A circular loop of radius R is in a uniform magnetic field that points in the y

Question

A circular loop of radius R is in a uniform magnetic field that points in the y direction. a) if the loop is moving in the yz plane at constant velocity ‘v’, calculate the amplitude of the emf induced around the perimeter of the loop. b) If, instead, the loop starts at rest in the xz plane and experiences constant acceleration ‘a’ in the y direction, calculate the amplitude of the emf induced around the perimeter of the loop. c) If, instead, the loop is at rest in the xz plane but is rotated about an axis parallel to the x direction with constant angular frequency ‘w’, calculate the amplitude and frequency ‘f’ (in Hz) of the emf induced around the perimeter of the loop.

Explanation / Answer

(A) now area vector and field vector are perendicular,

and flux = B.A = B A cos(theta)

flux will always be zero

hence no emf will be induced.

(B) now flux is zon-zero.

but flux is constant hence rate of change of flux is zero.

and emf = rate of change of magnetic flux = 0

(C) now flux will change with time.

flux = (pi R^2) (B) cos(wt)

e = d(flux)/dt = - pi R^2 B w sin(wt)

Amplitude = pi R^2 B w

frequency = w / 2pi

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