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Question: Answered & Verified by Expert
A circular current loop of magnetic moment $\mathrm{M}$ is in an arbitrary orientation in an external magnetic field $\mathbf{B}$. The work done to rotate the loop by $30^{\circ}$ about an axis perpendicular to its plane is
PhysicsMagnetic Effects of Current
Options:
  • A
    $\mathrm{MB}$
  • B
    $\sqrt{3} \frac{\mathrm{MB}}{2}$
  • C
    $\frac{\mathrm{MB}}{2}$
  • D
    zero
Solution:
2561 Upvotes Verified Answer
The correct answers are:
$\sqrt{3} \frac{\mathrm{MB}}{2}$
,
zero
When the axis of rotation of the loop is along B by $30^{\circ}$ about an axis perpendicular to its plane make no change in the angle made by axis of the loop with the direction of magnetic field. So, the work done to rotate the loop is zero.
$$
\mathrm{W}=\mathrm{MB} \cos 90^{\circ}=0
$$
When rotation not along B.
The work done to rotate the loop in uniform magnetic field $\mathrm{W}=\mathrm{MB}\left(\cos \theta_1-\cos \theta_2\right)$, where signs are as usual. So the workdone is
$$
\begin{aligned}
\mathrm{W} &=\mathrm{MB} \cos \theta\left(\theta=30^{\circ} \text { given }\right) \\
&=\mathrm{MB} \cos 30^{\circ}=\frac{\mathrm{MB} \sqrt{3}}{2}
\end{aligned}
$$

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