Question

An elastic conducting material is stretched into a circular loop of 11.2 cm radius. It is placed with its plane perpendicular to a uniform 0.880 T magnetic field. When released, the radius of the loop starts to shrink at an instantaneous rate of 68.8 cm/s. What emf is induced in volts in the loop at that instant?

Answer 1

Answer:

0.426 volts

Explanation:

It is given that,

The radius of a circular loop, r = 11.2 cm = 0.112 m

An elastic conducting material is stretched into a circular loop.

It is placed with its plane perpendicular to a uniform 0.880 T magnetic field.

The radius of the loop starts to shrink at an instantaneous rate of 68.8 cm/s, dr/dt = 0.688 m/s

We need to find the emf induced in the loop at that instant.

$\epsilon=\dfrac{-d\phi}{dt}\\\\=\dfrac{d}{dt}(BA)\\\\=\dfrac{d}{dt}(\pi r^2 B)\\\\=\pi B\dfrac{d}{dt}(r^2)\\\\=2\pi B r\dfrac{dr}{dt}\\\\=2\pi \times 0.88\times 0.112\times 0.688\\\\=0.426\ V$

So, the magnitude of induced emf is 0.426 volts.