Q. 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 v-axis (see figure). Take the vertically upward direction as the z-axis. A uniform magnetic field 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. (a) What is the direction of the current / in PQ ? (b) Find the magnetic force on the arm RS. (c) Find the expression for / in terms of ,a ,b and m. Physics Question Image

 2063  197 IIT JEEIIT JEE 2002Moving Charges and Magnetism Report Error

Solution:

Let the direction of current in wire PQ is from P to Q and its
magnitude be I
The magnetic moment of the given loop is

Torque on the loop due to magnetic forces is

We see that when the current in the wire PQ is from P to Q,
and are in opposite directions, so they can cancel each
other and the loop may remain in equilibrium. So, the
direction of current I in wire PQ is from P to Q. Further for
equilibrium of the loop

or
(b) Magnetic force on wire RS is

Solution Image