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

0.426 volts

Step-by-step 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=(-d\phi)/(dt)\\\\=(d)/(dt)(BA)\\\\=(d)/(dt)(\pi r^2 B)\\\\=\pi B(d)/(dt)(r^2)\\\\=2\pi B r(dr)/(dt)\\\\=2\pi * 0.88* 0.112* 0.688\\\\=0.426\ V`

So, the magnitude of induced emf is 0.426 volts.