Question

A certain elastic conducting material is stretched into a circular loop of 15.0 cm radius. It is placed with its plane perpendicular to a uniform 0.600 T magnetic field. When released, the radius of the loop starts to shrink at an instantaneous rate of 68.0 cm/s. What emf is induced in the loop at that instant?

Answer 1

The emf induced in the loop is 0.38 V.

Explanation:

The emf induced in any coil is directly proportional to the rate of change in flux linked with the coil as stated by Faraday's law.

Flux can be obtained by the product of magnetic lines of force with cross sectional area. As flux is the measure of magnetic lines of force crossing a certain cross sectional area.

As here the region is considered as circular loop, so the area will be area of the circle.

Then, $emf=\frac{d(phi)}{dt}$

phi = Magnetic field * Area

$emf = \frac{d(BA)}{dt} =B*2\pi*r\frac{dr }{dt}$

$emf = 0.6*2*3.14*0.15*0.68=0.38 V$

So, the emf induced in the loop is 0.38 V.