Question

An elastic conducting material is stretched into a circular loop of 10.9 cm radius. It is placed with its plane perpendicular to a uniform 0.797 T magnetic field. When released, the radius of the loop starts to shrink at an instantaneous rate of 107 cm/s. What emf is induced in volts in the loop at that instant

Answer 1

Induced emf,
`\epsilon=0.584\ V`

Step-by-step explanation:

It is given that,

Radius of the circular loop, r = 10.9 cm = 0.109 m

Magnetic field, B = 0.797 T

When released, the radius of the loop starts to shrink at an instantaneous rate of 107 cm/s,
`(dr)/(dt)=107\ cm/s=1.07\ m/s`

Due to change in loop of the loop, an emf is induced in the loop. It is given by :

`\epsilon=(d\phi)/(dt)`

`\phi` = magnetic flux

`\epsilon=(d(BA))/(dt)`

`\epsilon=B(d(\pi r^2))/(dt)`

`\epsilon=2\pi rB(dr)/(dt)`

`\epsilon=2\pi * 0.109 * 0.797* 1.07`

`\epsilon=0.584\ V`

So, the emf is induced in the loop at that instant is 0.584 volts. Hence, this is the required solution.