Class 12 Medical Physics - Magnetism And Matter

State any two properties of magnetic lines of force.

The magnetic field at any given point is specified by both a direction and a magnitude.
Magnetic lines of force start from the North Pole and end at the South Pole.
Two magnetic lines of force cannot intersect each other and they are continuous along the axis of the electromagnetic conductor.
The magnetic lines of force are uniform and strong at the center or inside of the conductor and they diverge as they move away from the conductor and as the distance increases. Eventually, the strength of the magnetic field is strong inside and they weaken as they closeness decreases.

A short bar magnet has a magnetic moment of $0.48 J T^{-1}$ . Give the direction and magnitude of the magnetic field produced by the magnet at a distance of 10 cm from the centre of the magnet on (a) the axis, (b) the equatorial lines (normal bisector) of the magnet.

Here

$M=0.48JT^{-1}, d=10cm=0.1m$

(a)

On axis,

$B=\dfrac{\mu_0}{4\pi}\dfrac{2M}{d^3}=10^{-7}\times \dfrac{2\times 0.48}{0.1^3}=0.96\times 10^{-4}T$

Direction is away from magnet on the axis on the North-side and towards the magnet on the axis on the South-side

(b) On the equatorial line of the magnet

$B=\dfrac{\mu_0}{4\pi}\dfrac{M}{d^3}=0.48\times 10^{-4}T$ along N-S direction.

Direction at equatorial line is same as direction from north pole to south pole.

(a) An iron ring of relative permeability $\mu_{r}$ has windings of insulated copper wire of $n$ turns per metre. When the current in the windings is $I$ , find the expression for the magnetic field in the ring.
(b) The susceptibility of a magnetic material is $0.9853$ . Identify the type of magnetic material. Draw the modification of the field pattern on keeping a piece of this material in a uniform magnetic field.

(a) :Copper wire windings on the iron ring forms a toroid.
Magnetic field due to a toroid is given by

$B = \mu n I$
where

$\mu$ is the permeability of the medium,

$n$ is the number of turns per unit length and

$I$ is the current flowing.
Also,

$\mu = \mu_r \mu_o$

$\implies \ B = \mu_r\mu_o nI$
(b) : Susceptibility of the magnetic material is given as

$\chi = 0.9853$
Since the magnetic susceptibility of paramagnetic material is positive. So the given substance must be a paramagnetic material.

Answer the question in at least $50$ words.
Give the characteristic of magnetic field lines.

The different characteristics of magnetic field lines are-

$(i)$ Magnetic field lines are always closed curves .

$(ii)$ The direction of magnetic field lines outside a magnet is from North pole to South Pole while inside a magnet the direction of magnetic field is from South pole to North pole.

$(iii)$ Two magnetic field lines never intersect each other.

$(iv)$ The density of magnetic field lines corresponds to the strength of magnetic field at that point in space.

$(v)$ Magnetic field lines can't abruptly decrease to zero at once from a finite value as in that case the direction of field at that point becomes indeterminate.

What is hysteresis? Define the terms 'coercivity' and 'retentivity' of a ferromagnetic material.

Hysteresis: The phenomenon in which the magnetic induction (

$\vec { B }$ ) lags behind with respect to the magnetizing field

$\vec { H }$ is called hysteresis.

It occurs when an external magnetic field is applied to a ferromagnet such as iron and the atomic dipoles align themselves with it. Even when the field is removed, part of the alignment will be retained: the material has become magnetized. Once magnetized, the magnet will stay magnetized indefinitely.

Retentivity: The property of the magnetic material to retain magnetism even in the absence of the magnetizing field is known as retentivity or remanence.

Coercivity: The magnetizing field (H) needed to demagnetize the magnetic material completely is known as its coercivity.

A small rod of bismuth is suspended freely between the poles of a strong magnet. It is found to arrange itself at right angles to the magnetic field. What is established by the observation?

A diamagnetic material gets induced magnetization in a direction opposite to the field. It aligns itself in the direction of weakest field.

A magnet has coercivity of $3\times 10^3$ $Am^{-1}$ . It is kept in a $10$ cm long solenoid with a total of $50$ turns. How much current has to be passed through the solenoid to demagnetize it?

$\mu_{\circ}H=\mu _{\circ}nI$

Given:

where

$H=3\times 10^{-3} Am^{-1}=$ coercivity

$n=$ number of turns per unit length

$=\dfrac{50}{0.1}=500m^{-1}$

To find:

$I=$ current

Now

$H=nI$

$3\times 10^{-3} Am^{-1}=500m^{-1}\times I$

$I=6\times 10^{-6}A=6\mu A$

In the Bohr model of hydrogen atom, the electron circulates around the nucleus in a path of radius $5.1\times{10}^{-11}\ m$ at a frequency $6.8\times{10}^{15}\ {s}^{-1}$ . Find the magnetic field set up at the centre of the orbit.

The circulating electron is equivalent to a circular current carrying loop,

$i=ef$

$=6.8\times 10^{15}\times 1.6\times 10^{-19}$

$=1.08\times 10^{-23} amp$

Magnetic field at the center

$B=\dfrac{\mu_0 i}{2a}=\dfrac{4\pi \times 10^{-7}\times 1.08\times 10^{-3}}{2\times 5.1\times 10^{-11}}$

$=13.3 weber/m^2$

A magnetising field of $1600\dfrac{A}{m}$ produces a magnetic flux $2.4 X 10^{-5} Wb$ in a bar of iron of cross section $0.2 cm^2$ .Calculate permeability and susceptibility of the bar:

Magnetic Induction

$B=\dfrac{Flux}{Area}=\dfrac{2.4\times 10^{-5}}{0.2\times 10^{-4}}$

$=1.2T$

Permeability

$\mu=\dfrac{B}{H}=\dfrac{1.2}{7.5\times 10^{-4}}=0.75\times10^{-3}$

Susceptibility

$X=624$

$\dfrac{u}{u_0}=1+X$

$\implies \dfrac{0.75\times 10^{-3}}{4\pi\times 10^{-7}}=1+X\implies X=624$

Ferrimagnetic those expected to have large magnetism but actually have small net magnetic moment e.g., magnetic $(Fe_{3}O_{4})$ , ferrites $(M^{2}+Fe_{2}O_{4})$ . This is because of unequal number of domains in opposite direction.

A ferrimagnetic material is one that has populations of atoms with opposing magnetic moments, as in antiferromagnetism; however, in ferrimagnetic materials, the opposing moments are unequal and a spontaneous magnetization remains. This happens when the populations consist of different materials or ions. (such as Fe²⁺ and Fe³⁺).
Ferrimagnetic materials are like ferromagnets in that they hold a spontaneous magnetization below the Curie temperature and show no magnetic order (are paramagnetic) above this temperature. However, there is sometimes a temperature below the Curie temperature, at which the two opposing moments are equal, resulting in a net magnetic moment of zero; this is called the magnetization compensation point.

Draw diagram to represent a uniform magnetic field in a given region.

Hint:-A uniform magnetic field is one that has the same strength and direction at all points. It is represented by a set of parallel lines that are equally spaced apart. The direction of the magnetic field lines points in the same direction as a north-south pole of a magnet points.

Diagram:-

If a particle of charge q is moving with velocity v along the z - axis and the magnetic field B is acting along x - axis, use the expression $\vec{F} = q (\vec{v} \times \vec{B} )$ to find the direction of the force F acting on it.

Given

v along x-axis

$\vec v=v\hat i$

B along y-axis

$\vec B=B\hat j$

$\vec F=q\vec v\times \vec B$

$\vec F=q(v\hat i)\times (B\hat j)$

$\vec F=qvB\hat k$

That is force is acting along z-axis.

Show diagrammatically the behaviour of magnetic field lines in the presence
of (i) paramagnetic and (ii) diamagnetic substances. How does one explain this
distinguishing feature?
OR
Draw the magnetic field lines distinguishing between diamagnetic and paramagnetic materials.
Give a simple explanation to account for the difference in the magnetic behaviour
of these materials.

A paramagnetic material tends to move from weaker field to stronger field region of the magnetic field. So, the number of lines of magnetic field increases when passing through it. Magnetic dipole moments are induced in the direction of magnetic field. Paramagnetic materials has a small positive susceptibility.
A diamagnetic material tends to move from stronger field to weaker field region of the magnetic field. So, the number of lines of magnetic field passing through it decreases. Magnetic dipole moments are induced in the opposite direction of the applied magnetic field. Diamagnetic materials has a negative susceptibility in the range

$(-1 \le x < 0)$ .
1676421_1781618_ans_e8c5c860105f49c7b3ddd19d32a278d1.png

A sample of the paramagnetic salt to which the magnetization
curve of Fig. applies is held at room temperature $(300 K)$ .
At what applied magnetic field will the degree of magnetic saturation of the sample be (a) $50\%$ and (b) $90\%$ ? (c) Are these fields
attainable in the laboratory?

(a) From Figure we estimate a slope of

$B/T = 0.50\, T/K$ when

$M/M_{max} = 50\%$ . So

$B = 0.50 \,T = (0.50 \,T/K)(300 \,K) = 1.5\times10^2$ T.

(b) Similarly, now

$B/T ≈ 2$ so

$B = (2)(300) = 6.0\times10^2 \,T$ .

in the lab.

A sample of the paramagnetic salt to which the magnetization
curve of Figure applies is to be tested to see whether it obeys
Curies law. The sample is placed in a uniform $0.50$ T magnetic field
that remains constant throughout the experiment. The magnetization M is then measured at temperatures ranging from $10$ to $300$ K.
Will it be found that Curies law is valid under these conditions?

For the measurements carried out, the largest ratio of the magnetic field to the
temperature is

$(0.50 \,T)/(10\, K) = 0.050\, T/K$ .

Look at Fig. to see if this is in the
region where the magnetization is a linear function of the ratio. It is quite close to the
origin, so we conclude that the magnetization obeys Curie’s law.

Answer the following question
Name the properties of a magnetic material that make it suitable for making
(a) a permanent magnetic and (b) a core of an electromagnetic.

(a) Permanent magnets are made of steel which is characterised by high retentivity and high coercivity.

(b) Electro magnets are made of soft iron which is characterised by high retentivity and low coercivity.

Answer the following question
What happens when a diamagnetic substance is placed in a varying magnetic
field?

A diamagnetic substance is attracted towards a region of weaker magnetic field.

Answer the following question.
State Gauss's law in magnetism. How is it different from Gauss's law in
electrostatic and why?

Gauss's Law in magnetism: The net magnetic flux through any closed surface is zero.

$\phi\ B.ds=0$
Gauss's Law in electrostatics: The net electric flux through any closed surface is

$\dfrac{1}{\varepsilon _0}$ times the net charge.

$\phi\ E.ds=\dfrac{q}{\varepsilon _0}$
The difference between the Gauss's law of magnetism and that for electrostatic is a reflection of the fact that magnetic monopole do not exist i.e. magnetic poles always exist in pairs.

Measurements in mines and boreholes indicate that Earth’s interior temperature increases with depth at the average rate of $30 C°/km$ . Assuming a surface temperature of $10°C$ , at what depth does iron cease to be ferromagnetic? (The Curie temperature of iron varies very little with pressure.)

The Curie temperature for iron is

$770°C$ . If x is the depth at which the temperature
has this value, then

$10°C + (30°C/km)x = 770°C$ . Therefore,

$x=\dfrac{770^ \circ C-10^\circ C}{30^ \circ C/km}=25\,km$

In Figure, a bar magnet lies near a paper cylinder.
(a) Sketch the magnetic field lines that pass through the surface of
the cylinder. (b) What is the sign of for every area on the
surface? (c) Does this contradict Gauss law for magnetism?
Explain.

(a) Since the field lines of a bar magnet point toward its South pole, then the

$\vec B$ arrows in one’s sketch should point generally toward the left and also towards the central
axis.

(b) The sign of

$\vec B⋅d\vec A$ for every

$d\vec A$ on the side of the paper cylinder is negative.

(c) No, because Gauss’ law for magnetism applies to an enclosed surface only. In fact, if
we include the top and bottom of the cylinder to form an enclosed surface

$S$ then

$\oint_s \vec B.d\vec A=0$ will be valid, as the flux through the open end of the cylinder near the
magnet is positive.

A sample of the paramagnetic salt to which the magnetization
curve of Fig. applies is immersed in a uniform magnetic field
of $2.0$ T. At what temperature will the degree of magnetic saturation of the sample be (a) $50%$ and (b) $90%$ ?

(a) Again from Figure, for

$M/M_{max} = 50\%$ we have

$B/T = 0.50$ . So $$T = B/0.50 =
2/0.50 = 4\, K$$.
(b) Now

$B/T = 2.0$ , so

$T = 2/2.0 = 1\,K$ .

The magnetic properties of the different materials A,B and C are shown in the following table:
Material Permeability Susceptibility Temperature dependence of susceptibility
A Low positive Small but negative Independent of temperature
B high Vert high $1$ Susceptibility decreases with temperature
C Grater than $1$ Small but positive Decreases with temperature

Which of the above three materials should be used for making an electromagnet and why?

The material to be used for making an electromagnetic should have high permeability and low retentivity. Moreover, less energy should be utilised for magnetisation of the material.

Thus, material

$B$ should be used for making the core of an electromagnet.

The susceptibility of a magnetic material is $2.6\times 10^{-5}$ . Identify the type of magnetic material and state its two properties.

The material having positive and small susceptibility is paramagnetic material. Properties
(i) They have tendency to move from a region of weak magnetic field to string magnetic field, i.e. they get weakly attracted to a magnet.
(ii) When a paramagnetic material is placed in an external field the field lines get concentrated inside the material and the fields inside is enhanced.

Write any three characteristics, a ferromagnetic substance should possess if it is to be used to make a permanent magnet. Give one example of such a material.

Characteristics for permanent magnet
(i) High permeability
(ii) High retentivity
(iii) High coercivity
Example: steel.

What is Curie law in magnetism?

Curie law. It states that the magnetic susceptibility of a paramagnetic material is inversely proportional to absolute temperature

$\therefore X\propto \dfrac{1}{T}=\dfrac{C}{T}$ where

$C$ is Curie constant.

The susceptibility of a magnetic materials $-4.2\times 10^{-6}$ . Name the type of magnetic material it represents.

Susceptibility of material is negative. so given material is diamagnetic.

