Question

A circular coil having 200 turns, $2.5 \times 10^{-4} \text{ m}^2$ area and carrying 100 $\mu$A current is placed in a uniform magnetic field of 1 T. Initially the magnetic dipole moment ($\vec{M}$) was directed along $\vec{B}$. Amount of work, required to rotate the coil through $90^\circ$ from its initial orientation such that $\vec{M}$ becomes perpendicular to $\vec{B}$, is ________ $\mu$J.

Answer 1

We know:

$W_{\text{ext}} = \Delta U + \Delta KE \quad (\text{P.E.} = -\vec{M} \cdot \vec{B})$

$= -MB \cos 90^\circ + MB \cos 0^\circ$

$W_{\text{ext}} = MB$

$= NIAB$

$= 200 \times 100 \times 10^{-6} \times 2.5 \times 10^{-4} \times 1 = 5 \, \mu\text{J}$