Answer to Question #157649 in Electricity and Magnetism for Priya

Question

A wire loop of resistance 20 ohm and radius 5.0cm is kept in the plane of this paper in a changing uniform magnetic field B vector.The direction of B vector is perpendicular to the plane of the page and points out of it. If the magnitude of the induced current in the loop is 3.0mA. determine the rate of change of the magnitude of the magnetic field B vector

Answer 1

By the Ohm's Law, we get:

$$I=\dfrac{\epsilon}{R},$$ $$\epsilon=IR=3.0\cdot10^{-3}\ A\cdot20\ \Omega=60\ mV.$$

From the other hand:

$$\epsilon=A_{loop}\dfrac{dB}{dt},$$ $$\dfrac{dB}{dt}=\dfrac{\epsilon}{A_{loop}}=\dfrac{\epsilon}{\pi r^2},$$ $$\dfrac{dB}{dt}=\dfrac{60\cdot10^{-3}\ V}{\pi\cdot (0.05\ m)^2}=7.64\ T.$$