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?

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

the minimum amperage that the current in this wire would have to have so that its weight is completely supported by the magnetic force due to earth's field, assuming that no other forces except gravity act on it