Question:
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
Solution:
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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