The variation of intensity of magnetisation $I$ and the applied magnetic field intensity $H$ for three magnetic materials $X,\ Y$ and $Z$ are as shown in the given graphs.
Identify the materials $X,\ Y$ and $Z$ .

$X-$ diamagnetic,

$Z-$ paramagnetic,

$Y-$ ferromagnetic

As manetization is the property of material and ,

$I_{diamagnetic}<I_{paramagnetic}<I_{ferromagnetic}$

A magnetic needle free to rotate in a vertical plane parallel to the magnetic meridian has its north tip down at $60^{o}$ with the horizontal. The horizontal component of the earth's magnetic field at the place is known at to be $0.4\ G$ . Determine the magnitude of the earth's magnetic field at the place.

Angle of dip,

$\theta=60^{o}$

$H=0.4\ G=0.4\times 10-4T$
If

$Be$ is earth's magnetic field, then

$H=B_{e}\cos \theta.\Rightarrow B_{e}=\dfrac{H}{\cos\theta}=\dfrac{0.4\times 10^{-4}T}{\cos 60^{o}}=\dfrac{0.4\times 10^{-4}T}{0.5}=0.8\times 10^{-4}T=0.8\ G$

Which of the following substances are diamagnetic? $Bi, Al, Na, Cu, Ca$ and $Ni$

Diamagnetic substances are (i )

$Bi$ and (ii)

$Cu$

The variation of intensity of magnetisation $I$ and the applied magnetic field intensity $H$ for three magnetic materials $X,\ Y$ and $Z$ are as shown in the given graphs
Shows graphically the variation of susceptibility with temperature for $X$ .

For

$X$ ,

For a diamagnetic substance , susceptibility is independent of temperature but a property of material.

1676656_1781661_ans_dfe546572c554811aea980acb8dbca37.png

The variation of intensity of magnetisation $I$ and the applied magnetic field intensity $H$ for three magnetic materials $X,\ Y$ and $Z$ are as shown in the given graphs
Put of $Y$ and $Z$ , which of the material will you prefer for making transformer cores and why?

$Y$ will be preferred to be used in the transformer core because it has high permeability and low hysteresis loss.

Why is the core of an electromagnet made of ferromagnetic materials?

Ferromagnetic material has a highly retentively. So on passing current through windings it gains sufficient magnetism immediately.

In what ways is the behaviour of a diamagnetic material different from that of a paramagnetic, when kept in an external magnetic field?

A diamagnetic specimen would move towards the weaker region of the field while a paramagnetic specimen would move towards the stronger region.

What is the basic difference between the atom and molecule of a diamagnetic and a paramagnetic material? Why are elements with even atomic number more likely to be diamagnetic?

Atoms/ molecules of a diamagnetic substance contain even number of electrons and these electrons from the pairs of opposite spin; while the atoms/molecules of a paramagnetic substance have excess of electrons spinning in the same direction.
The elements with even atomic number

$Z$ has even number of electrons in its atoms/ molecules, so they are more likely to form electrons pairs of opposite spin and hence more likely to be diamagnetic.

The magnetic field lines prefer to pass through iron than air. Explain why?

The magnetic field lines prefer to pass through iron than air because the permeability of iron is much larger than air.

What kind of ferromagnetic material is used for coating magnetic tapes in a cassette player or for building memory stores in a modern computer?

Ceramics are used for coating magnetic tapes in a cassette player or for building stores in a modern computer. Ceramics are specially treated barium-iron oxides and are also called ferrites.

Boojho kept a magnet close to an ordinary iron bar. He observed that the iron bar attracts a pin as shown in the figure.
What inference could he draw from this observation? Explain.

He could infer that the iron bar is induced with magnetic properties and the iron bar acts like a magnet till the magnet is kept on it.

1634610_1787960_ans_e9de9e5e6cf44dcc819a13ac22794fb4.PNG

1634610_1787960_ans_e9de9e5e6cf44dcc819a13ac22794fb4.PNG

State with reason, whether the following statement is true or false? The product of magnetic susceptibility and absolute temperature $XT$ is constant for a paramagnetic material.

Yes, according to Curle law,

$X\propto \dfrac{1}{T}.XT$ = constant is true for paramagnetic substances.

From molecular view point, discuss the temperature dependence of susceptibility for diamagnetism, Para magnetism and ferromagnetism.

Diamagnetism is due to orbital motion of electrons developing magnetic moments opposite to applied field and hence is not much affected by temperature.
Paramagnetic and ferromagnetism is due to alignments of atomic magnetic moments in the direction of the applied field. As temperature increases, this alignment is disturbed and hence susceptibilities of both decrease as temperature increases.

Fill in the blanks
In a magnet, __________ have the maximum attractive property.

The attractive property of a magnet is maximum at north and south poles both. Hence, at the ends magnet have the maximum attractive property.

Two magnetic lines of force never intersect each other. True/False?

Two magnetic lines of force never intersect each other. Each point on the field line gives the direction of magnetic field. Now if two magnetic field line intersect each other then at that point there will be two direction of magnetic field which is not possible.

State whether the following statement is True or False.

Ampere's swimming rule describes the direction of magnetic lines of force in a straight conductor.

The Right hand Thumb rule describes the direction of magnetic lines of force in a straight conductor.
Right hand thumb rule states that when an electric current passes through a straight wire that is held by the right hand with the thumb pointing upwards and the fingers curling up the
wire, the thumb points in the direction of the conventional current (from positive to negative), and the fingers point in the direction of the magnetic field.

A small magnet is suspended by a silk thread from a rigid support such that the magnet can freely swing. Describe its behaviour.

Earth has two geographic poles, the North Pole and the South Pole. They are the places on Earth's surface from where the Earth's imaginary spin axis passes through. Our planet also has two magnetic poles, the North Magnetic Pole and the South Magnetic Pole just like a bar magnet.
Hence, a freely suspended magnet will point in geographic north-south direction with north pole towards the geographic north, making some angle with the horizontal plane.

Sketch magnetic lines of force around a current carrying coil.

The magnetic field around a current carrying coil wraps around the coil as shown in the figure (Red is the coil and blue lines represents magnetic lines of force in the figure).

State the characteristics of magnetic lines of force.

Characteristics of magnetic lines of force:

The magnetic field at any given point is specified by both a direction and magnitude.
Magnetic lines of force start from the North Pole and end at the South Pole outside magnet.
Two magnetic lines of force cannot intersect each other and they are continuous along the axis of the electromagnetic conductor.
The magnetic lines of force are uniform and strong at the center or inside of the conductor and they diverge as they move away from the conductor and as the distance increases. Eventually, the strength of the magnetic field is strong inside and they weaken as the closeness decreases.

List two methods of producing magnetic fields.

$\textbf{There are following method to produce the magnetic field.}$

$\bullet$ Moving charge

$\bullet$ Permanent magnets,

$\bullet$ Electromagnets

$\bullet$ Current-carrying conductors.

Which of the following substances are para-magnetic?
$Bi, Al, Cu, Ca, Pb, Ni$

These are metals that are weakly attracted to magnets. The atoms of these substances contain electrons most of which spin in the same direction but not all This gives the atoms some polarity. They are only weakly influenced by a magnetic field and since some of the atoms can be turned to point their poles in the same direction, these metals can become very weak magnets. Their attractive force can only be measured with sensitive instruments. Hence Aluminium (Al) and Calcium (Ca) are paramagnetic.

The relative magnetic permeability of a magnetic material is $800$ . Identify the nature of magnetic material and state its own properties.

The substance is ferromagnetic as the relative magnetic permeability is very large.

Properties :

i) When the ferromagnetic material is placed in uniform magnetic field , it is strongly magnetise along magnetic field.

ii) It has large susceptibility.

The susceptibility of a magnetic material is $-2.6 \times {10}^{-5}$ . Identify the type of magnetic material and state its two properties.

As the given susceptibility is small and negative so it will be diamagnetic material.

The two properties of it are -

i) When it is placed in uniform magnetic field, it is feebly magnetise opposite to the magnetic field.

ii) The relative permeability is positive and less than one.

What are permanent magnets? Give one example.

The magnets which have high retentivity and coercivity are known as permanent magnets. The magnetization of permanent magnet is not easily destroyed even it is handled roughly or exposed in stray reverse magnetic field.

Example - refrigerator magnet.

A ________ is a region around a magnet where magnetic lines of force act.

A magnetic field is the region in the vicinity of magnet where the field lines are sufficient to feel the magnetic force.

Classify the following materials with regard to magnetism:
Manganese, Cobalt, Bismuth, Copper

Manganese is a paramagnetic material. Cobalt is the ferromagnetic material. Bismuth and copper are the diamagnetic materials.

What are diamagnetic substances? Give one example

Diamagnetic substances repel magnetic field. This is so because an applied magnetic field creates an induced magnetic field in them in the opposite direction, causing a repulsive force. Diamagnetic substances are composed of atoms which have no net magnetic moments,ie., all the orbital shells are filled and there are no unpaired electrons.

Water is a diamagnetic substance.

Why do magnetic field lines not intersect each other?

If magnetic field lines intersect each other, then at the intersection point there will be two directions of the same field which is not possible. Hence the field lines do not cross or intersect each other.

Write any three properties of magnetic lines of force.

The path along which the unit North pole moves in a magnetic field is known as magnetic lines of force.
(a) These magnetic lines of force are closed continuous curves. They start from the North pole and end on the South pole. No two magnetic lines of force can intersect each other.
(b) The tangent at any point on the magnetic lines of force gives the direction of the magnetic field at that point.
(c) Where the magnetic field is strong, the magnetic lines of force are crowded and where the field is weak, the magnetic lines of forces are far from each other.

State True or False.
Magnetic lines of force are closed continuous curves.

Magnetic lines of force are closed continuous curves and never intersect with each other.Hence the given statement is true.

Compare paramagnetism and ferro magnetism. Give examples of each.

Paramagnetism refers to materials like aluminum or platinum which become magnetized in a magnetic field but their magnetism disappears when the field is removed.
Ferromagnetism refers to materials (such as iron and nickel) that can retain their magnetic properties when the magnetic field is removed.

State and explain Curie's law.

Curie's Law:
In a paramagnetic material the magnetization of the material is directly proportional to an applied magnetic field. However, if the material is heated, the magnetization is inversely proportional to temperature.

i.e. M = C x ( B / T )

where,

M is the magnetisation

B is the magnetic field, measured in teslas

T is absolute temperature, measured in kelvins

C is a material-specific Curie constant

It was first discovered experimentally by French physicist, Pierre Curie. It holds for high temperatures, or weak magnetic fields.

What is Curie temperature?

Curie temperature is defined as the temperature at which certain materials lose their permanent magnetic properties, to be replaced by induced magnetism. The term Curie temperature is named after Pierre Curie who showed that magnetism was lost at critical temperature.

Draw the pattern of magnetic field lines for a bar magnet.

Magnetic field lines are closed continuous loops which start at the north pole of magnet and end at south pole. The magnetic field lines do not intersect each other. The pattern of magnetic field lines formed by the bar magnet is shown in the figure.

Classify the following materials with regard to magnetism:
Manganese, Cobalt, Nickel, Bismuth, Oxygen and Copper

Magnetism	Materials
Paramagnetic	Manganese and Oxygen
Diamagnetic	Bismuth and Copper
Ferromagnetic	Cobalt and Nickel

Distinguish between Para, Ferro and Diamagnetism.

Paramagnetism	Ferromagnetism	Diamagnetism
It has its own magnetic moment due to presence of unpaired electrons.	It has its own magnetic moment due to presence of unpaired electrons.	All the electron are paired so there is no permanent net magnetic moment per atom.
Paramagnetic materials have a small, positive susceptibility to magnetic fields. Paramagnetic materials include magnesium, molybdenum, lithium, and tantalum.	Ferromagnetic materials have a large, positive susceptibility to an external magnetic field. Iron, nickel, and cobalt are examples of ferromagnetic materials.	Diamagnetic materials have a weak, negative susceptibility to magnetic fields. Copper, silver, and gold, are diamagnetic.

Write two properties of magnetic lines of force.

The following are the two properties of magnetic lines of forces : -

1. They never cross one another.

2. They all have the same strength.

Define Curie temperature in magnetism.

Curie temperature is the temperature above which materials lose their permanent magnetic properties and behave as paramagnetic materials.

Out of the two magnetic materials, 'A' has relative permeability slightly greater than unity while 'B' has less than unity. Identify the nature of the materials 'A' and 'B'. Will their susceptibilities be positive or negative?

For a paramagnetic material, the relative permeability lies between

$1 < \mu_r < 1 + \varepsilon$ and its susceptibility lies between

$0 < X < \varepsilon$ .
Hence, 'A' is a para-magnetic material and its susceptibility is positive. This is because its relative permeability is slightly greater than unity. For a diamagnetic material, the relative permeability lies between

$0 \leq \mu_r < 1$ and its susceptibility lies between

$-1 < X < 0$ . Hence, 'B' is a diamagnetic material and its susceptibility is negative. This is because its relative permeability is less than unity. Here

$\mu_r$ and

$x$ refer to the relative permeability and susceptibility.

A rectangle has sides of lengths $6 cm$ and $8 cm$ . Two magnetic poles each of pole strength ' $m$ ' are placed at the ends of one side of smaller length and magnetic force acting between them is ' $F$ '. If they are moved to new positions of same rectangle so that they are diagonally opposite. Find the final force acting on each pole.

Force

$F$ action each magnet is

$F=K \dfrac{m_1 m_2}{8^{2} \times 10^{-4}}$ ..(1) where K is constant

When magnets are diagonally opposite then final force

$F'$

$F'=K \dfrac{m_1 m_2}{10^{2} \times 10^{-4}}$ ..(2)

From (1) and (2),

$F'=\dfrac{8^{2}}{10^{2}}F=\dfrac{64}{100}F$

$F'=\dfrac{16}{25}F$

Conductivity of metal decreases with temperature while conductivity of electrolytic conductors increases with temperature. Why ?

In metal, electron is responsible as the charge carrier. A systematic flow of electrons in one direction will cause the metal to conduct electricity efficiently. An increase in temperature will cause the electrons to get excited and this causes them to move in a not so orderly manner. Hence, they become less efficient as the charge carrier and conductivity decreases.

