NTA Abhyas JEE Main2020PhysicsElectromagnetic InductionPractice
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
Options
- A2 B L sin θ 2 g L 1 / 2
- BB L sin θ 2 2g L 1 / 2
- C2 B L sin θ 2 g L 3 / 2
- DB L sin θ 2 g L 2
Correct answer
A. 2 B L sin θ 2 g L 1 / 2
Step-by-step solution
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