Question

25. A circular coil of radius 5.0 cm and resistance 0.20Ω is placed in a uniform magnetic field perpendicular to the plane of the coil. The magnitude of the field changes with time according to B=0.50⋅e^-2tT. What is the magnitude of the current induced in the coil at the time t=2.0s?
Hint 1: Faradays Electromagnetic induction, interactive calculation, animation

A) 7.3mA
B) 9.2mA
C) 2.6mA
D) 4.2mA

Answer 1

Solution,

Emf E = -d(phi) /dt

Flux, phi = BA = 0.5 x e^(-0.2t) pi x (0.05)^2

-d(phi)/dt = -0.5 x π x (0.05)^2 x (-0.2) e^(-0.2t) = 7.854 x 10^-4 x e^('0.2t)

at t = 2 sec

E = 7.854 x 10^-4 x e^(-0.2 x 2) = 5.26 x 10^-4 V

Current I = E/R = 2.63 mA

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