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

Answer:

Induced emf, $\epsilon=0.584\ V$

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, $\dfrac{dr}{dt}=107\ cm/s=1.07\ m/s$

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

$\epsilon=\dfrac{d\phi}{dt}$

$\phi$ = magnetic flux

$\epsilon=\dfrac{d(BA)}{dt}$

$\epsilon=B\dfrac{d(\pi r^2)}{dt}$

$\epsilon=2\pi rB\dfrac{dr}{dt}$

$\epsilon=2\pi \times 0.109 \times 0.797\times 1.07$

$\epsilon=0.584\ V$

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