Magnetic Properties of Matter — Page 5 | JEE Physics

Q41

A bar magnet with a magnetic moment

5.0 \mathrm{Am}^{2}

is placed in parallel position relative to a magnetic field of

0.4 \mathrm{~T}

. The amount of required work done in turning the magnet from parallel to antiparallel position relative to the field direction is _____________.

A zero

B 1 J

C 2 J

D 4 J

Correct Answer

Option D

Solution

$W=-M B\left(\cos \theta_{2}-\cos \theta_{1}\right)$

\begin{aligned} = & -0.4 \times 5\left[\cos 180^{\circ}-\cos 0\right] \\\\ = & 4 \mathrm{~J} \end{aligned}

Q42

A solenoid of 1200 turns is wound uniformly in a single layer on a glass tube 2 m long and 0.2 m in diameter. The magnetic intensity at the center of the solenoid when a current of 2 A flows through it is :

A

\mathrm{1~A~m^{-1}}

B

\mathrm{2.4\times10^{-3}~A~m^{-1}}

C

\mathrm{1.2\times10^{3}~A~m^{-1}}

D

\mathrm{2.4\times10^{3}~A~m^{-1}}

Correct Answer

Option C

Solution

Number of turns per unit length $=\dfrac{1200}{2}=600$ So, Magnetic Intensity $H=n I$

\begin{aligned} & =600 \times 2 ~\mathrm{Am}^{-1} \\\\ & =1200 ~\mathrm{Am}^{-1} \end{aligned}

Q43

Given below are two statements: Statement I : The diamagnetic property depends on temperature. Statement II : The induced magnetic dipole moment in a diamagnetic sample is always opposite to the magnetizing field. In the light of given statements, choose the correct answer from the options given below.

A Statement I is incorrect but Statement II is true.

B Statement I is correct but Statement II is false.

C Both Statement I and Statement II are False.

D Both Statement I and Statement II are true.

Correct Answer

Option A

Solution

Statement I : The diamagnetic property depends on temperature.

This statement is incorrect.

Diamagnetism is an intrinsic property of materials that arises due to the presence of completely filled electron shells.

It does not depend on temperature.

Statement II : The induced magnetic dipole moment in a diamagnetic sample is always opposite to the magnetizing field.

This statement is true.

Diamagnetic materials have a negative magnetic susceptibility, which means that they oppose the applied magnetic field.

This results in the induced magnetic dipole moment being always opposite to the magnetizing field.

Q44

Match with .

List - I		List - II
(A)	Magnetic induction	(I)	Ampere meter2
(B)	Magnetic intensity	(II)	Weber
(C)	Magnetic flux	(III)	Gauss
(D)	Magnetic moment	(IV)	Ampere meter

A (A)-(III), (B)-(IV), (C)-(II), (D)-(I)

B (A)-(III), (B)-(II), (C)-(I), (D)-(IV)

C (A)-(III), (B)-(IV), (C)-(I), (D)-(II)

D (A)-(I), (B)-(II), (C)-(III), (D)-(IV)

Correct Answer

Option A

Solution

(A) The unit "gauss" is used to measure magnetic induction, also known as magnetic flux density, within the CGS system of units.

B = {\phi \over A} = {{\max well} \over {c{m^2}}} = gauss\,(CGS)

(B) Magnetic intensity (H) is defined as the product of the number of turns per unit length in a coil (n) and the current that it carries (I). i.e.

H = nI = {N \over L}I

Unit : A/m or Am $^{-1}$ (C) Magnetic flux,

\phi = BA

unit : weber (D) Magnetic moment (M) : magnetic moment of a current loop,

M = NIA

where, N = number of turns I = current A = Area So, unit = Am $^2$ Hence, option A is correct.

Q45

The free space inside a current carrying toroid is filled with a material of susceptibility

2 \times 10^{-2}

. The percentage increase in the value of magnetic field inside the toroid will be

A 0.1%

B 1%

C 2%

D 0.2%

Correct Answer

Option C

Solution

The magnetic susceptibility (

\chi_m

) of a material is the measure of how much the material becomes magnetized in response to an external magnetic field.

When the material is placed in a magnetic field, the net magnetic field (

B

) inside the material is the sum of the external magnetic field (

B_0

) and the field produced by the material itself (

B_{material}

). This relationship can be expressed as :

B = B_0 + B_{material}

Magnetic susceptibility is related to the relative permeability (

\mu_r

) of the material :

\mu_r = 1 + \chi_m

The magnetic field inside the toroid can be calculated using the following formula :

B = \mu_0 \mu_r H

where

\mu_0

is the permeability of free space,

\mu_r

is the relative permeability of the material, and

H

is the magnetic field strength.

Now, let's consider the percentage increase in the magnetic field when the material is placed inside the toroid.

The initial magnetic field (

B_0

) is given by :

B_0 = \mu_0 H

After the material is placed inside the toroid, the magnetic field becomes :

B = \mu_0 \mu_r H = \mu_0 (1 + \chi_m) H

The percentage increase in the magnetic field can be calculated as :

\frac{B - B_0}{B_0} \times 100\% = \frac{\mu_0 (1 + \chi_m) H - \mu_0 H}{\mu_0 H} \times 100\%

Substitute the value of

\chi_m = 2 \times 10^{-2}

:

\frac{B - B_0}{B_0} \times 100\% = \frac{(1 + 2 \times 10^{-2}) - 1}{1} \times 100\% = 2\%

Thus, the percentage increase in the value of the magnetic field inside the toroid is 2%.

