Question

An elastic conducting material is stretched into a circular loop of 9.65 cm radius. It is placed with its plane perpendicular to a uniform 1.14 T magnetic field. When released, the radius of the loop starts to shrink at an instantaneous rate of 75.6 cm/s. What emf is induced in volts in the loop at that instant?

Answer 1

The induced emf in the coil is 0.522 volts.

Step-by-step explanation:

Given that,

Radius of the circular loop, r = 9.65 cm

It is placed with its plane perpendicular to a uniform 1.14 T magnetic field.

The radius of the loop starts to shrink at an instantaneous rate of 75.6 cm/s ,
`(dr)/(dt)=-0.756\ m/s`

Due to the shrinking of radius of the loop, an emf induced in it. 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 * 9.65* 10^(-2)* 1.14* 0.756\\\\\epsilon=0.522\ V`

So, the induced emf in the coil is 0.522 volts.