Question

Magnetic flux in a circular coil of resistance $10\Omega$ changes with time as shown in figure. Cross indicates a direction perpendicular to paper inward. Match the following.

Answer 1

By lenz's law, induced current flows in a direction to oppose the cause.

At t = 1 s, magnetic flux is increasing. Hence, magnetic field due to induced current will be negative i.e. inside the plane of paper. Hence, current will flow anti-clockwise.

By similar argument, at t = 15 s, the current will flow anticlockwise.

$\left[A\right]\to 2$

$\left[D\right]\to 2$

At t = 9 s, magnetic flux is decreasing. Hence, magnetic field due to induced current will be positive i.e. outside the plane of paper. Hence, current will flow clockwise.

$\left[C\right]\to 1$

At t = 5 s, magnetic flux is constant. Hence no current will be induced.

$\left[B\right]\to 3$

By Faraday's law, induced emf in a loop is given by:

$\epsilon =\frac{d\varphi }{dt}$

Current is $i=\frac{\epsilon }{R}$

At t = 1 s, $i=\frac{10/2}{10}=0.5A$

At t = 9 s, $i=\frac{-10/2}{10}=-0.5A$

At t = 15 s, $i=\frac{10/2}{10}=0.5A$