Answer to Question #107539 in Electricity and Magnetism for Mridu smita raj

Question

A wire loop of resistance 10 ohm 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 inverse. Determine the magnitude and direction of the induced current in the loop

Answer 1

From the law of electromagnetic induction we write

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

Then the current is

$$I=\frac{\epsilon}{R}=\frac{\pi r^2}{R}\frac{dB}{dt}$$

$$I=\frac{(0.5)⋅\pi⋅0.1 ^2}{10}=1.57\ mA$$