Question

A rectangular loop PQRS made from a uniform wire has length a, width b and mass m. It is free to rotate about the arm PQ, which remains hinged along a horizontal line taken as the y-axis. Take the vertically upward direction as the z-axis. A uniform magnetic field $\overrightarrow{B}=(3\hat{i}+4\hat{k})B_0$ exists in the region. The loop is held in the x-y plane and a current I is passed through it. The loop is now released and is found to stay in the horizontal position in equilibrium. Find the magnetic force on the arm RS.

Answer 1

Force acting on arm:
$RS=I(\overrightarrow{I}\times \overrightarrow{B})$

$=I\left[\right(-b\hat{j})\times (3\hat{i}+4\hat{k}\left)B_0\right]$
$=I{B}_{0}b(3\hat{k}-4\hat{i})$