Answer to Question #118880 in Electricity and Magnetism for Rahul

Question

8. a) A wire loop of resistance 10 and radius 10 cm is kept in the plane of this
paper in a uniform magnetic field . B 
The direction of B 
is perpendicular to the
plane of the page and points out of it and its magnitude is increasing at the rate
of 0.50Ts . 1 Determine the magnitude and direction of the induced current in the
loop.

Answer 1

Given data

Resistance is $R=10 \Omega$

Rate of magnetic field is $\frac{dB}{dt}=0.50 T/s$

The induced emf in the loop is

$E=-A \frac{dB}{dt}=- \pi r^2 \frac{dB}{dt}$

$=- \pi (0.10 m)^2 (0.50 T/s)$

$=-0.0157 V$

So the magnitude of induced emf is $E=0.0157 V$ .

Magnitude of induced current is

$I= \frac{E}{R}=\frac{0.0157 V}{10 \Omega} =1.57*10^{-3} A=1.57 mA$

According to Lenz's law, the direction of induced emf is Clockwise.