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

Answer:

The induced emf in the coil is 0.522 volts.                        

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 , $\dfrac{dr}{dt}=-0.756\ m/s$

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

$\epsilon=\dfrac{-d\phi}{dt}\\\\\epsilon=\dfrac{-d(BA)}{dt}\\\\\epsilon=B\dfrac{-d(\pi r^2)}{dt}\\\\\epsilon=2\pi rB\dfrac{dr}{dt}\\\\\epsilon=2\pi \times 9.65\times 10^{-2}\times 1.14\times 0.756\\\\\epsilon=0.522\ V$

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