A simple pendulum with a bob of mass m and a conducting wire of length L , swings under gravity with an angular amplitude θ . If the horizontal component of the earth's magnetic field perpendicul

Question

A simple pendulum with a bob of mass m and a conducting wire of length L , swings under gravity with an angular amplitude θ . If the horizontal component of the earth's magnetic field perpendicular to the plane of motion of the pendulum is B , then the maximum emf induced across the pendulum is

TestHub · Accepted Answer

h = L - L cos ⁡ θ ⇒ h = L ( 1 - cos ⁡ θ ) ...(i) using energy conservation Δ K E = Δ P E ⇒ 1 2 m v 2 = m g h = m g L ( 1 − cos θ ) v= 2 g L 2 sin 2 ⁡ θ 2 ⇒ v = 2 g L sin ⁡ θ 2 Thus, maximum potential difference V m a x = B v L = B × 2 g L sin θ 2 L = 2 B L sin θ 2 g L 1 / 2

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