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 997: 16

Answer

a) $0\;\rm V/m$ b) $0.04\;\rm V/m$

Work Step by Step

We know that the strength of the induced electric field inside a solenoid is given by $$E_{\rm solenoid}=\dfrac{r}{2}\left| \dfrac{dB}{dt} \right|$$ Plug the known; $$E_{\rm solenoid}=\dfrac{r}{2}\left| -4.0\right|$$ $$E_{\rm solenoid}=2r\tag 1$$ $$\color{blue}{\bf [a]}$$ On the axis of the solenoid means at $r=0$. Plug into (1), $$E_{\rm solenoid}=2(0)=\color{red}{\bf 0}\;\rm V/m$$ $$\color{blue}{\bf [b]}$$ Here $r=2$ cm. Plug into (1), $$E_{\rm solenoid}=2(0.02)=\color{red}{\bf 0.04}\;\rm V/m$$
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