialty of the electricity reaching the galvanometer if the armatures of both the generators are made to rotate ?

What is the period of the armature.

Consider the arrangement shown in Figure. Assume that $$R = 6.00 \,\Omega, \,$$, and a uniform $$2.50-T$$ magnetic field is directed into the page. At what speed should the bar be moved to produce a current of $$0.500 \,A$$ in the resistor?

Which type of AC is produced here, single-phase or three-phase ?

How many cycles are completed in $$T / 2$$ seconds ?

(b) Now assume that the straight wire carries a current of 50 A and the loop is moved to the right with a constant velocity, v = 10 m/s. Calculate the induced emf in the loop at the instant when x = 0.2 m. Take a = 0.1 m and assume that the loop has a large resistance.

$$B\, =\, -B_0\, k\, \quad\, (r\, \leq \, a;\, a\, <\, R)$$, or $$ B\,=\,0$$ (otherwise).

What is the angular velocity of the wheel after the field is suddenly switched off?

**r** placed coplaner with a long, straight wire. The wire carries a current** i** given by $$i = {i_0}\sin \omega t.$$ . Find (a) the flux of the magnetic field through the square frame; (b) the emf induced in the frame and (c) the heat developed in the frame in the time interval 0 to $${{20\pi } \over \omega }$$ .

(a) Obtain an expression for the energy stored in a solenoid of self-inductance $$'L'$$ when the current though it grows from zero to $$'I'$$.

(b) A square loop MNOP of side 20 cm is placed horizontally in a uniform magnetic field acting vertically downwards as shown in the figure. The loop is pulled with a constant velocity of 20 cm $$s^{-1}$$ till it goes out of the field.

(i) Depict the direction of the induced current in the loop as it goes out of the field. For how long would the current in the loop persist?

(ii) Plot a graph showing the variation of magnetic flux and induced emf as a function of time.

(b) A square loop MNOP of side 20 cm is placed horizontally in a uniform magnetic field acting vertically downwards as shown in the figure. The loop is pulled with a constant velocity of 20 cm $$s^{-1}$$ till it goes out of the field.

(i) Depict the direction of the induced current in the loop as it goes out of the field. For how long would the current in the loop persist?

(ii) Plot a graph showing the variation of magnetic flux and induced emf as a function of time.

(a) the current in the loop in an instant when the speed of the wire PQ is v.

(b) the acceleration of the wire at this instant

(c) Velocity v as a function

Assume that friction and gravity are absent and a constant uniform magnetic field of 5 T exists as shown in figure. At t =0,the circuit is switched on and simultaneously a time varying external torque is applied on the rod so that it rotates about 'P' with a constant angular velocity 40 rad/s.Find the magnitude of this torque ( in 'P') when current reaches half of its maximum value.Neglect the self inductance of the loop formed by the circuit.

In Figure , a metal rod is forced to move with constant velocity $$\overrightarrow {v}$$ along two parallel metal rails, connected with a strip of metal at one end. A magnetic field of magnitude *B *= 0.350 T points out of the page.

(a) If the rails are separated by *L *= 25.0 cm and the speed of the rod is 55.0 cm/s, what emf is generated?

(b) If the rod has a resistance of $$18.0\Omega $$ and the rails and connector have negligible resistance, what is the current in the rod?

(c) At what rate is energy being transferred to thermal energy?

Scientific work is currently under way to determine whether weak oscillating magnetic fields can affect human health. For example, one study found that drivers of trains had a higher incidence of blood cancer than other railway workers, possibly due to long exposure to mechanical devices in the train engine cab. Consider a magnetic field of magnitude $$1.00 \times 10^{-3} \,T$$, oscillating sinusoidally at $$60.0 \,Hz$$. If the diameter of a red blood cell is $$8.00 \,mm$$, determine the maximum emf that can be generated around the perimeter of a cell in this field.

model (loop L) for a diamagnetic

material. (a) Sketch the magnetic

field lines within and about the material due to the bar magnet. What is the direction of (b) the loops net magnetic dipole moment $$\vec \mu$$,

(c) the conventional current i in the loop (clockwise or counterclockwise in the figure), and (d) the magnetic force on the loop?

A conduction rod of length $$'I'$$ with one end pivoted, is rotated with a uniform angular speed $$'\omega '$$ in a vertical plane, normal to a uniform magnetic field $$'B'$$. Deduce an expression for the emf induced in this rod.

If resistance of rod is $$R$$, what is the current induced in it?

How will the value of emf be affected if the number of spokes were increasde?

solenoid current drops from 1.5 A to zero in time interval $$\Delta t=25ms$$. What current is induced in the coil during $$\Delta

$$?

A rod of length $$I$$ is moved horizontally with a uniform velocity $$'v'$$ in a direction perpendicular to its length through a region in which a uniform magnetic field is acting vertically downward. Derive the expression for the emf induced across the ends of the rod.

What is the ratio $$\mathscr{E}_L/\mathscr{E}$$ of the inductor’s self-induced emf to the battery’s emf (a) just after

(b) at $$t = 2.00\tau

_L$$? (c) At what multiple of $$\tau

_L$$ will $$\mathscr{E}_L/\mathscr{E}=0.500$$?

(a) what will be magnetic induction at a point on the axis O Axis is at a distance R from each wire.

(b) What will be the field if current in one of the wires (say A) is switched off

(c) What if current in one of the wire (say) A is reversed

(ii) What happens if coil P is moved away from Q?

