Answer to Question #105793 in Electricity and Magnetism for Vishal Kumar

Question

A wire loop of resistance 10 ohm and radius 10cm 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 it's magnitude is increasing at the rate of 0.50Ts. Determine the magnitude and direction of the induced current in the loop

Answer 1

We write the law of electromagnetic induction

$\epsilon_i=\frac{\Delta \Phi} { \Delta t}=\frac{\Delta B \cdot S} { \Delta t}=\frac{\Delta B } { \Delta t}\cdot S$

Where

$\frac{\Delta B } { \Delta t}$ -the rate of change of the magnetic field

$S=\pi \cdot r^2$ -ring area

Then we write down Ohm’s law

$I_i=\frac{\epsilon_i}{R}=\frac{\Delta B } { \Delta t}\cdot \frac{S}{R}=0.5\cdot \frac{3.14 \cdot 0.1^2}{10}=1.57mA$