Answer to Question #85862 in Physics for Linda McAfee

Question

A circular loop in the plane of a paper lies in a 0.55 T magnetic field pointing into the paper. The loop's diameter changes from 19.0 cm to 6.8 cm in 0.54 s .What is the magnitude of the average induced emf?

Answer 1

Faraday's law states

$$\rm{emf}=-\frac{\Delta \Phi}{\Delta t}$$

The change in magnetic flux

$$\Delta \Phi=B\Delta A=B\pi (d_2^2-d_1^2)/4$$

Finally

$$\rm{emf}=-\frac{B\pi (d_2^2-d_1^2)}{4\Delta t}$$

$$=-\frac{0.55\times 3.14(0.068^2-0.190^2)}{4\times 0.54}=25.2\times 10^{-3} \;\rm{V}=25.2 \;\rm{mV}$$