Question

A certain elastic conducting material is stretched into a circular loop of 1.6 cm radius. It is placed with its plane perpendicular to a uniform 0.8 T magnetic field. When released, the radius of the loop starts to shrink at an instantaneous rate of 75.0cm/s. What emf is induced in the loop at that instant in units of V?

Answer 1

Answer:

Induced emf in the loop is 0.0603 volts.

Explanation:

It is given that,

Radius of the circular loop, r = 1.6 cm = 0.016 m

Magnetic field, B = 0.8 T

When released, the radius of the loop starts to shrink at an instantaneous rate of 75.0 cm/s, $\dfrac{dr}{dt}=75\ cm/s=0.75\ m/s$

We need to find the magnitude of induced emf at that instant. Induced emf is given by :

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

Where

$\phi$ is the magnetic flux, $\phi=B\times A$

$\epsilon=\dfrac{-d(BA)}{dt}$, A is the area of cross section

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

$\epsilon=-2\pi r B(\dfrac{dr}{dt})$

$\epsilon=-2\pi \times 0.016\times 0.8 \times 0.75\ m/s$

$\epsilon=0.0603\ V$

So, the induced emf in the loop is 0.0603 volts. Hence, this is the required solution.