University Physics with Modern Physics (14th Edition)

Published by Pearson
ISBN 10: 0321973615
ISBN 13: 978-0-32197-361-0

Chapter 29 - Electromagnetic Induction - Problems - Exercises - Page 984: 29.36

Answer

a. 2.81 mV/m. b. counterclockwise.

Work Step by Step

The magnitude of the induced electric field is given by Faraday’s Law. $$E(2 \pi r)=\frac{d}{dt}(B\pi r^2)= \pi r^2\frac{dB}{dt}$$ $$E=\frac{r}{2}\frac{dB}{dt}$$ $$E=\frac{0.0225m}{2}(0.250T/s)=2.81mV/m$$ b. The field points toward the viewer (on the magnetic south pole) and it is decreasing. The induced current makes a field that is directed toward the viewer, to help out the decreasing field strength. By the right hand rule, the induced current is counterclockwise.
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