Question

Potential energy of a current loop placed inside some magnetic field does not depend upon magnetic moment of the loop.Enter 1 if True and 0 if False.

Answer 1

For the current loop ABCD in magnetic field $\overrightarrow{B}$

Let current flowing = I

Area enclosed = A and

$\mu$ = magnetic dipole moment.

Now torque expression

$\tau =\mu \times B_{\text{ext}}$

$\tau =\mu B_{\text{ext}}\sin \theta$

Thus potential energy,

$U=\int \tau d\theta$

$=\int \mu B\sin \theta d\theta$

$U=-\mu B\cos \theta$

Thus U depends of $\mu$