Question

a circular loop of wire radius r is perpendicular to a magnetic field whose magnitude as a function of time t is given by the equations B=bt^2 + ct, where b and c are positive, nonzero constants. What is the magnitude of the emf induced in the loop as a function of time t?

Answer 1

Radius = R theta = 0 degree B = bt^2 + ct Induced emf from law = -d/dt (BA cos degree) = -A dB/dt = -pi R^2 (d/dt (bt^2 + ct)) = -pi R^2 [2 bt + c] = pi R^2 (2 bt + c) option (E)

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