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?

Engineering

Physics

Magnetic Moment

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) and (b), respectively

(b) and (d), respectively

(b) and (c), respectively

(a) and (c), respectively

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Since $\vec{B}$ is uniform, only torque acts on a current carrying loop. $\vec{τ} = (I \vec{A}) \times \vec{B}$

$\vec{A} = \hat{A} for (b) \vec{A} = - A \hat{k} for (d) .$

for (b) and A = – Akˆ

$∴ \vec{τ} = 0$ for both these cases.

The energy of the loop in the $\vec{B} field is : U = - I \vec{A} \cdot \vec{B},$ which is minimum for (b).