Question

An elastic conducting material is stretched into a circular loop of 9.75 cm radius. It is placed with its plane perpendicular to a uniform 1.06 T magnetic field. When released, the radius of the loop starts to shrink at an instantaneous rate of 56.9 cm/s. What emf is induced in volts in the loop at that instant?

Answer 1

0.37 V

Step-by-step explanation:

emf = dΦ/dt, where

Φ = BA, so then

emf = d(BA)/dt

Recall that A = πr², on substituting for that too we have

emf = d(Bπr²)/dt

Since B is a constant, when we differentiate, we have

emf = Bπ d(r²)/dt

emf = Bπ 2r.dr/dt, on rearranging

emf = 2πrB dr/dt,

Now we go ahead and substitute the values given from the question so that

emf = 2 * 3.142 * 0.0975 * 1.06 * 0.569

emf = 0.370 V

Therefore, the induced emf in volts is 0.37 V