A square coil with n turns and an edge length l carries a current i . It is placed on a smooth horizontal plate. A uniform magnetic field B is present in a direction parallel to one of its edges. The total mass of the coil is M . Determine the minimum value of B required for the coil to start tipping over.

Step-by-step solution

The magnetic moment of the square coil is given by = n i A = n i l^2 . Since the magnetic field B is parallel to one of the edges of the coil, it lies in the plane of the coil. The angle between the magnetic moment vector (which is perpendicular to the plane of the coil) and the magnetic field B is 90^ . The torque exerted by the magnetic field on the coil is _ B = B 90^ = n i l^2 B . This magnetic torque tends to lift one edge of the coil and tip it over the opposite edge. The restoring torque is provided by the w