Acircular coil has a radius r and n turns and is in a uniform magnetic field that depends only on time, b = b(t). the angle of the coil is θ to the direction of the field and the total curcuit has resistance r. find an expression for the current i.

(N x π x r^2 x Cosθ) / R x dB(t) / dt

Explanation:

radius = r , Number of turns = N, B = B(t), Angle = θ, Resistance = R

induced emf = rate of change of magnetic flux

e  = - N x dΦ / dt

e = - N x d(B A Cosθ) / dt

e = - N x A x Cosθ x dB(t) / dt

e = - N x π x r^2 x Cosθ x dB(t) / dt

where, negative sign shows the direction of induced emf in the coil.

induced current, i = induced emf / resistance

i = - (N x π x r^2 x Cosθ) / R x dB(t) / dt

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