In electrolyte, it is the ions (both positive and negative) that is responsible as the charge carrier. An increase in temperature will increase the energy of the ions and they will move faster. Hence its efficiency as charge carrier increases and this will cause the conductivity to increase.

Write the causes of energy loss and ways to reduce them in transformer (any four).

Energy losses and removal
(i) Copper loss: Some part of the energy is wasted in the form of heat due to the heating effect of current in primary and secondary coil, because it has some resistance. This loss cannot be removed.
(ii) Iron loss: Eddy current is produced in the iron core of the transformer causes heating. This loss is called iron loss. To minimize this loss, the core is made laminated.
(iii) Magnetic flux leakage: All the magnetic flux produced by primary coil do not link with secondary coil. Therefore, some energy is wasted. To minimize this loss, soft iron core is used.
(iv) Hysteresis loss: Some of the energy is wasted in magnetization and demagnetization of core duet a.c. This is called hydsteresis loss. It is minimized by taking soft iron core.

State the characteristics of magnetic field lines.

A magnetic force experienced around the region of a magnet is called magnetic field. The characteristics of magnetic field lines are as follows:

(i) The magnetic field lines of a magnet start from the North Pole(N) and reach the South Pole(S) and these lines are in the north-south direction inside the magnet.

(ii) The region in which the field lines are at close distance to each other has a strong magnetic field and if the field lines are at far distance from each other, the region has a weak magnetic field. Near the poles of a magnet, the field lines are at close distance from each other so there is strong magnetic field.

(iii) The magnetic field is a very vector quantity. So it has magnitude and direction both. The tangent is drawn at any point of a magnetic field line.

(iv) Magnetic field lines do not intersect each other.

Define magnetic lines of force and state its two properties.

Magnetic lines of force determine the alignment and orientation of miniature test magnets in a magnetic field.

1. Magnetic lines of force start from the north pole and end at the south pole.

2. They are continuous through the body of magnet

3. Magnetic lines of force can pass through iron more easily than air.

4. Two magnetic lines of force can not intersect each other.

5. They tend to contract longitudinally.

6. They tend to expand laterally.

Few iron nails and screws got mixed with wood shavings while a carpenter was working with them. How can you help him in getting the nails and screws back from the scrap without wasting his time by searching with his hands?

With the help of a magnet we can attract all iron nails and screws and can separate them from the wooden shavings. As iron nails and screws are magnetic materials and will get attracted to the magnet, whereas wooden shavings are non-magnetic.

A square frame $PQRS$ of side $20\ cm$ , made up of a conducting wire is placed in a magnetic field of $1$ tesla as shown. The magnetic field is perpendicular to the plane of the frame directed upwards. An electric current of $2A$ enters at the edge $P$ of the frame and exist from the edge $R$ . Find out the magnetic forces acting on the sides of the frame.

$0.020\ N$ on each side
Directed downwards on

$PQ$ and

$SR$ .

Draw the hysteresis curve for ferromagnetic substance. Show coercivity and retentivity on the curve.

1130213_693998_ans_2902ecc2575d46c9adadbfe27dfb7370.png

Explain Curie's law for a paramagnetic substance.

Curie law states that magnetization of paramagnetic substance is directly proportional to the external magnetic field applied. But as the substance is heated, it's magnetization is inversely proportional to the temperature of substance.
Thus magnetization of paramagnetic substance

$M = \dfrac{CB}{T}$
where

$C$ is curie constant,

$B$ is external magnetic field and

$T$ is the temperature of substance.

Write whether the given statement is true or false : The magnetic susceptibility $(X_m)$ of a paramagnetic substance has a small negative value.

The given statement is FALSE.
As the magnetic susceptibility (

) of para magnetic substance is very small but positive (

) .

A uniform magnetic field gets modifies as shown in Figure below , when two speciments X and Y are placed in it . Identyfy wether speciment X and Y are diagramatic , paramagnetic or ferromagnetic .

X is diamagnetic and

Y is ferromagnetic.

X is diamagnetic as it expels magnetic lines Y is paramagnetic or ferromagnetic as it pulls the magnetic lines into it.

The susceptibility of magnesium at $300 \,K$ is $1.2 \times 10^5$ . What will be its susceptibility at $200 \,K$ ?

According to curic law,

$X=\dfrac{C}{T}$

$C=$ Curic temperature

$T=$ Temperature in Helium
So,

$X \propto \dfrac{1}{T}$
Now given

$X_11.2\times 10^{-5}$

$T_1=300$

$X_2=?$

$T_2=200$
So,

$\dfrac{X_1}{X_2}=\dfrac{T_2}{T_1}$

$\Rightarrow \dfrac{1.2\times 10^{-5}}{X_2}=\dfrac{200}{300}$

$\Rightarrow X_2=1.2\times 10^{-5}\times \dfrac{300}{200}$

$=1.8\times 10^{-5}$

Write definition of Curie temperature for ferromagnetic substance.

The temperature at which a ferromagnetic substance becomes para magnetic is called curie temperature curie temperature of curie point

$T_C$
Cause : when ferromagnetic sample heated, its magnetization decreases due to the increase in the administration of its domains. At high temperature, the domain structure disintegrates & the ferromagnetic substance becomes para magnetic

Draw hysteresis curve (B-H curve) for a ferromagnetic substance

Hysteresis curve for ferromagnetic substance
* Ferromagnetic material has high retentivity & low coercivity
1205106_1514095_ans_76255981879740d1ae08e68d0f9e06ad.png

1205106_1514095_ans_76255981879740d1ae08e68d0f9e06ad.png

When a electric current is passed through ant wire, a magnetic filed is produced around it. Then why an electric iron connecting cable does not attract nearby iron objects when electric current is switched on through it?

Because the strength field produced by the cable of the electric iron is quiet weak.

In New Hampshire, the average horizontal component of Earth’s magnetic field in $1912$ was $16 \mu T$ , and the average inclination or “dip” was $73°$ . What was the corresponding magnitude of Earth’s magnetic field?

As we know,

The horizontal component of the Earth’s magnetic field is given by

$B_h= Bcosφ_i$ ,

where B is the magnitude of the field and

$φ_i$ is the inclination angle. Thus

$B=\dfrac{B_h}{\cos \phi_i}=\dfrac{16\,\mu T}{\cos 73^\circ}=55\,\mu T$

How can you distinguish between diamagnetic and paramagnetic rods?

When suspended freely in a magnetic field,

1. the paramagnetic rod sets itself parallel to the field, and

2. the diamagnetic rod itself perpendicular to the field.

Define retentivity.

The magnetic induction left behind in the sample after the magnetising field has been removed is called residual magnetism or retentivity.

Give two examples of paramagnetic substances.

$(i)CuCl_{2}$

$(ii)Oxygen$

What are the behaviour of diamagnetic, paramagnetic and ferromagnetic substances in non-uniform magnetic field?

1. When placed in a non-uniform magnetic field, a diamagnetic substance moves from stronger to the weaker parts of the field.

2. When placed in a non-uniform magnetic field, a paramagnetic substance moves from weaker to the stronger parts of the field.

3. When a ferromagnetic substance is placed in non-uniform magnetic field, it moves from weaker to the stronger parts of the field.

The Curie temperature for a ferromagnetic substance is $300 K$ . If magnetic susceptibility of the substance is $0.6$ at $450 K$ temperature, then find out Curie constant.

Curie temperature

$T_{C} = 300 K$

Temperature

$T = 450K$

Magnetic Susceptibility

$X_{m} = 0.6$

$\because \chi_{m} = \dfrac{C}{T-T_{C}}$

$0.6 = \dfrac{C}{450-300}$

$C = 0.6\times 150$

$\therefore$ Curie Constant

$C=90K$

At which place on a magnet, its magnetic force is maximum ?

The magnetic force will be maximum at poles.

In an exhibition, a plastic car with an iron piece fixed inside it is made to run on a wooden table by sliding a strong magnet below it. The experiment failed when a steel table was used instead.Explain the reason.

Steel table has high permeability. It permit magnetic flux to pass through it therefore we cannot slide the car using magnet.

A physics teacher suspends two pointers in a magnetic field. One pointer is made of brass and the other is a magnet.
She holds the pointers in the initial positions shown in the two upper circle of figure. She then releases the pointers.
In the lower circles of figure, draw the settles final positions of the two pointers.

The magnetic field lines point from the north pole to the south pole.

so Brass point will not be affected by magnetic field. and remain as it is

whereas magnet pointer in align in the direction of magnetic field with south pointing upward and north pointing in downward direction.

What are the difference in the magnetic properties of iron and steel?

Tron becomes a more intense magnet on magnetic induction. But that magnetic power is temporary. When the permanent magnet is removed it losses its magnetic power. In the presence of a magnet, steel doesn't acquire the magnetic power like that of a soft iron. But steel retains most of its magnetic power after removing the permanent magnet.

Three diagrams in the following figures show the magnetic field lines between the poles of the magnets. Identify the poles between $A, B, C, D, E,$ and $F$ .

A- north
B- south
C- south
D- south
E-south
F-south

Distinguish between a bar magnet and an electromagnet.

Bar Magnets

The bar magnet is a permanent magnet.

It produces a comparatively weak force of attraction.

The strength of a bar magnet cannot be changed.

The polarity of a bar magnet is fixed and cannot be changed.

Electromagnets

An electromagnet is a temporary magnet.

It produces a very strong magnetic force.

The strength of an electromagnet can be changed by changing the number of turns in its coil or by changing the current passing through it.

The polarity of an electromagnet can be changed by changing the direction of current in its coil.

Explain why, two magnetic lines of force do not intersect.

The magnetic lines of force do not intersect one another due to the fact that the resultant force on a north pole at any point can be only in one direction. But if the two magnetic lines of force intersect one another, then the resultant force on a north pole placed at the point of intersection will be along directions, which is not possible.

Magnetic field lines of two magnets are shown in fig. A and fig. B.
Select the figure that represents the correct pattern of field lines. Give reasons for your answer. Also name the poles of the magnets facing each other.

Figure B represents the correct pattern of field lines. In figure A, field lines cross each other which is not possible because if they cross each other, at the point of intersection, there would be two directions of field lines. In figure B, field lines are emerging in nature, so poles of magnet facing each other are north poles while opposite faces will have south polarity.

(a) Draw a diagram to represent a uniform magnetic field in a given region.
(b) List two properties of magnetic field lines.

(a) Equidistant parallel line indicates a uniform magnetic field in a given region.

(b) Properties of magnetic field lines are:

The magnetic field lines of a magnet form continuous closed loops, i.e. outside the magnet, they emerge from north pole and merge at the south pole and inside the magnet, the direction of field lines is from its south pole to its north pole.
The degree of closeness of field lines indicates the strength of magnetic field.
Field lines never cross each other.

1994931_1951521_ans_0b7ef461278a47858b9dfb9b6860cf1d.png

$N = 300$ turns of this wire are uniformly wound on a permanent magnet shaped as a cylinder whose length is equal to $l = 15\ cm$ . When a current $I = 3.0\ A$ was passed through the wiring the field outside the magnet disappeared. Find the coercive force $H_{c}$ of the material from which the magnet was manufactured.

The coercive force

$H_c$ is just the magnetic field within the cylinder. This is by circulation theorem,

$\displaystyle H_c=\frac{NI}{l}=6\:kA/m$

(from

$\displaystyle\oint{\vec{H}\cdot d\vec{r}}=I$ , total current, considering a rectangular contour.)

A thin iron ring with mean diameter $d = 50\ cm$ supports a winding consisting of $N = 800$ turns carrying current $I = 3.0\ A$ . The ring has a cross-cut of width $b = 2.0\ mm$ . Neglecting the scattering of the magnetic flux at the gap edges, and using the plot shown in Fig., find the permeability of iron under these conditions.

From the theorem on circulation of vector

$\vec{H}$ ,

$\displaystyle H\pi d+\frac{Bb}{\mu_0}=NI$ or,

$\displaystyle B=\frac{\mu_0NI}{b}-\frac{\mu_0\pi d}{b}H=(1.51-0.987)H$ ,

Where

$B$ is in Tesla and

$H$ in

$kA/m$ . Besides,

$B$ and

$H$ are interrelated as in the figure shown below of the text. Thus we have to solve for

$B$ ,

$H$ graphically by simultaneously drawing the two curves (the hysterisis curve and the straight line, given above) and find the point of intersection. It is at

$H\approx0.26\:kA/m$ ,

$B=1.25\:T$
Then

$\displaystyle\mu=\frac{B}{\mu_0H}\approx4000$ .

Three identical specimens of a magnetic materials nickel, antimony and aluminium are kept in a non-uniform magnetic field. Draw the modification in the field line in each case. Justify your answer.

This happens because,
(i) Nickel is a ferromagnetic substance.
(ii) Antimony is a diamagnetic substance.
(iii) Aluminium is a para diamagnetic substance.
1138232_1207593_ans_9886f3547de34cb5af7299d0947e1a92.jpg

1138232_1207593_ans_9886f3547de34cb5af7299d0947e1a92.jpg

Discuss the special properties of ferromagnetic materials.

When ferromagnetic materials are placed in an external uniform magnetic field, they get strongly magnetized in the direction of the external magnetic field.
When these materials are placed in an external non-uniform magnetic field, they tend to move from the weaker part to the stronger part of the field.
All the atoms of the ferromagnetic materials have a resultant magnetic dipole moment even in the absence of any external magnetic field.
When a thin rod of ferromagnetic substance is placed in an external uniform magnetic field, it comes to rest with its axis parallel to magnetic field.
Their magnetic susceptibility is positive and very high.
Ferromagnetic substances remain magnetised even after the removal of the magnetizing field.
If a watch glass containing a small quantity of a ferromagnetic liquid is placed in between two opposite magnetic poles, the liquid shows and elevation in the middle.
if such a material is filled in a UTube and if one end of this tube is placed in a magnetic field, the level rises in that end.
When a ferromagnetic gas is introduced in between the pole pieces of a magnet, it spreads in the direction of the field.

Write two examples of ferromagnetic substance.

Ferromagnetic substances are the substances which are strongly attracted by the external magnetic field and these substance contains magnetic properties even if the external magnetic field is removed.
Iron and Nickel are the two examples of ferromagnetic substance.

What happens to ferromagnetic substance heated above Curie temperature?

The Curie temperature is the temperature above which it loses its ferromagnetism and converts to paramagnetic substance. This occurs due the disorderness in the electronic arrangement.

