A magnetic bar of length \(l\) having pole strength \(m\), is held in different uniform magnetic fields \(B\), with its axis oriented at different angles \((\theta)\) with the direction of the field \(B\) as in the given configurations. Arrange these configurations according to the magnitude of the torques acting on the bar in decreasing order.
A. \(B = 4\,\mathrm{T}, \theta = 30^\circ\)
B. \(B = 6\,\mathrm{T}, \theta = 60^\circ\)
C. \(B = 8\,\mathrm{T}, \theta = 45^\circ\)
D. \(B = 4\,\mathrm{T}, \theta = 90^\circ\)
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → C, B, D, A
A bar magnet of pole strength m and length l has magnetic moment \( M = ml \). In a uniform field the torque on it is
\( \displaystyle \tau = MB\sin\theta = mlB\sin\theta \)
Since ml is the same in every case, the torque is proportional to \( B\sin\theta \).
(A) \( B = 4\,\mathrm{T}, \theta = 30^\circ \) — \( 4 \times \sin 30^\circ = 4 \times 0.5 = 2.0 \)
(B) \( B = 6\,\mathrm{T}, \theta = 60^\circ \) — \( 6 \times \sin 60^\circ = 6 \times 0.866 \approx 5.20 \)
(C) \( B = 8\,\mathrm{T}, \theta = 45^\circ \) — \( 8 \times \sin 45^\circ = 8 \times 0.707 \approx 5.66 \)
(D) \( B = 4\,\mathrm{T}, \theta = 90^\circ \) — \( 4 \times \sin 90^\circ = 4 \times 1 = 4.0 \)
In decreasing order: C, B, D, A.