Magnetic Properties of Matter — Page 3 | JEE Physics

Q21

A small bar magnet placed with its axis at 30o with an external field of 0.06 T experiences a torque of 0.018 Nm. The minimum work required to rotate it from its stable to unstable equilibrium position is :

A 6.4

\times

10-2 J

B 9.2

\times

10-3 J

C 7.2

\times

10-2 J

D 11.7

\times

10-3 J

Correct Answer

Option C

Solution

Torque on a bar magnet :

\tau = MB\,\sin \theta

Here, $\theta$ = 30º, I = 0.018 N-m, B = 0.06 T

0.018 = M \times 0.06 \times 0.5

\Rightarrow M = 0.6\,A{m^2}

W = {U_f} - {U_i}

= MB(\cos {\theta _i} - \cos {\theta _f})

= 0.6 \times 0.06(1 - ( - 1))

= 7.2 \times {10^{ - 2}}\,J

Q22

Magnetic materials used for making permanent magnets (P) and magnets in a transformer (T) have different properties of the following, which property best matches for the type of magnet required?

A T : Large retentivity, small coercivity

B P : Large retentivity, large coercivity

C P : Small retentivity, large coercivity

D T : Large retentivity, large coercivity

Correct Answer

Option B

Solution

Option (2) is correct as permanent magnet should have high coercivity & retentivity.

Q23

A paramagnetic sample shows a net magnetisation of 6 A/m when it is placed in an external magnetic field of 0.4 T at a temperature of 4 K. When the sample is placed in an external magnetic field of 0.3 T at a temperature of 24 K, then the magnetisation will be:

A 4 A/m

B 1 A/m

C 0.75 A/m

D 2.25 A/m

Correct Answer

Option C

Solution

According to curies law

\chi

= {{C{B_{ext}}} \over T}

$\Rightarrow$

6 = {{C \times 0.4} \over 4}

\Rightarrow C = 60

$\therefore$ Case - II :

\chi

= {{60 \times 0.3} \over {24}}

= {{60 \times 3} \over {240}} = {3 \over 4} = 0.75\,A/m

Q24

A soft ferromagnetic material is placed in an external magnetic field. The magnetic domains :

A may increase or decrease in size and change its orientation.

B increase in size but no change in orientation.

C decrease in size and changes orientation.

D have no relation with external magnetic field.

Correct Answer

Option A

Solution

Atoms of ferromagnetic material in unmagnetised state form domains inside the ferromagnetic material.

These domains have large magnetic moment of atoms.

In the absence of magnetic field, these domains have magnetic moment in different directions.

But when the magnetic field is applied, domains aligned in the direction of the field grow in size and those aligned in the direction opposite to the field reduce in size and also its orientation changes.

Q25

In a ferromagnetic material, below the curie temperature, a domain is defined as :

A a macroscopic region with zero magnetization.

B a macroscopic region with saturation magnetization.

C a macroscopic region with randomly oriented magnetic dipoles.

D a macroscopic region with consecutive magnetic dipoles oriented in opposite direction.

Correct Answer

Option B

Solution

In a ferromagnetic material, below the curie temperature a domain is defined as a macroscopic region with saturation magnetization.

Q26

A magnet hung at

45^{\circ}

with magnetic meridian makes an angle of

60^{\circ}

with the horizontal. The actual value of the angle of dip is -

A

\tan ^{-1}\left(\sqrt{\dfrac{3}{2}}\right)

B

\tan ^{-1}(\sqrt{6})

C

\tan ^{-1}\left(\sqrt{\dfrac{2}{3}}\right)

D

\tan ^{-1}\left(\sqrt{\dfrac{1}{2}}\right)

Correct Answer

Option A

Solution

\tan 60^\circ = {{{B_0}\sin \delta } \over {{B_0}\cos \delta \cos 45^\circ }}

\Rightarrow \tan \delta = \sqrt {{3 \over 2}}

\Rightarrow \delta = {\tan ^{ - 1}}\left( {\sqrt {{3 \over 2}} } \right)

Q27

Which of the following statements are correct? (A) Electric monopoles do not exist whereas magnetic monopoles exist. (B) Magnetic field lines due to a solenoid at its ends and outside cannot be completely straight and confined. (C) Magnetic field lines are completely confined within a toroid. (D) Magnetic field lines inside a bar magnet are not parallel. (E)

\chi

=

-

1 is the condition for a perfect diamagnetic material, where x is its magnetic susceptibility. Choose the correct answer from the options given below :

A (A) and (B) only

B (B) and (C) only

C (C) and (E) only

D (B) and (D) only

Correct Answer

Option C

Solution

(a) Electric monopoles exist while magnetic monopoles do not exist. (b) Magnetic field lines at the ends and outside of solenoid cannot be confined. (c) Magnetic field lines are confined within a toroid. (d) Magnetic field lines inside a bar magnet are parallel. (e) For perfectly diamagnetic material

\chi

= -1.

Q28

At an angle of 30

^\circ

to the magnetic meridian, the apparent dip is 45

^\circ

. Find the true dip :

A

{\tan ^{ - 1}}\sqrt 3

B

{\tan ^{ - 1}}{1 \over {\sqrt 3 }}

C

{\tan ^{ - 1}}{2 \over {\sqrt 3 }}

D

{\tan ^{ - 1}}{{\sqrt 3 } \over 2}

Correct Answer

Option D

Solution

A\tan \delta = \tan \delta '\cos \theta

= \tan 45^\circ \cos 30^\circ

\tan \delta = 1 \times {{\sqrt 3 } \over 2}

\delta = {\tan ^{ - 1}}\left( {{{\sqrt 3 } \over 2}} \right)

Q29

The magnetic susceptibility of a material of a rod is 499. Permeability in vacuum is 4

\pi

\times

10

-

7 H/m. Absolute permeability of the material of the rod is :

A 4

\pi

\times

10

-

4 H/m

B 2

\pi

\times

10

-

4 H/m

C 3

\pi

\times

10

-

4 H/m

D

\pi

\times

10

-

4 H/m

Correct Answer

Option B

Solution

$\mu$ = $\mu$ 0 (1 + xm) = 4 $\pi$ $\times$ 10 $-$ 7 $\times$ 500 = 2 $\pi$ $\times$ 10 $-$ 4 H/m

Q30

Choose the correct option

A True dip is always equal to apparent dip.

B True dip is not mathematically related to apparent dip.

C True dip is less than the apparent dip.

D True dip is always greater than the apparent dip.

Correct Answer

Option C

Solution

Let apparent dip $\theta$

a

.

\tan ({\theta _a}) = {{\tan ({\theta _T})} \over {\cos \phi }}

\Rightarrow {\theta _a} \ge {\theta _T}

$\therefore$ True dip is less than apparent dip.