What is the unit of ratio $\dfrac {E}{H}$ ?

The unit of

$\frac { E }{ H }$ is volt/ampere or ohm.

Draw neat labelled diagrams of showing magnetic field with pencil only:

Magnetic field is a region around a magnetic material or a moving electric charge within which the force of magnetism acts.
966017_1062063_ans_aa1a7629c44d40e898396748f5b22de2.png

966017_1062063_ans_aa1a7629c44d40e898396748f5b22de2.png

The individual plates composing the earth's crust are called________.

Earth's crust is divided into two types

$.$ Oceanic crust and continental crust

$.$ The transition zone between these two types of crust is sometimes called the conrad discontinuity silicates

$.$

$,$ the individual plates composing the earth's crust are called

$continental\,\,crust.$

Column II gives approximate values of magnetic field due to source given in column I

This are some fact and information so

Magnetic field due to the sources are following:
A) At surface of neutron star is

$10^8 T$
B) Near big electromagnet

$1.5 T$
C) At earth surface

$10^{-4}T$
D) In interstellar space

$10^{-5} T$

Why does a magnetic compass needle pointing North and South in the absence of a nearby magnet get deflected when a bar magnet or a current carrying loop is brought near it. Describe some salient features of magnetic lines of force concept :

When electric current passes through the conductor it behaves like a bar magnet and an induced EMF is created which generates magnetic lines of force around it. Thus, when a magnetic compass that is pointing in the north-south direction according to the earth's magnetic field, shows deflection with respect to the strength of the magnetic field that is superposition of magnetic field created by the current carrying conductor and of earth. Features of magnetic lines of force, The magnetic field at any given point is specified by both a direction and a magnitude.Magnetic lines of force start from the North Pole and end at the South Pole. Two magnetic lines of force cannot intersect each other and they are continuous along the axis of the electromagnetic conductor. The magnetic lines of force are uniform and strong at the center or inside of the conductor and they diverge as they move away from the conductor and as the distance increases. Eventually, the strength of the magnetic field is strong inside and they weaken as they closeness decreases.

State two differences between an electromagnet and a permanent magnet.

An electromagnet is simply a coil of wire. It is usually wound around an iron core. However, it could be wound around an air core, in which case it is called a solenoid. When connected to a current source, the electromagnet becomes energized, creating a magnetic field just like a permanent magnet. The magnetic flux density is proportional to the magnitude of the current flowing in the wire of the electromagnet.
Differences between electromagnet and permanent magnet are as follows:

	Permanent Magnets	Electromagnets
1	A permanent magnet is an object made from a material that is magnetized and creates its own persistent magnetic field. As the name suggests, a permanent magnet is 'permanent'. This means that it always has a magnetic field and will display a magnetic behavior at all times.	An electromagnet is made from a coil of wire which acts as a magnet when an electric current passes through it. Often an electromagnet is wrapped around a core of ferromagnetic material like steel, which enhances the magnetic field produced by the coil
2	Permanent magnets magnetic properties exist when the magnet is magnetized.	An electromagnetic magnet only displays magnetic properties when an electric current is applied to it.
3	Permanent magnet strength depends upon the material used in its creation.	The strength of an electromagnet can be adjusted by the amount of electric current allowed to flow into it. As a result, the same electromagnet can be adjusted for different strength levels.

A short bar magnet placed in a horizontal plane has its axis aligned along the magnetic north-south direction. Null points are found on the axis of the magnet at 14 cm from the centre of the magnet. The earth's magnetic field at the place is 0.36 G and the angle of dip is zero. What is the total magnetic field on the normal bisector of the magnet at the same distance as the null-point (i.e., 14 cm) from the centre of the magnet? (At null points, field due to a magnet is equal and opposite to the horizontal component of earth's magnetic field.)

At null point(and along the axis), earth's magnetic field and bar's magnetic field are opposite in direction.

On equatorial line, bar's magnetic field is opposite in direction to its field on the axis. Hence, on equatorial line, the two fields add up.

As the null points are on the axis of the bar magnet, therefore,

$B_1=\dfrac{\mu_0}{4\pi}\dfrac{2M}{d^3}=H$

On the equatorial line of magnet at same distance(d), field due to the magnet is

$B_2=\dfrac{\mu_0}{4\pi}\dfrac{M}{d^3}=\dfrac{B_1}{2}=\dfrac{H}{2}$

Therefore total magnetic field at this point on equatorial line is

$B=B_2+H=\dfrac{3H}{2}=\dfrac{3}{2}\times 0.36G=0.54G$

Answer the following questions:
(a) Why does a paramagnetic sample display greater magnetisation (for the same magnetising field) when cooled?
(b) Why is diamagnetism, in contrast, almost independent of temperature?
(c) If a toroid uses bismuth for its core, will the field in the core be (slightly) greater or (slightly) less than when the core is empty?
(d) Is the permeability of a ferromagnetic material independent of the magnetic field? If not, is it more for lower or higher fields?
(e) Magnetic field lines are always nearly normal to the surface of a ferromagnet at every point. (This fact is analogous to the static electric field lines being normal to the surface of a conductor at every point.) Why?
(f) Would the maximum possible magnetisation of a paramagnetic sample be of the same order of magnitude as the magnetisation of a ferromagnet?

(a) This is because at lower temperatures, the tendency to disrupt the alignment of dipoles(due to magnetizing field) decreases on account of reduced random thermal motion.

(b) In a diamagnetic sample, each molecule is not a magnetic dipole in itself.Therefore random thermal motion of molecules does not affect the magnetism of the specimen. That is why diamagnetism is independent of temperature.

(d) No, permeability of ferromagnetic material is not independent of magnetic field. As is clear from hysteresis curve,

$\mu$ is greater for lower fields.

(e) Magnetic field lines are always nearly normal to the surface of a ferromagnet at every point. The proof of this important fact is based on the boundary conditions of magnetic fields (B and H) at the interface of two media.

(f) The maximum possible magnetisation of a paramagnetic sample can be of the same order of magnitude as the magnetisation of a ferromagnet. For this, a high magnetising fields for saturation will be required.

Answer the following questions:
(a) Explain qualitatively on the basis of domain picture the irreversibility in the magnetisation curve of a ferromagnet.
(b) The hysteresis loop of a soft iron piece has a much smaller area than that of a carbon steel piece. If the material is to go through repeated cycles of magnetisation, which piece will dissipate greater heat energy?
(c) 'A system displaying a hysteresis loop such as a ferromagnet, is a device for storing memory? Explain the meaning of this statement.
(d) What kind of ferromagnetic material is used for coating magnetic tapes in a cassette player, or for building 'memory stores' in a modern computer?
(e) A certain region of space is to be shielded from magnetic fields. Suggest a method.

(a) Since in a ferromagnetic substance the magnetic properties are due to alignment of domains, therefore on withdrawing the magnetizing field the original domain formation does not take place.

(b) Carbon steel piece, because heat lost per cycle is proportional to the area of hysteresis loop.

(c) Magnetization of a ferromagnet is not a single-valued function of magnetizing field. Its value for a particular field depends both on the field and also on the history of magnetization. In other words, the value of magnetization is a record of 'memory' of its cycle of magnetization. If information bits can be made to correspond to these cycles, the system with such a hysteresis loop can act as a device for storing information.

(d) Ceramic(specially treated barium iron-oxides) also called ferites.

(e) Surround the region by soft-iron rings. Magnetic field lines will be drawn into the rings, and the enclosed space will be free of magnetic field. But this shielding is only approximate, unlike the perfect electric shielding of a cavity in a conductor placed in an external electric field.

If the bar magnet is turned around by $180^{o}$ , where will the new null points be located?

When a bar magnet is turned by

$180^0$ , then the null points are obtained on the equatorial line. So, magnetic field on the equatorial line at a distance

$d'$ is given by

$B'= \dfrac{\mu_0 M}{4 \pi d'^3}= H$ -----------------------------(1)

As the magnetic field is equal to the horizontal component of the earth magnetic field.

As we know that, magnetic field

$B_1= \dfrac{\mu_0 2 M}{4 \pi d^3}= H$ -------------------------- (2)

From both (1) and (2) we have

$\dfrac{\mu_0 M}{4 \pi d'^3}= \dfrac{\mu_0 2M}{4 \pi d^3}$

$d'^3= \dfrac{d^3}{2} = \dfrac{{14}^3}{2}$

$d'= 11.1 cm$

Thus, the null points are located on the equatorial line at a distance of

$11.1cm$

Show diagrammatically the behaviour of magnetic field lines in the presence of
(i) paramagnetic and
(ii) diamagnetic substances. How does one explain this distinguishing feature?

Behaviour of magnetic field lines in (fig) i and ii.

Main distinguishing feature:

Paramagnetic	Diamagnetic
1) It tends to move from weaker to stronger region 2) Field lines passing through it is higher.	1) It tends to move from higher to lower strength region 2) Field lines passing through it is lower.

Show diagramatically the behavior of magnetic field lines in the presence of (i) paramagnetic and (ii) diamagnetic substances. How does one explain this distinguishing feature.

Diamagnetic substances have relative permeability less than 1 and hence, magnetic field lines do not prefer to pass through the material.

Paramagnetic substances have relative permeability greater than 1 and hence, magnetic field lines prefer to pass through the material.

Distinguish between 'paramagnetic' and 'ferromagnetic' substances.

Sr. No.	Paramagnetic substance	Ferromagnetic substance
1	Substances which are weakly attracted by a magnet are called paramagnetic substances.	Substances which arestrongly attracted by amagnet are calledferromagnetic substances
2	Paramagnetic materials lose their magnetism on removal of the external field and hence cannot be used to make permanent magnets	Ferromagnetic materials retain some magnetism on removal of external field and hence can be used to make permanent magnets.
3	The susceptibility is positive but small.	The susceptibility is positive but very high.
4	Aluminium, manganese, chromium and platinum are some examples of paramagnetic substances.	Iron, nickel, cobalt, gadolinium, dysprosium and their alloys are some examples of ferromagnetic substances.

The magnetic field in a given region is uniform. Draw a diagram to represent it.

Uniform magnetic field is represented by parallel magnetic field lines in same direction.

At a certain temperature, a ferromagnetic material becomes paramagnetic. What is this temperature called?

The temperature at which a ferromagnetic material becomes paramagnetic is called curie temperature.

State the characteristics of the magnetic lines of force.

1. Magnetic lines of force start from the North Pole and end at the South Pole.

2. They are continuous through the body of the magnet or closed continuous curves.

3. Magnetic lines of force can pass through iron more easily than air.

4. Two magnetic lines of force can not intersect each other.

5. They tend to contract longitudinally.

6. They tend to expand laterally.

7. Magnetic lines of force are crowded near poles and far away from each other at the center of the magnet.Hence the magnetic field is maximum near the poles and minimum at the center.

Explain the term hysteresis.

It is found that the magnetisation

$M$ always lags behind the magnetising field

$H$ . The lagging of

$M$ behind

$H$ is called hysteresis.

In other word, the phenomenon in which the value of a physical property lags behind changes in the effect causing it, as for instance when magnetic induction lags behind the magnetizing force.

What are the changes observed at the transition temperature in superconductors?

At the transition temperature in superconductor the following changes are observed.
i) The electrical resistivity drops to zero.
ii) The conductivity becomes infinity.
iii) The magnetic flux lines are excluded from the material.

Draw the variation of magnetic field (B) with magnetic intensity (H) when a ferromagnetic material is subjected to a cycle of magnetisation.

A well labelled graph has been drawn.

Write three properties of ferromagnetic materials.

These are the following properties of ferromagnetic materials.

1. All ferromagnetic materials become para-magnetic above a temperature called Curie temperature.

2. Permeability is greater than 1.

3. Magnetic susceptibility is large and positive.

Write two properties of a material suitable for making (a) a permanent magnet, and (b) an electromagnet.

The material used for making a permanent magnet should possess high value of coercivity (intensity of the applied magnetic field required to reduce the magnetization of that material to zero after the magnetization of the sample has been driven to saturation) and also a resonable value of the retentivity ( capacity to remain magnetized after the external magnetizing field has ceased to exist).
On the other hand the materials suitable for making electromagnets should have-high retentivity and low coercivity .

Define transition temperature.

The temperature at which electrical resistivity of the material suddenly drops of zero and the material changes from normal conductor to a super conductor is called the Transition temperature or critical temperature

${ T }_{ C }$ .

Write three difference between diamagnetic and paramagnetic substances.

Diamagnetic Material	Paramagnetic Material
Do not have permanent dipole moment	Have permanent dipole moment
Spin alignment : no spin moment	Spin alignment: All spins moment are randomly oriented
No interaction exist between dipoles	The interaction between the dipoles is not interacting among themselves.

Why do the lines of the magnetic field not cross each other?

If magnetic field line intersect each other then magnetic field line will have two different directions at the crossing point.This is not possible.So they do not intersect.

Depending on the magnetic property, the materials are classified in to diamagnetic, paramagnetic and ferro magnetic. The behaviour of magnetic field lines near a magnetic substance is shown in the figure. Which material corresponds to the figure.

Magnetic field lines through different kinds of substances is shown in the attached figure. It can hence be concluded that the material shown in the figure is either paramagnetic or ferromagnetic.

Compare the magnetic properties of diamagnetic ,paramagnetic and ferro magnetic substance.

Based on their behavior in a magnetizing field, materials are classified as diamagnetic, paramagnetic, and ferromagnetic substances.

(i) Susceptibility - Diamagnetic substances have a susceptibility of a low negative value and it is independent of temperature. Paramagnetic substances have a Susceptibility of a low positive value and it is inversely proportional to the absolute temperature. Ferromagnetic substances have a large susceptibility value and it is inversely proportional to the absolute temperature.

(ii) Permeability - Diamagnetic substances have a permeability of slightly less than one. Paramagnetic substances have a permeability of greater than one. Ferromagnetic substances have a very large permeability value.

(iii) Coercivity - Ferromagnetic substances have a positive coercivity value. Diamagnetic and paramagnetic substances have zero coercivity value.

The attached picture shows the lines near a paramagnetic and a diamagnetic substance when placed in an external magnetic field.

1001236_1062430_ans_eb89b89080474428ba6e337cc4fc601c.png

What we have learnt about heating effect of electric current. In studied about magnets and magnetic lines of force .

