NEET Magnetism and Matter — Set 20

Question 1

A dipole with $ m = 0.4 \, \text{A m}^2 $ in $ B = 0.8 \, \text{T} $ at $ 60^\circ $ has torque:

Accepted Answer

$ \tau = m B \sin\theta $. Given: $ m = 0.4 \, \text{A m}^2 $, $ B = 0.8 \, \text{T} $, $ \theta = 60^\circ $, $ \sin 60^\circ = \frac{\sqrt{3}}{2} \approx 0.866 $. $ \tau = 0.4 \times 0.8 \times 0.866 \approx 0.277 \, \text{N m} \approx 0.28 \, \text{N m} $.

Question 2

A bar magnet with magnetic moment $ 0.8 \, \text{A m}^2 $ is placed at a distance of $ 0.4 \, \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} $).

Accepted Answer

The magnetic field along the axis is $ B = \frac{\mu_0}{4\pi} \frac{2m}{r^3} $. Given: $ m = 0.8 \, \text{A m}^2 $, $ r = 0.4 \, \text{m} $, $ \frac{\mu_0}{4\pi} = 10^{-7} $. Substitute: $ B = 10^{-7} \times \frac{2 \times 0.8}{(0.4)^3} = 10^{-7} \times \frac{1.6}{0.064} = 2.5 \times 10^{-6} \, \text{T} $.

Question 3

A paramagnetic material with $ \chi = 8 \times 10^{-4} $ in $ H = 2500 \, \text{A m}^{-1} $ has magnetization $ M $:

Accepted Answer

$ M = \chi H $. Given: $ \chi = 8 \times 10^{-4} $, $ H = 2500 \, \text{A m}^{-1} $. $ M = 8 \times 10^{-4} \times 2500 = 2 \, \text{A m}^{-1} $.

NEET Physics: Magnetism and Matter — Practice Set 20

Q1. A dipole with \( m = 0.4 \, \text{A m}^2 \) in \( B = 0.8 \, \text{T} \) at \( 60^\circ \) has torque:

Q2. A bar magnet with magnetic moment \( 0.8 \, \text{A m}^2 \) is placed at a distance of \( 0.4 \, \text{m} \) along its axis. What is the magnetic field \( B \) at that point? (Take \( \mu_0 = 4\pi \times 10^{-7} \, \text{T m A}^{-1} \)).

Q3. A paramagnetic material with \( \chi = 8 \times 10^{-4} \) in \( H = 2500 \, \text{A m}^{-1} \) has magnetization \( M \):

Q4. A bar magnet with \( m = 0.75 \, \text{A m}^2 \) produces a field at \( 0.15 \, \text{m} \) on its equatorial line. What is \( B \)? (Take \( \mu_0 = 4\pi \times 10^{-7} \, \text{T m A}^{-1} \)).

Q5. A dipole with \( m = 0.8 \, \text{A m}^2 \) in a field \( B = 0.3 \, \text{T} \) at \( 90^\circ \) has potential energy:

Q6. A bar magnet with magnetic moment \( 0.9 \, \text{A m}^2 \) is placed at a distance of \( 0.3 \, \text{m} \) along its axis. What is the magnetic field \( B \) at that point? (Take \( \mu_0 = 4\pi \times 10^{-7} \, \text{T m A}^{-1} \)).

Q7. A bar magnet produces a field of \( 5 \times 10^{-6} \, \text{T} \) at \( 0.5 \, \text{m} \) on its equatorial line. What is its magnetic moment? (Take \( \mu_0 = 4\pi \times 10^{-7} \, \text{T m A}^{-1} \)).

Q8. A solenoid with 1100 turns per meter and current \( 2 \, \text{A} \) has a core with \( \mu_r = 250 \). What is \( B \) inside? (Take \( \mu_0 = 4\pi \times 10^{-7} \, \text{T m A}^{-1} \)).

Q9. The magnetic potential energy of a dipole with moment \( 0.4 \, \text{A m}^2 \) in a uniform magnetic field of \( 0.5 \, \text{T} \) when aligned at \( 30^\circ \) to the field is:

Q10. The magnetic field contribution \( B_m \) due to a material with \( M = 1.6 \times 10^5 \, \text{A m}^{-1} \) is: (Take \( \mu_0 = 4\pi \times 10^{-7} \, \text{T m A}^{-1} \)).