Q46

A bar magnet is released from rest along the axis of a very long vertical copper tube. After some time the magnet will

A move down with almost constant speed

B move down with an acceleration equal to

\mathrm{g}

C move down with an acceleration greater than

\mathrm{g}

D oscillate inside the tube

Correct Answer

Option A

Solution

When a bar magnet is released from rest along the axis of a very long vertical copper tube, it will move down with an almost constant speed after some time.

As the magnet falls, it moves through the copper tube, inducing eddy currents in the tube.

These eddy currents, in turn, create an opposing magnetic field that opposes the motion of the magnet.

The opposing force generated by the eddy currents acts as a damping force, which slows down the magnet's acceleration.

Eventually, the magnet reaches a terminal velocity, at which point the gravitational force pulling the magnet downward is balanced by the opposing force from the eddy currents.

At this terminal velocity, the magnet moves down with an almost constant speed.

Q47

Given below are two statements: Statement I : For diamagnetic substance, $$-1 \leq \chi Statement II : Diamagnetic substances when placed in an external magnetic field, tend to move from stronger to weaker part of the field. In the light of the above statements, choose the correct answer from the options given below

A Both Statement I and Statement II are true

B Statement I is correct but Statement II is false

C Both Statement I and Statement II are False

D Statement I is incorrect but Statement II is true.

Correct Answer

Option A

Solution

Both Statement I and Statement II are true.

Statement I: For diamagnetic substances, the magnetic susceptibility (χ) lies between -1 and 0.

This is because diamagnetic substances have a negative magnetic susceptibility, which means they have a tendency to oppose the applied magnetic field.

Statement II: Diamagnetic substances, when placed in an external magnetic field, experience a force that tends to move them from stronger to weaker parts of the field.

This is due to the fact that diamagnetic substances oppose the applied magnetic field and try to minimize their exposure to it.

Q48

Given below are two statements: one is labelled as Assertion

\mathbf{A}

and the other is labelled as Reason

\mathbf{R}

Assertion A : Electromagnets are made of soft iron. Reason R : Soft iron has high permeability and low retentivity. In the light of above, statements, choose the most appropriate answer from the options given below.

A Both A and R are correct and R is the correct explanation of A

B A is not correct but R is correct

C A is correct but R is not correct

D Both A and R are correct but R is NOT the correct explanation of A

Correct Answer

Option A

Solution

Both Assertion A and Reason R are correct, and R is indeed the correct explanation of A.

Electromagnets are commonly made of soft iron because of its high permeability, which allows it to easily magnetize in response to an external magnetic field.

Its low retentivity is also desirable because it allows the magnetization to be easily reversed or removed once the external field is removed.

This combination of properties makes soft iron ideal for electromagnets, which require rapid and efficient changes in magnetization.

Q49

The magnetic moment of a bar magnet is

0.5 \mathrm{~Am}^2

. It is suspended in a uniform magnetic field of

8 \times 10^{-2} \mathrm{~T}

. The work done in rotating it from its most stable to most unstable position is:

A

4 \times 10^{-2} \mathrm{~J}

B

16 \times 10^{-2} \mathrm{~J}

C

8 \times 10^{-2} \mathrm{~J}

D Zero

Correct Answer

Option C

Solution

\begin{aligned} W & =\int_0^{180} d \tau \cdot d \theta \\ & =m B(\cos 0-\cos 180) \\ & =0.5 \times 8 \times 10^{-2}(2) \\ & =8 \times 10^{-2} \mathrm{~J} \end{aligned}

Q50

Paramagnetic substances: A. align themselves along the directions of external magnetic field. B. attract strongly towards external magnetic field. C. has susceptibility little more than zero. D. move from a region of strong magnetic field to weak magnetic field. Choose the most appropriate answer from the options given below:

A A, B, C Only

B A, C Only

C A, B, C, D

D B, D Only

Correct Answer

Option B

Solution

Paramagnetic substances exhibit specific characteristics in the presence of an external magnetic field.

Understanding these characteristics will help us choose the most appropriate answer.

Let's discuss each statement individually: A. align themselves along the directions of external magnetic field.

This is true.

Paramagnetic substances have unpaired electrons, and under the influence of an external magnetic field, the atomic dipoles (due to those unpaired electrons) tend to align themselves in the direction of the magnetic field.

B. attract strongly towards external magnetic field.

This statement is the cause of some confusion.

Paramagnetic substances are attracted towards an external magnetic field, but the keyword here is strongly.

Compared to ferromagnetic substances, the attraction is relatively weak.

Given the context of the options provided, saying they are "strongly" attracted could be misleading, but it is undeniable they are attracted nevertheless.

C. has susceptibility little more than zero.

This is correct.

The magnetic susceptibility of paramagnetic materials is positive, meaning they are attracted to magnetic fields, but it is small in magnitude, typically greater than zero but far less than the susceptibility of ferromagnetic materials.

D. move from a region of strong magnetic field to weak magnetic field.

This statement is incorrect for paramagnetic substances.

They are attracted to magnetic fields, implying they move from a region of weaker magnetic field to a stronger magnetic field, not the other way around.

Taking these points into account, the most accurate answer would be: Options B: A, C Only A) They indeed align along the direction of an external magnetic field, and C) Their susceptibility is indeed a little more than zero, indicating a weak attraction to magnetic fields.

Statement B can be considered incorrect not in its entirety that they are attracted, but in the use of the term "strongly," and D is certainly incorrect regarding their movement in magnetic fields.