(iii) State any two methods of inducing current in a coil.

unit-vector notation, what is the initial acceleration of an electron released at (a) point a (radial distance r = 5.0 cm), (b) point b (r = 0), and (c) point c (r = 5.0 cm)?

*a*, a circular loop of wire is concentric with a solenoid and lies in a plane perpendicular to the solenoid’s central axis. The loop has radius 6.00 cm. The solenoid has radius 2.00 cm, consists of 8000 turns/m, and has a current *$$i_{sol}$$* varying with time *t *as given in Figure *b*, where the vertical axis scale is set by *$$i_s=1.00A$$* and the horizontal axis scale is set by *$$t_s=2.0s$$*. Figure *c *shows, as a function of time, the energy *$$E_{th}$$* that is transferred to thermal energy of the loop; the vertical axis scale is set by $$E_s=100.0nJ$$.What is the loop’s resistance?

(a) Suppose $$K$$ is open and the rod is moved with a speed of $$12cm$$ $$s^{-1}$$ in the direction shown. Give the polarity and magnitude of the induced emf.

(b) Is there an excess charge build up at the ends of the rods when $$K$$ is open? What is $$K$$ is closed?

(c) With $$K$$ open and the rod moving uniformly, there is no net force on the electrons in the rod $$PQ$$ even through they do experience magnetic force due to the motion of the rod. Explain.

(d) What is the retarding force on the rod when $$K$$ is closed?

(e) How much power is required (by an external agent) to keep the rod moving at the same speed ($$=12cm$$ $$s^{-1}$$) when $$K$$ is closed? How much power is required when $$K$$ is open?

(f) How much power is dissipated as heat in the closed-circuit? What is the source of this power?

(g) What is the induced emf in the moving rod if the magnetic field is parallel to the rails instead of being perpendicular?

To monitor the breathing of a hospital patient, a thin belt is girded around the patient's chest. The belt is a $$200$$-turn coil. When the patient inhales, the area encircled by the coil increases by $$39.0 \,cm^2$$. The magnitude of the Earth's magnetic field is $$50.0 \mu T$$ and makes an angle of $$28.0^{o}$$ with the plane of the coil. Assuming a patient takes $$1.80 \,s$$ to inhale, find the average inducede mf in the coil during this time interval.

A circular loop of wire is located in a uniform and constant magnetic field. Describe how an emf can be induced in the loop in this situation.

A strong electromagnet produces a uniform magnetic field of $$1.60 \,T$$ over a cross-sectional area of $$0.200 m^2$$. A coil having $$200$$ turns and a total resistance of $$20.0 \Omega$$ is placed around the electromagnet. The current in the electromagnet is then smoothly reduced until it reaches zero in $$20.0 \,ms$$. What is the current induced in the coil?

How will it move and where will it be in time $$t$$ after the beginning of motion?

A flat loop of wire consisting of a single turn of cross sectional area $$8.00 \,cm^2$$ is perpendicular to a magnetic field that increases uniformly in magnitude from $$0.500 \,T$$ to $$2.50 \,T$$ in $$1.00 \,s$$. What is the resulting induced current if the loop has a resistance of $$2.00 \,\Omega$$?

Determine the time $$t$$ during which the electron moves in the solenoid.

When a wire carries an AC current with a known frequency, you can use a Rogowski coil to determine the amplitude $$I_{max}$$ of the current without disconnecting the wire to shunt the current through a meter. The Rogowski coil, shown in Figure, simply clips around the wire. It consists of a toroidal conductor wrapped around a circular return cord. Let $$n$$ represent the number of turns in the toroid per unit distance along it. Let A represent the cross-sectional area of the toroid. Let $$I(t) = I_{max} \sin \omega t$$ represent the current to be measured.

(a) Show that the amplitude of the emf induced in the Rogowski coil is $$\varepsilon_{max}= \mu_0 n A\omega I_{max}$$.

(b) Explain why the wire carrying the unknown current need not be at the center of the Rogowski coil and why the coil will not respond to nearby currents that it does not enclose.

Review. Figure shows a bar of mass $$m =0.200 \,kg$$ that can slide without friction on a pair of rails separated by a distance $$l= 1.20 \,m$$ and located on an inclined plane that makes an angle $$\theta = 25.0^{o}$$ with respect to the ground. The resistance of the resistor is $$R = 1.00 \Omega$$ and a uniform magnetic field of magnitude $$B = 0.500 \,T$$ is directed downward, perpendicular to the ground, over the entire region through which the bar moves. With what constant speed $$v$$ does the bar slide along the rails?

A helicopter (Figure) has blades of length $$3.00 \,m$$, extending out from a central hub and rotating at $$2.00 \,rev/s$$. If the vertical component of the Earths magnetic field is $$50.0 \mu T$$, what is the emf induced between the blade tip and the center hub?

- Alternating Current Extra Questions
- Atoms Extra Questions
- Current Electricity Extra Questions
- Dual Nature Of Radiation And Matter Extra Questions
- Electric Charges And Fields Extra Questions
- Electromagnetic Induction Extra Questions
- Electromagnetic Waves Extra Questions
- Electrostatic Potential And Capacitance Extra Questions
- Magnetism And Matter Extra Questions
- Moving Charges And Magnetism Extra Questions
- Nuclei Extra Questions
- Ray Optics And Optical Instruments Extra Questions
- Semiconductor Electronics: Materials, Devices And Simple Circuits Extra Questions
- Wave Optics Extra Questions