Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (3rd Edition)

Published by Pearson
ISBN 10: 0321740904
ISBN 13: 978-0-32174-090-8

Chapter 33 - Electromagnetic Induction - Exercises and Problems - Page 998: 30

Answer

${\bf 26.2}\;\rm mV$

Work Step by Step

We have here a loop and a changing flux, so we must have an induced current. We know that the induced emf $\varepsilon$ is given by $$\varepsilon=\left|\dfrac{d\Phi}{dt}\right|$$ where $\phi =AB\cos\theta$ and here $A$ is constant, so that $$\varepsilon=A\cos\theta\left|\dfrac{dB}{dt}\right|$$ And for $N$ turns. $$\varepsilon=\pi r^2N \cos\theta\left|\dfrac{dB}{dt}\right|$$ $$\varepsilon=\pi r^2N \cos\theta\left|\dfrac{B_f-B_i}{\Delta t}\right|$$ Plug the known; $$\varepsilon=\pi (0.01)^2(100)\cos60^\circ\left|\dfrac{1.5-0.5}{0.6}\right|$$ $$\varepsilon=\color{red}{\bf 26.2}\;\rm mV$$
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