Electricity could be produced through magnetism by motion. He discovered that when a magnet was moved inside a coil of copper wire, a tiny electric currentflows through the wire. ... These lines of force would cause a current to flow in a coil of wire, when the coil is rotated between the poles of a magnet

Give the characteristics of magnetic field lines.

The characteristics of magnetic field lines are as follows:

1. The direction of the magnetic field at any point is given by the tangent to the field lines at that point.

2. Magnetic field lines never cross each other.

3. The density of the magnetic field lines gives the intensity of magnetic field at any point on the space.

4. Magnetic field lines are always close and continuous, there is no beginning and the ending of the magnetic field lines.

Explain ferromagnetism on the basis of domain theory?

Weiss proposed a concept of ferromagnetic domains. According to his postulate neighboring atoms of the ferromagnetic materials due to interactions from several number of very regions. Those regions were called domains. His theory is also named as domain theory of ferromagnetism.

The domains are aligned along the direction of the applied magnetic field grow in size that is they align opposite to the field direction which gets reduced. In the presence of a weak external field, the magnetization in the material occurs mostly by the process of domain growing. In the presence of a strong magnetic field, the material gets magnetized by the process of alignment. When the field is removed the boundaries of domain do not recover their original position and the material is not completely demagnetized but some magnetism still remains.

Why don't two magnetic lines of force intersect with each other?

Tangent at a point to the magnetic field line gives the direction of the net magnetic field at that point. If the magnetic field lines intersect, there will be be two directions of net magnetic field which is not possible. So, magnetic field lines do not intersect each other.

Mention the desired properties of magnetic materials used in making electromagnets.

Permanent magnet- low permeability, high retentivity and high coercivity

Electromagnet - high permeability, low retentivity and low coercivity

List the factors on which the strength of magnetic field produced by
(a) a current-carrying straight conductor
(b) current carrying solenoid depends.

(1)Magnetic field due to straight conductor at a point

$B = \dfrac{\mu_o I}{2\pi d}$

So, magnetic field depends on the current flowing and distance

$(d)$ of that point.

(2)Magnetic field due to solenoid

$B = \dfrac{\mu N \ i}{l}$

So, the magnetic field depends on the current flowing, the number of turns in solenoid and length of the solenoid.

List the properties of magnetic lines of force

Properties of Magnetic lines of force are as follows:

(i) They flow from the south pole to the north pole within a material and north pole to south pole in air

(ii) They never cross each other

(iii) They all have the same strength

(iv) Their density decreases(mainly they spread out) when they move from an area of higher permeability to an area of lower permeability

(v) Their density decreases with increasing distance from the poles.

(vi) The expansion of lines of magnetic field accrue in lateral position and contraction in longitudinal position.

Explain the following:
(i) Why do magnetic lines of force form continuous closed loops?
(ii) Why are the field lines repelled (expelled) when a diamagnetic material is placed in an external uniform magnetic field?

(i) Magnetic lines of force form continuous closed loops because a magnet is always a dipole and as a result, the net magnetic flux of a magnet is always zero.

(ii) When a diamagnetic substance is placed in an external magnetic field, a feeble magnetism is induced in opposite direction. So, magnetic lines of force are repelled.

1676362_1327171_ans_0fdc8f6879d64f518e50009f9b629482.png

Draw the diagram for the diamagnetic liquid kept in watch glass shows a rise in the middle..

When placed in a non-uniform magnetic field, it tends to move from stronger to weaker regions of the magnetic field. For example, when a diamagnetic liquid in a watch glass is placed on two pole pieces lying close to each other, we observe a depression in the middle and when the pole pieces are placed sufficiently apart, then we observe depressions at the sides .
1448539_1393829_ans_020d4b74e8e34a93b64409db95b5476c.JPG

1448539_1393829_ans_020d4b74e8e34a93b64409db95b5476c.JPG

Write SI unit of magnetic dipole moment.

Magnetic dipole moment

$M = Current \times Area$

So, its SI unit is

$A \ m^2$

What are diamagnetic substances?

Those substances which are weakly repelled by the external magnetic field are known as diamagnetic substances. For example : copper, bismuth etc

Suppose we want to verify the analogy between electrostatic and magnetostatic by an explicit experiment. Consider the motion of
(i) electric dipole $\underset{p}{\rightarrow }$ in an electrostatic field $\underset{E}{\rightarrow }$ and (iii) magnetic dipole $\underset{m}{\rightarrow }$ in a magnetic field. $\underset{B}{\rightarrow }$ . Write down a set of conditions on $\underset{E}{\rightarrow }$ , $\underset{B}{\rightarrow }$ , $\underset{p}{\rightarrow }$ , $\underset{m}{\rightarrow }$ so that the two motions are verified to be identical. (Assume identical initial conditions. )

Let

$\theta$ is the angle between

$\underset{m}{\rightarrow }$ and

$\underset{B}{\rightarrow }$ .

$\therefore$ Torque on magnetic dipole in a magnetic field B is

c' =

$\underset{m}{\rightarrow }$

$sin \theta$ ............... I

Similarly of \theta is the angle between electric dipole moment

$\underset{p}{\rightarrow }$ and electric field E then torque on electric dipole in E is

C' =

$\underset{P}{\rightarrow }$

$\underset{E}{\rightarrow }$

$sin \theta$ ................. II

For if motoin in I and II of electric and magnetic dipole identical then C'=C

Describe an experiment to show that the maximum attractive property is at the poles of a magnet.

Take a bar magnet and place a steel pin at some distance. We observe that nothing happens. Now, bring the steel pin near the pole of the bar magnet. We notice that pin sticks to the magnet. This experiment shows that the maximum magnetic force acts at the poles of the magnet.

What is meant by the directional property of magnets?

Directional property of magnets states that a freely suspended magnet always points towards the geographical north-south direction. Every magnet, irrespective of its shape, has a north pole and a south pole.

Fill in the blanks
Rough handling destroys the ______ properties of a magnet.

A magnet can be destroyed by rough handling, by dropping it several times, by hammering it repeatedly and by heating.

The perpendicular bisector of the line joining the two poles of a magnet is called ________.

The perpendicular bisector of the line joining the two poles of a magnet is called magnetic equator.

The north pole of the imaginary magnet of the earth is near the geographic ________ pole.

The north pole of the imaginary magnet of the earth is near the geographic south pole.

State three ways of demagnetizing a magnet.

A magnet can be demagnetized in the following ways
1. rough handling
2. hammering the magnet several times.
3. passing an alternating current around the magnet.
4. dropping the magnet on the floor several times.
5. heating the magnet to a very high temperature.

You are provided with two similar bars, one is a magnet and the other is a soft iron bar. How will you distinguish between them without the use of any other magnet or bar?
[Hint: A magnet when suspended freely will rest only in north-south direction, but soft iron bar will rest in any direction]

To distinguish between a magnet and soft iron bar, simply suspend both freely. A magnet will come to rest only in north-south direction whereas the soft iron bar will rest in any direction.

Explain: When two pins are hung by their heads from the same pole of a magnet, their pointed ends move apart.

This occurs because like poles repel each other. Hence, their pointed ends move apart.

Mention two properties of magnetic field lines.

Two properties of magnetic field lines are following:
The magnetic field lines originate from North Pole of the magnet and ends in its south pole by convention.
The magnetic field lines are closed in and continuous curve

Explain: Several soft iron pins can cling, one below the other, from the pole of a magnet.

It is because the magnet induces magnetism in the iron nail that gets attracted by the magnet and grips to it. The magnetized nail tends to magnetize other nails around it through the process of magnetic induction and thereby attracts it. The process continues unless the force of attraction on the first nail manages to balance the net weight of all the nails in the chain.

Can two magnetic field lines intersect each other? Give reason to your answer.

No, two magnetic field lines do not intersect each other. If they would intersect, there would be two directions of the field at the specific point which is not possible.

Sketch four magnetic field lines as obtained in a limited space on a horizontal plane in the earths magnetic field alone.

Four magnetic field lines as obtained in a limited space on a horizontal plane in the earth’s magnetic field alone are as sketched below:
1714896_1809509_ans_e96d3fa39627494fa545bca824e414d2.png

1714896_1809509_ans_e96d3fa39627494fa545bca824e414d2.png

Name the magnetic substance whose nature does not change by changing the normal temperature.

The magnetic behaviour of diamagnetic substance does not change by changing the normal temperature.

What is magnetic hysteresis?

The phenomenon of the lagging of magnetic induction behind the magnetising field when a specimen of magnetic material is subjected to a cycle of magnetization is called hysteresis.

The magnetic susceptibility of substance is $-0.085.$ What type of substance this is?

Diamagnetic substance. Because for diamagnetic substance, magnetic susceptibility is negative and always less than.

Write Curie-Weiss law and what is Curie temperature for iron?

Curie-Weiss law : Above the Curie point i.e., in the paramagnetic phase, the susceptibility varies with temperature as

$X_{m}=\dfrac{C^{'}}{T-T_{C}}(T>T_{C})$

Where

$C^{'}$ is a constant. This is modified Curie's law for a ferromagnetic material above the Curie temperature. It is also known as Curie-Weiss law. Curie temperature for iron is

$1043 K$ .

Why soft iron is used in making electromagnet?

Soft iron is preferred in electromagnets because of its

1. high permeability and

2. low retentivity and coercivity.

What do you mean by magnetic hysteresis curve ? Draw hysteresis curve and define terms related to it.

Magnetic Hysteresis Curve The relation between

$B$ and

$H$ in ferromagnetic materials is complex. It is often not linear and it depends on the magnetic history of the sample.

$Figure 8.31$ depicts the behaviour of the material as we take it through one cycle of magnetisation. Let the material be unmagnetised initially. We place it in a solenoid and increase the current through the solenoid. (Figure 8.30). The magnetic field B in the material rises and saturates as depicted in the curve Oab. This behaviour represents the alignment and merger of domains until no further enhancement is possible. It is pointless to increase the current (and hence the magnetic intensity H) beyond this. Next, we decrease H and reduce it to zero. At

$H = 0$ , B # 0. This is represented by the curve

$Oc$ . The value of

$B$ at

$H = 0$ is called retentivity or remanence. In figure 8.31,

$BR - 1.2 T$ , where the subscript R denotes retentivity. The domains are not completely randomised even though the external driving field has been removed. Next, the current in the solenoid is reversed and slowly increased. Certain domains are flipped until the net field inside stands nullified. This is represented by the curve cd. The value of H at d is called coercivity. As the reversed current is increased in magnitude, we once again obtain saturation. The curve

$Od$ depicts this. Next, the current is reduced (curve ef) and reversed (curve eb). The cycle repeats itself. Note that the curve Ob does not retrace itself as

$H$ is reduced. For a given value of

$H, B$ is not unique but depends on previous history of the sample. This phenomenon is called hysteresis. Ferromagnetic materials can be divided into two categories.

1.soft ferromagnetic materials

2. Hard ferromagnetic materials

Soft ferromagnetic materials have narrow hysteresis loop. Consequently, they have low retentivity, low coercivity and low hysteresis loss. But they have high relative magnetic permeability. Hard ferromagnetic materials have wide hysteresis loop. Consequently, they have high retentivity, high coercivity and large hysteresis loss

A study of B-H loops reveals the following informations :

(i) For a given H, B is more for soft iron than steel. So soft iron has a greater permeability.

(ii) As permeability of soft iron is greater than steel, so soft iron has a greater susceptibility than steel.

(iii) The retentivity of soft iron is greater than the retentivity of steel.

(iv) The coercivity of soft iron is less than the coercivity of steel.

1757545_1837117_ans_f8b184c3044b43a8b34309b2d68426d5.png

How will you select materials for making electromagnets and permanent magnets ? Write the uses also.

The material used for making cores of electromagnets should have high initial permeability, low retentivity. Electromagnets are used in telephone, electric bell, electric motor, dynamo, communication and they are also used to separate magnetic substances from mixtures.

The material used for making permanent magnets must have high retentivity, high coercivity and high permeability. They are used in galvanometer, ammeter, voltmeter and loudspeaker.

Suitable materials for making permanent magnets are

Cobalt steel :

$Fe + Co + W+ Cr + Mn + C$

Carbon steel :

$Fe + C + Mn$

Alnico :

$Fe + Al + Ni + + Co + Cu$

Ticonal :

$Co + Fe + Ni + Al + Ti + Cu$

The material used for making cores of transformers must have high initial permeability, low hysteresis loss and low retentivity. Permalloy is best alloy for this. Also transformer steel (

$4%$ silicon in soft iron), Mumetal

$(Fe + Cu + Ni + Mn)$ are also used in making transformer core.

Electromagnet: As shown in figure 8.33, take a soft iron rod and wind a large number of turns of insulated copper wire over it. When we pass a current through the solenoid, a magnetic field is set up in the space within the solenoid. The high permeability of soft iron increases the field one thousand times. The end of the solenoid at which the current in the solenoid seems to flow anticlockwise acts as N pole and other one as S-pole. When the current in the solenoid is switched off, the soft iron rod looses its magnetism almost completely due to its low retentivity.

Properties of Electromagnets

1. The materials which have low retentivity.

2. The materials which have high permeability

Permanent magnets : Permanent magnets are made of the materials which have high retentivity high coercivity and high permeability for Example : Steel.

1757638_1837122_ans_52b05e1323e6499ca89114550e3762d4.png

What is Gauss's law in magnetism? What does it represent?

Gauss's law in magnetism : It states that the surface integral of the magnetic field

$\overset{\rightarrow}{B}$ over a closed surface S is equal zero.

$\phi \overset{\rightarrow}{B}.\overset{\rightarrow}{dS}=0$

Gauss's law indicates that there are no sources or sinks of magnetic field inside a closed surface.

What are the uses of hysteresis curve?

A study of B-H loops reveals the following information:

(i) For a given H, B is more for soft iron than steel. So soft iron has a greater permeability.

(ii) As permeability of soft iron is greater than steel, so soft iron has a greater susceptibility than steel.

(iii) The retentivity of soft iron is greater than the retentivity of steel.

(iv) The coercivity of soft iron is less than the coercivity of steel.

1757466_1836129_ans_20d97a40a9904ffe8f675ba4b4fdfc18.png

Explain paramagnetism and specify its characteristics. Write five differences between diamagnetic and paramagnetic substance.

Paramagnetic Substances

Paramagnetic substances are those which develop feable magnetisation in the direction of the magnetising field. Such substances are feebly attracted by magnets and tend to move from weaker to stronger parts of a magnetic field.

