A magnetic field in a certain region


A magnetic field in a certain region is given by B = Bo cos ωt k and a coil of radius a with resistance R is placed in the x-y plane with its centre at the origin in the magnetic field. Find the magnitude and the direction of the current at (a, 0, 0) at t =π ω /2, t =π /2ω and t =3π/ω


The direction of the magnetic field is along the z-axis.

Φ = B.A = BA cos θ

Using Faraday’s law of electromagnetic induction,

I = Boπa2ꞷ/R sin ꞷt

Therefore, current at t = π ω /2 = I = Boπa2ꞷ/R sin ꞷt = 1

Current at t = π /2ω = I = Boπa2ꞷ/R sin ꞷt = -Boπa2ꞷ/R

Current t = 3π/ω = I = Boπa2ꞷ/R sin ꞷt = I = -Boπa2ꞷ/R

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