A coil of 200 turns and area 0.20 m² is rotated at half a revolution per second and is placed in uniform magnetic field of 0.01 T perpendicular to axis of rotation of the coil. The maximum voltage generated in the coil is (2π/β) volt. The value of β i s ____.
Physics · Electromagnetic Induction · faradays law and question based on it
JEE Mains 2024 01 Feb Evening Shift

Question

A coil of 200 turns and area 0.20 m² is rotated at half a revolution per second and is placed in uniform magnetic field of 0.01 T perpendicular to axis of rotation of the coil. The maximum voltage generated in the coil is (2π/β) volt. The value of β i s ____.

Physics · Electromagnetic Induction · faradays law and question based on it

JEE Mains 2024 01 Feb Evening Shift

G1 Physics · Accepted Answer

Magnetic flux: Φ = NAB cos(ωt) Maximum induced emf: ε(max) = NABω Given: N = 200 A = 0.20 m² B = 0.01 T Half revolution per second gives: f = 0.5 Hz ω = 2πf = π rad/s Therefore: ε(max) = 200 × 0.20 × 0.01 × π = 0.4π V = 2π/5 V Comparing with 2π/β: β = 5