NEET Magnetism and Matter — Set 22

Question 1

A magnetic needle with magnetic moment $ 0.1 \, \text{A m}^2 $ is placed in a uniform magnetic field of $ 0.2 \, \text{T} $ at an angle of $ 60^\circ $ with the field. What is the torque acting on it?

Accepted Answer

Torque on a magnetic dipole is $ \tau = m B \sin\theta $. Given: $ m = 0.1 \, \text{A m}^2 $, $ B = 0.2 \, \text{T} $, $ \theta = 60^\circ $, $ \sin 60^\circ = \frac{\sqrt{3}}{2} \approx 0.866 $. Substitute: $ \tau = 0.1 \times 0.2 \times 0.866 = 0.01732 \, \text{N m} \approx 0.017 \, \text{N m} $.

Question 2

A solenoid produces $ B = 1.5 \, \text{T} $ with a core of $ \mu_r = 500 $ and $ n = 2000 \, \text{m}^{-1} $. What is the current $ I $? (Take $ \mu_0 = 4\pi \times 10^{-7} \, \text{T m A}^{-1} $).

Accepted Answer

$ B = \mu_0 \mu_r n I $, so $ I = \frac{B}{\mu_0 \mu_r n} $. Given: $ B = 1.5 \, \text{T} $, $ \mu_r = 500 $, $ n = 2000 \, \text{m}^{-1} $, $ \mu_0 = 4\pi \times 10^{-7} $. $ I = \frac{1.5}{4\pi \times 10^{-7} \times 500 \times 2000} = \frac{1.5}{1.256 \times 10^{0}} \approx 1.194 \, \text{A} \approx 1.2 \, \text{A} $.

Question 3

A material’s susceptibility becomes negative and large when:

Accepted Answer

A superconductor has a susceptibility of $ \chi = -1 $ (large and negative) when it transitions to the superconducting state below its critical temperature, expelling all magnetic fields via the Meissner effect, a unique property among materials.

NEET Physics: Magnetism and Matter — Practice Set 22

Q1. A magnetic needle with magnetic moment \( 0.1 \, \text{A m}^2 \) is placed in a uniform magnetic field of \( 0.2 \, \text{T} \) at an angle of \( 60^\circ \) with the field. What is the torque acting on it?

Q2. A solenoid produces \( B = 1.5 \, \text{T} \) with a core of \( \mu_r = 500 \) and \( n = 2000 \, \text{m}^{-1} \). What is the current \( I \)? (Take \( \mu_0 = 4\pi \times 10^{-7} \, \text{T m A}^{-1} \)).

Q3. A material’s susceptibility becomes negative and large when:

Q4. A material with \( B = 0.55 \, \text{T} \) and \( H = 3500 \, \text{A m}^{-1} \) has \( M \): (Take \( \mu_0 = 4\pi \times 10^{-7} \, \text{T m A}^{-1} \)).

Q5. A dipole with \( m = 0.2 \, \text{A m}^2 \) in \( B = 0.8 \, \text{T} \) at \( 45^\circ \) has torque:

Q6. A paramagnetic material with \( \chi = 3 \times 10^{-3} \) in \( H = 400 \, \text{A m}^{-1} \) has magnetization \( M \):

Q7. A bar magnet with magnetic moment \( 1.0 \, \text{A m}^2 \) is placed at a distance of \( 0.5 \, \text{m} \) along its axis. What is the magnetic field \( B \) at that point? (Take \( \mu_0 = 4\pi \times 10^{-7} \, \text{T m A}^{-1} \)).

Q8. A material with susceptibility \( \chi = 5 \times 10^{-3} \) has a relative permeability \( \mu_r \) of:

Q9. A material with \( B = 0.2 \, \text{T} \) and \( H = 1000 \, \text{A m}^{-1} \) has magnetization \( M \). What is \( M \)? (Take \( \mu_0 = 4\pi \times 10^{-7} \, \text{T m A}^{-1} \)).

Q10. Which material retains magnetization after the external field is removed and is used in permanent magnets?