A simple pendulum with bob of mass m and conducting wire of length L swings under gravity through an angle . The component of earth's magnetic field in the direction perpendicular to swing is B. Maximum e.m.f. induced across the pendulum is ( g= acceleration due to gravity)

Step-by-step solution

The maximum induced electromotive force occurs when the pendulum bob attains its maximum velocity at the lowest point of its swing, where the motion is perpendicular to the magnetic field. The induced emf is given by ε = BLv , with v representing the instantaneous velocity perpendicular to the field. Using conservation of energy, the gravitational potential energy at maximum displacement converts entirely to kinetic energy at the lowest point. The vertical drop from maximum angular displacement θ is h = L(1 - θ) =