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 32 - The Magnetic Field - Exercises and Problems - Page 956: 10

Answer

${\bf 750}\;\rm A$

Work Step by Step

We know that the magnetic field of a long straight current wire is given by $$B=\dfrac{\mu_0I}{2\pi d}$$ Hence, the maximum current needed is given by $$I_{\rm max}=\dfrac{2\pi d B_{\rm max}}{\mu_0}$$ We need to find the magnetic field at the surface of the wire which is at a distance of $d=r=1.5\;\rm mm$ where the maximum field allowed is $B_{\rm max}=0.1\;\rm T$. $$I_{\rm max}=\dfrac{2\pi d (0.1)}{4\pi \times 10^{-7}}$$ $$I_{\rm max}=\dfrac{ (1.5\times 10^{-3}) (0.1)}{2 \times 10^{-7}}$$ $$I_{\rm max}=\color{red}{\bf 750}\;\rm A$$
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