Question

The torque and magnetic potential energy of a magnetic dipole in most stable position in a uniform magnetic field($\overline{B}$) having magnetic moment ($\overline{m}$) will be.

• A. $-$mB, zero
• B. mB, zero
• C. Zero, mB
• D. Zero, $-$mB

Answer 1

Answer: (D)

The correct option is D Zero, $-$mB
Torque, $\overline{\tau }=\overrightarrow{m}\times \overrightarrow{B}=mB\sin \theta$
and magnetic potential energy $U_m=\overrightarrow{m}\cdot \overrightarrow{B}=mB\cos \theta$
at $\theta =0^o$ the dipole will be in most stable position
$\tau =mB\sin \theta =mB\sin 0^o=0$
and $U_m=-mB\cos \theta =-mB\cos {\theta }^o=-mB$