Question

An elastic conducting material is stretched into a circular loop of 14.8 cm radius. It is placed with its plane perpendicular to a uniform 0.814 T magnetic field. When released, the radius of the loop starts to shrink at an instantaneous rate of 88.4 cm/s. What emf is induced in volts in the loop at that instant

Answer 1

Answer: 0.666 V

Explanation:

Given

Radius of the loop, r = 14.8 cm = 0.148 m

Magnetic field present, B = 0.814 T

Rate of shrinking, dr/dt = 88.4 cm/s = 0.884 m/s

emf = dΦ/dt , where Φ = BA

emf = d(BA)/dt, where A = πr²

emf = d(Bπr²)/dt

if B is constant, then

emf = Bπ d(r²)/dt, on differentiating, we have,

emf = Bπ * 2r dr/dt

emf = 2πrB dr/dt, now if we substitute the values, we have

emf = 2 * 3.142 * 0.148 * 0.814 * 0.884

emf = 6.284 * 0.106

emf = 0.666 V