Question

A certain elastic conducting material is stretched into a circular loop of 12.0 cm radius. It is placed with its plane perpendicular to a uniform 0.800 T magnetic field. When released, the radius of the loop starts to shrink at an instantaneous rate of 75.0 cm/s . What emf is induced in the loop at that instant

Answer 1

The induced emf in the loop is 0.452 volts.

Step-by-step explanation:

Given that,

Radius of the circular loop, r = 12 cm = 0.012 m

Magnetic field, B = 0.8 T

When released, the radius of the loop starts to shrink at an instantaneous rate of,
`(dr)/(dt)=75\ cm/s=0.75\ m/s`

The induced emf in the loop is equal to the rate of change of magnetic flux. It is given by :

`\epsilon=(-d\phi)/(dt)\\\\\epsilon=(-d(BA))/(dt)\\\\\epsilon=B(-d(\pi r^2))/(dt)\\\\\epsilon=2\pi rB(-dr)/(dt)\\\\\epsilon=2\pi * 0.12* 0.8* 0.75\\\\\epsilon=0.452\ V`

So, the induced emf in the loop is 0.452 volts.