Examples : Aluminium (Al), chromium (Cr), manganese, (Mn), platinum (Pt), Ca, Sb, Na, Li, Mg Tungsten, copper chloride, salt solution etc.

Explanation of Paramagnetism

According to Langevin, the atoms or molecules of a paramagnetic material possess a permanent magnetic moment either due to the presence of some unpaired electron or due to the non-cancellation of the spins of two electrons because of special reason. In the absence of an external magnetic field, the atomic dipoles are randomly oriented due to their ceaseless random motion, as shown in figure 8.27 (a). There is no net magnetisation.

When a strong enough field is applied and the temperature is low enough, the field tends to align the atomic dipoles in its own direction, producing a weak magnetic moment in the direction of magnetic field. The material tends to move from a weak field region to a strong field region. This phenomenon is paramagnetism.

When a paramagnetic material is placed in a magnetic field, the lines of force prefer to pass through it than through the surrounding air i. e., the lines of force get slightly more concentrated inside the material, as shown in figure. When a glass pot containing a paramagnetic liquid is placed over two closely lying opposite poles of magnet, the liquid accumulates and elevates in the middle and thins out near the poles. When the poles are moved apart the field at the poles becomes stronger than that at the centre and the liquid moves towards the poles.

Experimentally, the intensity of magnetisation of a paramagnetic substance is proportional to magnetic field Bo and inversely proportional to temperature T.

$I \alpha \frac{B_{0}}{T}$

$I =C \frac{B_{0}}{T}$

Here, C is Curie constant

$\because B_{0}=\mu_{0}H$

$\therefore I=C \frac{\mu_{0}H}{T}$

$\frac{I}{H}=C \frac{\mu_{0}}{T}$

Diamagnetic Substances

Diamagnetic substances are those which develop feable magnetisation in the opposite direction of the magnetising field. Such substances are feebly repelled by magnets and tend to move from stronger to weaker parts of a magnetic field.

Examples : Cu, Zn, Sb, Bi, Hg, H2, N2, Au, Ag, Pb, air water, diamond silicon, quartz, alcohol, marble, glass, helium, argon, salts like sodium choride etc

Explanation of Diamagnetism

The simplest explanation for diamagnetism is as follows. Electrons in an atom orbiting around nucleus possess orbital angular momentum. These orbiting electrons are equivalent to current-carrying loop and thus possess orbital magnetic moment. Diamagnetic substances are those in which resultant magnetic moment in an atom is zero. When magnetic field is applied, those electrons having orbital magnetic moment in the same direction slow down and those in the opposite direction speed up. This happens due to induced current in accordance with Lenz's law, which you will study later. Thus, the substance develops a net magnetic moment in opposite direction to that of the applied field and hence repulsion.

The most exotic diamagnetic materials are super conductors. These are metals, cooled to a very low temperature which exhibits both perfect conductivity and perfect diamagnetism. Here the field lines are completely expelled. The susceptibility

$X_{m}$ of diamagnetic materials is small and negative. The relative permeability

$\mu_{r}(1 + X_{m})$ is positive but less than 1 for a diamagnetic material. A superconductor repels a magnet and is repelled by the magnet. The phenomenon of perfect diamagnetism in superconductors is called the Meissner effect.

When a glass pot containing a diamagnetic liquid is placed between two closely lying (3 -4 mm apart) poles of a magnet, the liquid is found to move towards the poles causing a depression in the middle. This indicates that the field is stronger in the middle than that near the poles. Now if the poles are moved apart sufficiently, the magnetic field at the middle becomes weaker than that near the poles. Consequently the liquid accumulates in the middle and becomes thin near the poles.

1757551_1837119_ans_3addf6c06a594ad4b3c0cc599047af66.png

What is Curie temperature ? How magnetic susceptibility of dia, para and ferro magnetic substances depend on temperature ? Explain and write essential law for it.

Curie Law and Curie Temperature
The magnetic susceptibility of a paramagnetic material varies inversely as the absolute temperature,

$i.e, X_{m} \alpha \,\,\frac{1}{T}\,\, or \,\,X_{m}=\frac{C}{T}$
where, C is a constant called the Curie constant and this equation is known as Curie's law. The susceptibility of ferromagnetic material decreases with temperature in accordance with Curie-Weiss law

$X_{m}=\frac{C}{T-T_{C}}$ ......(1)
here,

$T_{C}$ is Curie temperature of Ferromagnetic substances.
Curie Temperature : The temperature of transition from ferromagnetism to paramagnetism is called the Curie temperature

$T_{C}$ . Table 1 lists the Curie temperatures of certain ferromagnets. The susceptibility above the Curie temperature i.e., in the paramagnetic phase is described by

$X=\frac{C}{T-T_{C}}(T>T_{C})$
Table1: Curie temperature

$T_{C}$ of some Ferromagnetic materials

$Material$	$T_{r}(K)$
Cobalt	1394
Iron	1043
Nickel	631
Gadolinium	317

Magnetic lines of force form closed curve. Why?

The direction of magnetic field lines outside magnet is from N to S pole while inside is S to N pole. So they form closed magnetic field lines.

Answer the following :
The earth's field departs from its dipole shape substantially at large distances (greater than about 30,000 km). What agencies may be responsible for this distortion?

At large distances, the earth's magnetic field gets modified by the fields produced by the motion of ions in the earth's ionosphere.

Earth’s field departs from its dipole shape substantially at large distances (greater than about 30,000 km) because of the presence of the ionosphere. In this region, the earth’s field gets modified because of the field of single ions. While in motion, these ions produce the magnetic field associated with them.

What does the hysteresis loop represent?

Hysteresis loop is a four-quadrant

$B-H$ graph from where the hysteresis loss, coercive force, and retentively of

$s$ magnetic material are obtained.

To understand hysteresis loop, we suppose to take a magnetic material to use as a core around which insulated wire is wound. The coils are connected to the supply

$(DC)$ through the variable resistor to vary the current

$l$ . We know that current

$l$ is directly proportional to the value of magnetizing force

$(H)$ as Where

$N=$ no.of the turn of the coil, and

$l$ is the effective length of the coil. The magnetic flux density of this core is

$B$ which is directly proportional to magnetizing force

$H$ .

Now, we should be familiar with some important terms related to hysteresis Loop.

From the hysteresis loop, a number of primary magnetic properties of a material can be determined.

1. Retentivity: A measure of the residual flux density corresponding to the saturation induction of a magnetic material. In other words, it is a material's ability to retain a certain amount of residual magnetic field when the magnetizing force is removed after achieving saturation. (The value of

$B$ at point

$b$ on the hysteresis curve.)

2.Residual Magnetism or Residual Flux- the magnetic flux density that remains in a material when the magnetizing force is zero. Note that residual magnetism and retentivity are the same when the material has been magnetized to the saturation point. However, the level of residual magnetism may be lower than the retentivity value when the magnetizing force did not reach the saturation level.

3.Coercive Force- The amount of revers magnetic field which must be applied to a magnetic material to make the magnetic flux return to zero.(The value of Hat point

$c$ on the hysteresis curve.)

4.Permeability- A property of a material that describes the ease with which a magnetic flux is established in the component.

5.Reluctance- Is the opposition that a ferromagnetic material shows to the establishment of a magnetic field. Reluctance is analogous to the resistance in an electric circuit.

1763719_1841893_ans_2d88416f17a045458a25cd6cb6647a67.png

Discuss the Curie law for paramagnetic material.

Curie's Law:

In a paramagnetic material, the magnetization of the material is directly proportional to an applied magnetic field. However, if the material is heated, the magnetization is inversely proportional to temperature.

$i.e. M=C \times (B/T)$

where,

$M$ is the magnetisation

$B$ is the magnetic field, measured in teslas

$T$ is absolute temperature, measured in kelvins

$C$ is a material-specified Curie constant

It was first discovered experimentally by a French physicist, Pierre Curie. it holds for high temperatures or weak magnetic fields.

What does the paramagnetic sample display greater magnetisation ( for the same magnetising field ) when cooled ?

When cooled, the tendency of the thermal agitation to disrupt the alignment of magnetic dipoles decreases in case of paramagnetic materials. Hence they display grater magnetisation.

Which property of soft iron makes it useful for preparing electromagnet?

Soft iron has very permeability, which means, the magnetism is high even for a small magnetic field.

Also, soft iron turns into a magnetic itself as soon as electricity is passed through it and loses its magnetic properties as soon as the current stops flowing.

Thus, with a switch of a button, the electromagnet can be switched off as the flow of electricity is switched off. this explains that soft iron has less retentivity which makes it ideal to form a core of electromagnets.

The susceptibility of a paramagnetic material is $X$ at $27^o C$ . At what temperature is susceptibility be $X/3$ ?

$X \alpha \frac{1}{T}$

Thus,

$\frac{K}{K/3}=\frac{T}{300}$

$\therefore T=900K=627^o C$

What happens to a ferromagnetic material when its temperature increases above curie temperature?

The ferromagnetic substances are those types of substances in which the strong magnetism is applied in the direction of the magnetic field. At a certain critical temperature, the magnetism is lost. Above curie temperature, a substance loses its magnetic properties.

Hence, when a ferromagnetic substance heated above curie temperature, its ferromagnetic properties get lost and it converts to paramagnetic substances.

Write any two properties of a magnet .

Hint: A magnet is an object or material that generates a magnetic field.

Explanation:

A magnet has two properties:

$\bullet$ It always has two poles, a north pole and a south pole.

$\bullet$ Magnetic poles that are similar repel one other, whereas those that are unlike attract each other.

Magnetic field lines are always nearly normal to the surface of a ferromagnet at every point. (This fact is analogous to the static electric field lines being normal to the surface of a conductor at every point.) Why?

One of the reason for the fact is that, when a material has

$\mu_r >>1,$ the field lines meet the material nearly normally.

Why is diamagnetism, in contrast, almost independent of temperature?

The almost of a diamagnetic do not have intrinsic magnetic dipole moment. On placing a diamagnetic sample in a magnetic field, the magnetic moment of the sample is always opposite to the direction of the field. It is not affected by the thermal motion of the dipoles.

Is the permeability of a ferromagnetic material independent of the magnetic field? If not, is it more for lower or higher fields?

No, the permeability of a ferromagnetic material depends upon the applied magnetic. Field. Its value is large for the small values of the applied field. The graph between

$B$ and

$H$ is of the shapes as shown:-
It follows that value

$B$ is quite large for comparatively small values of

$H$ .

1768153_1842932_ans_9415d3329ef4485da3eeb761b8d78ff0.png

Observe the depiction of magnetic fields of two types of magnets.
How can you find out the polarity of these magnets using a magnetic compass ?

If the North end of the compass needle is j pointing toward your magnet, if it attract you have found the South pole of your j magnet. Rotate the other side of your magnet toward the compass; the South end of the compass needle will now be pointing directly to the North pole of your magnet.

Would the maximum possible magnetisation of a paramagnetic sample be of the same order of magnitude as the magnetisation of a ferromagnet?

Yes, a paramagnetic sample with saturated magnetisation will have the same. order of magnetisation as the magnetisation of a ferromagnetic substance. However , the saturared magnetisation will require magnetising field too high to achive. Further there may be a minor difference in the strengths of the atomic dipoles of paramagnetic and ferromagnetic materials.

In which direction does a suspended magnet come to rest ?

Magnet comes to rest in N-S (North - South) direction.

Two short bar magnets with magnetic moments 400 ab-amp $cm^2$ and 800 ab-amp $cm^2$ are placed with their axis in the same straight line with similar poles facing each other and with their centres at 20 cm from each other. Find the force of repulsion.

${ \overline { P } }_{ 1 }=400$ at amp

${ cm }^{ 2 }$

${ \overline { P } }_{ 2 }=800$ at amp

${ cm }^{ 2 }$

dist. b/w centrest

$=20cm$

${ B }_{ 1 }=\dfrac { { \mu }_{ 0 } }{ 4\pi } \left( \dfrac { { 2M }_{ 1 } }{ { r }^{ 3 } } \right)$

${ F }_{ 2 }={ M }_{ 2 }\dfrac { d{ B }_{ 1 } }{ dr } ={ M }_{ 2 }\dfrac { d }{ dr } \left( \dfrac { { \mu }_{ 0 } }{ 4\pi } \times \dfrac { 2{ M }_{ 1 } }{ { r }^{ 3 } } \right)$

$=2{ M }_{ 1 }{ M }_{ 2 }\times \dfrac { { \mu }_{ 0 } }{ 4\pi } \left( \dfrac { -1 }{ { r }^{ 6 } } \times { 3r }^{ 2 } \right)$

$=\dfrac { -3{ M }_{ 1 }{ M }_{ 2 } }{ 2\pi } \times { \mu }_{ 0 }\left( \dfrac { 1 }{ { r }^{ 4 } } \right)$

$=-3\times \dfrac { 400\times 800\times 4\pi \times { 10 }^{ -7 } }{ 2\pi \times { \left( 20 \right) }^{ 4 } }$

${ F }_{ 2 }=12\times { 10 }^{ -1 }N$

$(-)ve$ sign the direction only.

1211915_878470_ans_ead70d153b624e16a479a50b3fc9bd38.jpg

State any two advantages of electromagnets over permanent magnets.

Two advantages of electromagnets over permanent magnets are :
(1) : The magnetic strength of electromagnets can either be increased or decreased but this cannot be done in permanent magnets.
(2) : Magnetic power of electromagnets is more than compared to permanent magnets.
Due to these advantages, electromagnets have more application than permanent magnets.

Calculate the magnetic field at the point O of a loop with current $i$ whose shape is as shown in the figure.

Magnetic field at the center due to a current carrying circular part is given by,

$B=\cfrac{\mu_{0}I\theta}{2\pi r}$

$\theta_{1}=\cfrac{\pi}{2}$ ,

$\theta_{2}=\cfrac{3\pi}{2}$

$r_{1}=a$ ,

$r_{2}=b$

$\therefore B=\cfrac{\mu_{0}I\theta_{1}}{2\pi r_{1}}+\cfrac{\mu_{0}I\theta_{2}}{2\pi r_{2}}$

$=\cfrac{\mu_{0}I}{2 \pi\times a\times 2}\times \pi+\cfrac{\mu_{0}I}{2\pi b}\times\cfrac{3\pi}{2}$

$=\cfrac{\mu_{0}I}{4a}+\cfrac{3\mu_{0}I}{4b}$

1152117_956566_ans_a6c01236afb64cc2bec5459196a1925d.png

A short bar magnet of magnetic moment $5.5\times 10^{-2}JT^{-1}$ is placed with its axis perpendicular to the earth's field direction. At what distance from the centre of the magnet, the resultant field is inclined at $45^0$ with earth's field on (a) its normal bisector and (b) its axis. Magnitude of the earth's field at the place is given to be $0.42G$ . Ignore the length of the magnet in comparison to the distance involved.

