Question

An elastic conducting material is stretched into a circular loop of 14.7 cm radius. It is placed with its plane perpendicular to a uniform 0.963 T magnetic field. When released, the radius of the loop starts to shrink at an instantaneous rate of 74.5 cm/s. What emf is induced in volts in the loop at that instant?

Answer 1

Answer: 0.66 V

Explanation:

Given

Magnetic field, B = 0.963 T

Instantaneous rare = 74.5 cm/s = 0.745 m/s

radius, r = 14.7 cm = 0.147 m

We will use the formula

emf = dΦ/dt

emf = d(BA)/dt

emf = d(Bπr²)/dt

if B is constant, then we can say

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

emf = Bπ (2r dr/dt)

emf = 2πrB dr/dt substituting each values, we have

emf = 2 * 3.142 * 0.147 * 0.963 * 0.745

emf = 0.66 V

Therefore, the induced emf in the loop at that instant is 0.66 V