Question

A current loop with a current $I$ is placed in a magnetic field $B$ , the potential energy will not depend upon:

• A. orientation of loop with respect to direction of magnetic field.
• B. alignment of magnetic moment.
• C. current in the loop.
• D. material of the wire.

Answer 1

Answer: (D)

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,

$U=\int \tau d\theta$

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

$U=\mu B\cos \theta$

As $U=IAB$ since

Thus U depends on

i) orientation $\left(\theta \right)$

ii) Alignment of magnetic moment $\left(\mu \right)$

iii) Current = I