1423289_1013799_ans_fad8af8f21a542c2ae3767fcb894ba2a.jpg

A telephone cable at a place has four long straight horizontal wires carrying a current of 1.0 A in the same direction east to west. The earth's magnetic field at the place is 0.39 G, and the angle of dip is 35∘ .The magnetic declination is nearly zero. What are the resultant magnetic fields at points 4.0 cm below the cable?

Number of horizontal wires in the telephone cable,

$n=4$
Current in each wire,

$I=1.0 A$
Earth's magnetic field at a location ,

$H=0.39 G=0.39$ x

${10^{ - 4}} T$
Angle of dip at the location,

$\delta = {35^ \circ }$
Angle of declination,

$\theta \sim {0^ \circ }$
For a point 4 cm below the cable:
Distance,

$r=4 cm=0.04 m$
The horizontal component of earth's magnetic field can be written as:

${H_h} = H\cos \delta - B$
Where ,
B=Magnetic field at 4 cm due to current I in the four wires

$= 4 \times \dfrac{{{\mu _0}I}}{{2\pi r}}$

${\mu _0} =$ Permeability of the free space

$= 4\pi \times {10^{ - 7}}Tm\,{A^{ - 1}}$

$\therefore B = 4 \times \dfrac{{4\pi \times {{10}^{ - 7}} \times 1}}{{2\pi \times 0.04}}$

$B = 2 \times {10^{ - 9}}$
1160766_1069707_ans_51105c1664634a46b155cd9568a7b92e.png

The susceptibility of magnetic material is $- 4.2 \times 10^{-6}$ . Name the type of magnetic material it represents.

Since susceptibility of the magnetic material is negative so the magnetic material is diamagnetic.

How does the magnetic energy resembles with the electrostatic energy stored in a capacitor?

The energy stored in the form of potential energy in the capacitor is given as

$U = \frac{1}{2}C{V^2}$

Storing energy in a capacitor is amount of work done is transporting charge from one plate to the other.

The inductor stores energy in the magnetic field that is created by it when it carries current. The relation is given as

$U = \frac{1}{2}L{{\rm I}^2}$

The energy in the inductor remains stored as long as the current keeps on flowing through it.

What are magnetic field lines? How is the direction of magnetic field at a point in a magnetic field determined using field lines?

A magnetic field line is the path along which a free north-pole tends to move. The direction of a magnetic field at a point is determined by placing a small compass needle. The N - pole of compass indicates the direction of magnetic field at that point.

Explain the magnetic elements of the earth's magnetic field.

The elements are:

Magnetic declination (q)

Magnetic inclination (d)

Horizontal component (BH)

Magnetic declination:

The small angle between magnetic axis and geographic axis at a place is defined as magnetic declination at that place. It is represented by θ.

Magnetic Inclination:

Magnetic dip, dip angle, or magnetic inclination is the angle made with the horizontal by the compass needle of a vertically held compass. This angle varies at different points on the Earth's surface. Positive values of inclination indicate that the magnetic field of the Earth is pointing downward, into the Earth, at the point of measurement. The value can be measured with an instrument typically known as a dip circle.

(1)At equator the magnetic field is parallel to the horizon so there will be zero angle of dip.

(2) At poles the magnetic field is almost vertical, here the dip will me maximum.

Horizontal component :

It is the component of earth’s magnetic field along the horizontal direction.

So the angle of dip is the angle between earth’s magnetic field i.e. B and the horizontal component i.e. BH.

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Write on expression for vector from of magnetic force on a moving charge.

Lorentz magnetic force is given by:

$\vec F = q(\vec V \times \vec B)$ ; q is the magnitude of the moving charge.

The direction of the magnetic force is perpendicular to the plane containing the velocity vector and the magnetic field vector.

Explain an analogy between magnetic dipole moment $M$ of circular current loop and electric dipole moment $P$ of electric dipole.

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What is magnetic dipole? Derive an expression for magnetic field intensity at a point on the equatorial tine of a bur magnet.

1225029_1512332_ans_efa1694e627443fb8184ab30eb7ef133.jpeg

What is the value of magnetic field within a hollow sphere made of ferromagnetic substance? Hence explain magneto static shielding..

The magnetic field within, hollow sphere of ferromagnetic substance is zero. Magneto static shielding means to shield any specimen from magnetic effects by placing it within a hollow region of a ferromagnetic substance.

The figure gives the magnetization curve for a paramagnetic material. The vertical axis scale is set by $a = 0.15$ , and the horizontal axis scale is set by $b = 0.2$ T/K. Let $\mu_{sam}$ be the measured net magnetic moment of a sample of the material and $\mu_{max}$ be the maximum possible net magnetic moment of that sample.According to Curie’s law, what would be the ratio $\mu_{sam}/\mu_{max}$ were the sample placed in a uniform magnetic field of magnitude $0.800$ T, at a temperature of $2.00$ K?

The section explains the terms used in this problem and the connection between M and μ. The graph in Figure gives a slope of

$\dfrac{M/M_{max}}{B_{ext}/T}=\dfrac{0.15}{0.20\,T/K}=0.75\,K/T$

Thus ,we can write

$\dfrac{\mu}{\mu_{max}}=(0.75\,K/T)\dfrac{0.800 \,T}{2.00 \,K}=0.30$

A $0.50$ T magnetic field is applied to a paramagnetic gas
whose atoms have an intrinsic magnetic dipole moment of $1.0 \times 10^{-23} \, J/T$ . At what temperature will the mean kinetic energy of
translation of the atoms equal the energy required to reverse such
a dipole end for end in this magnetic field?

Let us use,

$K=\dfrac{3}{2}kT=|\vec \mu.\vec B-(-\vec \mu.\vec B)|=2\mu B$

which leads to

$T=\dfrac{4\mu B}{3k}=\dfrac{4(1.0 \times 10^{-23}\,J/T)(0.50\,T)}{3(1.38 \times10^{-23}\,J/k)}=0.48\,K$

Two wires, parallel to the z-axis and a distance $4r$ apart, carry equal currents i in opposite directions, as shown in Figure. A circular cylinder of radius r and length L has its axis on the z-axis, midway between the wires. Use Gauss’ law for magnetism to derive an expression for the net outward magnetic flux through the half of the cylindrical surface above the x-axis. (Hint: Find the flux through the portion of the xz plane that lies within the cylinder.)

From Gauss’ law for magnetism, the flux through

$S_1$ is equal to that through

$S_2$ , the portion of the xz plane that lies within the cylinder. Here the normal direction of

$S_2$ is +y. Therefore,

$Φ_B(S_1)=Φ_B(S_2)=\int^r_{-r}B(x)L\,dx=2\int^r_{-r}B_{Left}(x)L\,dx==2\int^r_{-r}\dfrac{\mu_0 i}{2\pi}\dfrac{1}{2r-x}L \,dx=\dfrac{\mu_0 i L}{\pi}ln\,3$

What are magnetic field lines? How is the direction of a magnetic field at a point determined? Mention two important properties of magnetic field lines.

The magnetic field lines of force are the lines drawn in a magnetic field along which a hypothetical north magnetic pole would move if it is free to do so. The direction of a magnetic field at a point is the direction of the resultant force acting on a hypothetical north pole placed at that point. The tangent at any point on the magnetic field line gives the direction of magnetic field at that point. The direction of the magnetic field at a point can be found by placing a small magnetic compass at that point. The north end of the needle indicates the direction of the field.

Two important properties of the magnetic lines of force are:
(i) The magnetic lines of force start from north pole and terminate at south pole. Inside the magnet they travel from south pole to north pole. Thus, they are closed curves.
(ii) They do not intersect each other because at the point of intersection there will be two directions of same magnetic field which is impossible

The saturation magnetization $M_{max}$ of the ferromagnetic metal nickel is $4.70 \times 10^5\, A/m$ . Calculate the magnetic dipole moment of a single nickel atom. (The density of nickel is $8.90\, g/cm^3$ and its molar mass is $58.71\, g/mol$ .)

The saturation magnetization corresponds to complete alignment of all atomic dipoles and is given by

$M_{sat} = μn$ , where n is the number of atoms per unit volume and μ is the magnetic dipole moment of an atom. The number of nickel atoms per unit volume is

$n = ρ/m$ , where ρ is the density of nickel. The mass of a single nickel atom is calculated using

$m = M/N_A$ , where M is the atomic mass of nickel, and

$N_A$ is Avogadro’s constant. Thus,

$n=\dfrac{\rho N_A}{M}=\dfrac{(8.90\,g/cm^3)(6.02 \times 10^{23} \,atoms/mol)}{58.71\,g/mol}=9.126 \times 10^{22}\,atoms/cm^3$

$=9.126 \times 10^{28}\,atoms/m^3$
The dipole moment of a single atom of nickel is

$\mu=\dfrac{M_{sat}}{n}=\dfrac{4.70 \times 10^5\,A/m}{9.126 \times 10^{28}\,m^3 }=5.15 \times 10^{-24}\,A.m^2$

The exchange coupling mentioned in Module as being responsible for ferromagnetism is not the mutual magnetic interaction between two elementary magnetic dipoles. To show this, calculate (a) the magnitude of the magnetic field a distance of $10$ nm away, along the dipole axis, from an atom with magnetic dipole moment $1.5 \times 10^{-23} J/T$ (cobalt), and (b) the minimum energy required to turn a second identical dipole end for end in this field. (c) By comparing the latter with the mean translational the kinetic energy of $0.040\, eV$ , what can you conclude?

(a) The field of a dipole along its axis is given by Eq. 30-29:

$B =\dfrac{μ_0}{2\pi}\,\dfrac{\mu}{z^3}$ , where μ is the dipole moment and z is the distance from the dipole. Thus,

$B=\dfrac{(4\pi \times 10^{-7}\,T.m/A)(1.5 \times 10^{-23} \,J/T)}{2\pi(10 \times 10^{-9}\,m)}=3.0 \times 10^{-6}\,T$

(b) The energy of a magnetic dipole

$\vec μ$ in a magnetic field

$\vec B$ is given by

$U=-\vec \mu.\vec B=-\mu\cos \phi$

where

$φ$ is the angle between the dipole moment and the field. The energy required to turn it end-for-end (from

$φ = 0°$ to

$φ = 180°$ ) is

$ΔU=2\mu B=2(1.5 \times 10^{-23}\,J/T)(3.0 \times 10^{-6}T)=9.0 \times 10^{-29}\,J=5.6 \times 10^{-10}\,eV$

The mean kinetic energy of translation at room temperature is about

$0.04\, eV$ . Thus, if dipole-dipole interactions were responsible for aligning dipoles, collisions would easily randomize the directions of the moments and they would not remain aligned.

In what way is Gauss's law in magnetism different from that used in
electrostatics? Explain briefly.
The Earth's magnetic field at the Equator is approximately $0.4\ G$ .Estimate the Earth's magnetic dipole moment. Given: Radius of the Earth $=6400\ km$ .

As we know that
Isolated positive or negative charge exists freely. So, Gauss's law states that

$\phi \overrightarrow { E } .d \overrightarrow { S} = \dfrac{1}{\varepsilon _0} [q]$
Isolated magnetic poles do not exist. So, Gauss's law states that

$\phi \overrightarrow { B } .d \overrightarrow { S} =0$
Magnetic field intensity at the equator is

$B=\dfrac{\mu _0}{4 \pi}. \dfrac{m}{R^3}=10^{-7}\dfrac{m}{R^3}$

$\therefore \ \ \ m=10^7.BB |R^3|$

$=10^7 \times 0.4 \times 10^{-4} \times (6400 \times 10^3)^3$

$=1.1 \times 10^{23} \ Am^2$

What is the circulation of magnetic field? Explain

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Ampres Law(30)
Niobium metal becomes a superconductor when cooled below $9 \,K$ . Its super conductivity is destroyed when the surface magnetic field exceeds $0.100 \,T$ . In the absence of any external magnetic field, determine the maximum current a $2.00$ -mm-diameter niobium wire can carry and remain superconducting.

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Analysis Model: Particle in a Field (Magnetic)(4)
Consider an electron near the Earths equator. In which direction does it tend to deflect if its velocity is
(a) directed downward?
(b) Directed northward?
(c) Directed westward?
(d) Directed southeastward?

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Material	Permeability	Susceptibility	Temperature dependence of susceptibility
A	Low positive	Small but negative	Independent of temperature
B	high	Vert high $1$	Susceptibility decreases with temperature
C	Grater than $1$	Small but positive	Decreases with temperature

Magnetism And Matter - Class 12 Medical Physics - Extra Questions

State any two properties of magnetic lines of force.

A short bar magnet has a magnetic moment of 0.48JT−10.48 J T^{-1} . Give the direction and magnitude of the magnetic field produced by the magnet at a distance of 10 cm from the centre of the magnet on (a) the axis, (b) the equatorial lines (normal bisector) of the magnet.

Answer the question in at least 5050 words.Give the characteristic of magnetic field lines.

What is hysteresis? Define the terms 'coercivity' and 'retentivity' of a ferromagnetic material.

A small rod of bismuth is suspended freely between the poles of a strong magnet. It is found to arrange itself at right angles to the magnetic field. What is established by the observation?

A magnet has coercivity of 3×1033\times 10^3 Am−1Am^{-1}. It is kept in a 1010cm long solenoid with a total of 5050 turns. How much current has to be passed through the solenoid to demagnetize it?

In the Bohr model of hydrogen atom, the electron circulates around the nucleus in a path of radius 5.1×10−11 m5.1\times{10}^{-11}\ m at a frequency 6.8×1015 s−16.8\times{10}^{15}\ {s}^{-1}. Find the magnetic field set up at the centre of the orbit.

