A rigid square wire loop of total mass M and side length L carries a steady current I . The loop initially lies in the xy -plane and one of its sides is hinged along the y -axis, allowing the loop to rotate freely about it. The current flows in a counter-clockwise direction when viewed from the positive z -axis. If a uniform magnetic field B = B₀ i is switched on, the magnitude of the initial angular acceleration of

Step-by-step solution

The magnetic dipole moment of the current-carrying loop is given by M = I A . Since the loop lies in the xy -plane and the current is counter-clockwise when viewed from the positive z -axis, the area vector points in the positive z -direction. The area of the square loop is A = L^2 . Thus, M = I L^2 k . The torque experienced by the loop in the magnetic field B = B₀ i is: = M B = (I L^2 k ) (B₀ i ) = I L^2 B₀ ( k i ) = I L^2 B₀ j This torque acts entirely along the y -axis, which is the axis of rotation (the hinge)