Question

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

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

Answer 1

Answer: (D)

Torque, $\vec{\tau} = \vec{m} \times \vec{B} = mB \,sin \theta$
and magnetic potential energy $U_{m} = \vec{m}.\, \vec{B} = mB \,cos\,\theta$
at $\quad \theta = 0^{\circ}$ the dipole will be in most stable position
$\tau = mBsin\theta = mBsin \,0^{\circ} = 0$
and $U_{m} = -mB \,cos\theta = -mBcos \,0^{\circ} = - mB$