A magnetising field of 1600Am1600\dfrac{A}{m}produces a magnetic flux 2.4X10−5Wb2.4 X 10^{-5} Wb in a bar of iron of cross section 0.2cm20.2 cm^2 .Calculate permeability and susceptibility of the bar:

Ferrimagnetic those expected to have large magnetism but actually have small net magnetic moment e.g., magnetic (Fe3O4)(Fe_{3}O_{4}), ferrites (M2+Fe2O4)(M^{2}+Fe_{2}O_{4}). This is because of unequal number of domains in opposite direction.

Draw diagram to represent a uniform magnetic field in a given region.

If a particle of charge q is moving with velocity v along the z - axis and the magnetic field B is acting along x - axis, use the expression →F=q(→v×→B)\vec{F} = q (\vec{v} \times \vec{B} ) to find the direction of the force F acting on it.

A sample of the paramagnetic salt to which the magnetizationcurve of Fig. applies is held at room temperature (300K)(300 K).At what applied magnetic field will the degree of magnetic saturation of the sample be (a) 50%50\% and (b) 90%90\% ? (c) Are these fieldsattainable in the laboratory?

Answer the following questionName the properties of a magnetic material that make it suitable for making(a) a permanent magnetic and (b) a core of an electromagnetic.

Answer the following questionWhat happens when a diamagnetic substance is placed in a varying magneticfield?

Answer the following question.State Gauss's law in magnetism. How is it different from Gauss's law inelectrostatic and why?

In Figure, a bar magnet lies near a paper cylinder.(a) Sketch the magnetic field lines that pass through the surface ofthe cylinder. (b) What is the sign of for every area on thesurface? (c) Does this contradict Gauss law for magnetism?Explain.

A sample of the paramagnetic salt to which the magnetizationcurve of Fig. applies is immersed in a uniform magnetic fieldof 2.02.0 T. At what temperature will the degree of magnetic saturation of the sample be (a) 5050% and (b)9090%?

The susceptibility of a magnetic material is 2.6×10−52.6\times 10^{-5}. Identify the type of magnetic material and state its two properties.

Write any three characteristics, a ferromagnetic substance should possess if it is to be used to make a permanent magnet. Give one example of such a material.

What is Curie law in magnetism?

The susceptibility of a magnetic materials −4.2×10−6-4.2\times 10^{-6}. Name the type of magnetic material it represents.

The variation of intensity of magnetisation II and the applied magnetic field intensity HH for three magnetic materials X, YX,\ Y and ZZ are as shown in the given graphs.Identify the materials X, YX,\ Y and ZZ.

Which of the following substances are diamagnetic? Bi,Al,Na,Cu,CaBi, Al, Na, Cu, Ca and NiNi

The variation of intensity of magnetisation II and the applied magnetic field intensity HH for three magnetic materials X, YX,\ Y and ZZ are as shown in the given graphsShows graphically the variation of susceptibility with temperature for XX.

The variation of intensity of magnetisation II and the applied magnetic field intensity HH for three magnetic materials X, YX,\ Y and ZZ are as shown in the given graphsPut of YY and ZZ, which of the material will you prefer for making transformer cores and why?

Why is the core of an electromagnet made of ferromagnetic materials?

In what ways is the behaviour of a diamagnetic material different from that of a paramagnetic, when kept in an external magnetic field?

What is the basic difference between the atom and molecule of a diamagnetic and a paramagnetic material? Why are elements with even atomic number more likely to be diamagnetic?

The magnetic field lines prefer to pass through iron than air. Explain why?

What kind of ferromagnetic material is used for coating magnetic tapes in a cassette player or for building memory stores in a modern computer?

Boojho kept a magnet close to an ordinary iron bar. He observed that the iron bar attracts a pin as shown in the figure.What inference could he draw from this observation? Explain.

State with reason, whether the following statement is true or false? The product of magnetic susceptibility and absolute temperature XTXT is constant for a paramagnetic material.

From molecular view point, discuss the temperature dependence of susceptibility for diamagnetism, Para magnetism and ferromagnetism.

Fill in the blanksIn a magnet, __________ have the maximum attractive property.

Two magnetic lines of force never intersect each other. True/False?

State whether the following statement is True or False.Ampere's swimming rule describes the direction of magnetic lines of force in a straight conductor.

A small magnet is suspended by a silk thread from a rigid support such that the magnet can freely swing. Describe its behaviour.

Sketch magnetic lines of force around a current carrying coil.

State the characteristics of magnetic lines of force.

List two methods of producing magnetic fields.

Which of the following substances are para-magnetic?Bi,Al,Cu,Ca,Pb,NiBi, Al, Cu, Ca, Pb, Ni

The relative magnetic permeability of a magnetic material is 800800. Identify the nature of magnetic material and state its own properties.

The susceptibility of a magnetic material is −2.6×10−5-2.6 \times {10}^{-5}. Identify the type of magnetic material and state its two properties.

What are permanent magnets? Give one example.

A ________ is a region around a magnet where magnetic lines of force act.

Classify the following materials with regard to magnetism:Manganese, Cobalt, Bismuth, Copper

What are diamagnetic substances? Give one example

Why do magnetic field lines not intersect each other?

Write any three properties of magnetic lines of force.

State True or False.Magnetic lines of force are closed continuous curves.

Compare paramagnetism and ferro magnetism. Give examples of each.

State and explain Curie's law.

What is Curie temperature?

Draw the pattern of magnetic field lines for a bar magnet.

Classify the following materials with regard to magnetism:Manganese, Cobalt, Nickel, Bismuth, Oxygen and Copper

Distinguish between Para, Ferro and Diamagnetism.

Write two properties of magnetic lines of force.

Define Curie temperature in magnetism.

Out of the two magnetic materials, 'A' has relative permeability slightly greater than unity while 'B' has less than unity. Identify the nature of the materials 'A' and 'B'. Will their susceptibilities be positive or negative?

Conductivity of metal decreases with temperature while conductivity of electrolytic conductors increases with temperature. Why ?

Write the causes of energy loss and ways to reduce them in transformer (any four).

State the characteristics of magnetic field lines.

Define magnetic lines of force and state its two properties.

Few iron nails and screws got mixed with wood shavings while a carpenter was working with them. How can you help him in getting the nails and screws back from the scrap without wasting his time by searching with his hands?

Draw the hysteresis curve for ferromagnetic substance. Show coercivity and retentivity on the curve.

Explain Curie's law for a paramagnetic substance.

Write whether the given statement is true or false : The magnetic susceptibility (Xm)(X_m) of a paramagnetic substance has a small negative value.

A uniform magnetic field gets modifies as shown in Figure below , when two speciments X and Y are placed in it . Identyfy wether speciment X and Y are diagramatic , paramagnetic or ferromagnetic .

The susceptibility of magnesium at 300K300 \,K is 1.2×1051.2 \times 10^5. What will be its susceptibility at 200K200 \,K?

Write definition of Curie temperature for ferromagnetic substance.

Draw hysteresis curve (B-H curve) for a ferromagnetic substance

When a electric current is passed through ant wire, a magnetic filed is produced around it. Then why an electric iron connecting cable does not attract nearby iron objects when electric current is switched on through it?

In New Hampshire, the average horizontal component of Earth’s magnetic field in 19121912 was 16μT16 \mu T, and the average inclination or “dip” was 73°73°. What was the corresponding magnitude of Earth’s magnetic field?

How can you distinguish between diamagnetic and paramagnetic rods?

Define retentivity.

Give two examples of paramagnetic substances.

What are the behaviour of diamagnetic, paramagnetic and ferromagnetic substances in non-uniform magnetic field?

The Curie temperature for a ferromagnetic substance is 300K300 K. If magnetic susceptibility of the substance is 0.60.6 at 450K450 K temperature, then find out Curie constant.

At which place on a magnet, its magnetic force is maximum ?

A short bar magnet has a magnetic moment of $0.48 J T^{-1}$ . Give the direction and magnitude of the magnetic field produced by the magnet at a distance of 10 cm from the centre of the magnet on (a) the axis, (b) the equatorial lines (normal bisector) of the magnet.

Answer the question in at least $50$ words.
Give the characteristic of magnetic field lines.

A magnet has coercivity of $3\times 10^3$ $Am^{-1}$ . It is kept in a $10$ cm long solenoid with a total of $50$ turns. How much current has to be passed through the solenoid to demagnetize it?

In the Bohr model of hydrogen atom, the electron circulates around the nucleus in a path of radius $5.1\times{10}^{-11}\ m$ at a frequency $6.8\times{10}^{15}\ {s}^{-1}$ . Find the magnetic field set up at the centre of the orbit.

A magnetising field of $1600\dfrac{A}{m}$ produces a magnetic flux $2.4 X 10^{-5} Wb$ in a bar of iron of cross section $0.2 cm^2$ .Calculate permeability and susceptibility of the bar:

Ferrimagnetic those expected to have large magnetism but actually have small net magnetic moment e.g., magnetic $(Fe_{3}O_{4})$ , ferrites $(M^{2}+Fe_{2}O_{4})$ . This is because of unequal number of domains in opposite direction.

If a particle of charge q is moving with velocity v along the z - axis and the magnetic field B is acting along x - axis, use the expression $\vec{F} = q (\vec{v} \times \vec{B} )$ to find the direction of the force F acting on it.

A sample of the paramagnetic salt to which the magnetization
curve of Fig. applies is held at room temperature $(300 K)$ .
At what applied magnetic field will the degree of magnetic saturation of the sample be (a) $50\%$ and (b) $90\%$ ? (c) Are these fields
attainable in the laboratory?

Answer the following question
Name the properties of a magnetic material that make it suitable for making
(a) a permanent magnetic and (b) a core of an electromagnetic.

Answer the following question
What happens when a diamagnetic substance is placed in a varying magnetic
field?

Answer the following question.
State Gauss's law in magnetism. How is it different from Gauss's law in
electrostatic and why?

In Figure, a bar magnet lies near a paper cylinder.
(a) Sketch the magnetic field lines that pass through the surface of
the cylinder. (b) What is the sign of for every area on the
surface? (c) Does this contradict Gauss law for magnetism?
Explain.

A sample of the paramagnetic salt to which the magnetization
curve of Fig. applies is immersed in a uniform magnetic field
of $2.0$ T. At what temperature will the degree of magnetic saturation of the sample be (a) $50%$ and (b) $90%$ ?

The susceptibility of a magnetic material is $2.6\times 10^{-5}$ . Identify the type of magnetic material and state its two properties.

The susceptibility of a magnetic materials $-4.2\times 10^{-6}$ . Name the type of magnetic material it represents.

The variation of intensity of magnetisation $I$ and the applied magnetic field intensity $H$ for three magnetic materials $X,\ Y$ and $Z$ are as shown in the given graphs.
Identify the materials $X,\ Y$ and $Z$ .

Which of the following substances are diamagnetic? $Bi, Al, Na, Cu, Ca$ and $Ni$

The variation of intensity of magnetisation $I$ and the applied magnetic field intensity $H$ for three magnetic materials $X,\ Y$ and $Z$ are as shown in the given graphs
Shows graphically the variation of susceptibility with temperature for $X$ .

The variation of intensity of magnetisation $I$ and the applied magnetic field intensity $H$ for three magnetic materials $X,\ Y$ and $Z$ are as shown in the given graphs
Put of $Y$ and $Z$ , which of the material will you prefer for making transformer cores and why?

Boojho kept a magnet close to an ordinary iron bar. He observed that the iron bar attracts a pin as shown in the figure.
What inference could he draw from this observation? Explain.

State with reason, whether the following statement is true or false? The product of magnetic susceptibility and absolute temperature $XT$ is constant for a paramagnetic material.

Fill in the blanks
In a magnet, __________ have the maximum attractive property.

State whether the following statement is True or False.

Ampere's swimming rule describes the direction of magnetic lines of force in a straight conductor.

Which of the following substances are para-magnetic?
$Bi, Al, Cu, Ca, Pb, Ni$

The relative magnetic permeability of a magnetic material is $800$ . Identify the nature of magnetic material and state its own properties.

The susceptibility of a magnetic material is $-2.6 \times {10}^{-5}$ . Identify the type of magnetic material and state its two properties.

Classify the following materials with regard to magnetism:
Manganese, Cobalt, Bismuth, Copper

State True or False.
Magnetic lines of force are closed continuous curves.

Classify the following materials with regard to magnetism:
Manganese, Cobalt, Nickel, Bismuth, Oxygen and Copper

Write whether the given statement is true or false : The magnetic susceptibility $(X_m)$ of a paramagnetic substance has a small negative value.

The susceptibility of magnesium at $300 \,K$ is $1.2 \times 10^5$ . What will be its susceptibility at $200 \,K$ ?

In New Hampshire, the average horizontal component of Earth’s magnetic field in $1912$ was $16 \mu T$ , and the average inclination or “dip” was $73°$ . What was the corresponding magnitude of Earth’s magnetic field?

The Curie temperature for a ferromagnetic substance is $300 K$ . If magnetic susceptibility of the substance is $0.6$ at $450 K$ temperature, then find out Curie constant.

Three diagrams in the following figures show the magnetic field lines between the poles of the magnets. Identify the poles between $A, B, C, D, E,$ and $F$ .

Magnetic field lines of two magnets are shown in fig. A and fig. B.
Select the figure that represents the correct pattern of field lines. Give reasons for your answer. Also name the poles of the magnets facing each other.

(a) Draw a diagram to represent a uniform magnetic field in a given region.
(b) List two properties of magnetic field lines.

What is the unit of ratio $\dfrac {E}{H}$ ?

If the bar magnet is turned around by $180^{o}$ , where will the new null points be located?

Show diagrammatically the behaviour of magnetic field lines in the presence of
(i) paramagnetic and
(ii) diamagnetic substances. How does one explain this distinguishing feature?

List the factors on which the strength of magnetic field produced by
(a) a current-carrying straight conductor
(b) current carrying solenoid depends.

Explain the following:
(i) Why do magnetic lines of force form continuous closed loops?
(ii) Why are the field lines repelled (expelled) when a diamagnetic material is placed in an external uniform magnetic field?

Fill in the blanks
Rough handling destroys the ______ properties of a magnet.

You are provided with two similar bars, one is a magnet and the other is a soft iron bar. How will you distinguish between them without the use of any other magnet or bar?
[Hint: A magnet when suspended freely will rest only in north-south direction, but soft iron bar will rest in any direction]