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. (a) and (b) respectively
• B. (b) and (d) respectively
• C. (a) and (c) respectively
• D. (b) and (c) respectively

Answer 1

Answer: (B)

(b) and (d) respectively

Answer 2

For equilibrium $\vec{\tau}=0$
$\vec{\tau}=M B \sin \theta\, \hat{n}$
If, $\sin \theta=0 ; \vec{\tau}=0$
If angle between $\vec{ M }$ and $\vec{ B }$ is zero, then stable equilibrium
If angle between $\vec{ M }$ and $\vec{ B }$ is $\pi$, then unstable equilibrium