Question

A rectangular loop of sides 10 cm and 5 cm carrying a current I of 12 A is placed in different orientations as shown in the figures below :

If there is a uniform magnetic field of 0.3 T in the positive z direction, in which orientations the loop would be in
(i) stable equilibrium and (ii) unstable equilibrium?

• A. (1) and (3), respectively
• B. (2) and (4), respectively
• C. (2) and (3), respectively
• D. (1) and (2), respectively

Answer 1

The correct option is B (2) and (4), respectively

Since $\overrightarrow{B}$ is uniform, only torque acts on a current carrying loop. $\overrightarrow{\tau }=\left(I\overrightarrow{A}\right)\times \overrightarrow{B}$
$\overrightarrow{A}=A\hat{k}for\left(b\right)$ and $\overrightarrow{A}=-A\hat{k}$ for (d).
$\therefore \overrightarrow{\tau }=0$ for both these cases.
The energy of the loop in the $\overrightarrow{B}$ field is: $U=-I\overrightarrow{A}.\overrightarrow{B}$ which is minimum for (b)