Physics: Principles with Applications (7th Edition)

Published by Pearson
ISBN 10: 0-32162-592-7
ISBN 13: 978-0-32162-592-2

Chapter 21 - Electromagnetic Induction and Faraday's Law - Problems - Page 622: 49

Answer

$5\times10^{15}J$

Work Step by Step

The magnetic energy density is given by equation 21–10. $$u=\frac{Energy}{Volume}=\frac{1}{2}\frac{B^2}{\mu_o}$$ Solve for the energy. The volume of a thin shell, as we have here, is the surface area of the shell multiplied by its thickness. $$Energy=(Volume) \frac{1}{2}\frac{B^2}{\mu_o}$$ $$=(4\pi (6.38\times10^6m)^2(10^4m)) \frac{1}{2}\frac{(0.50\times10^{-4}T)^2}{4 \pi \times10^{-7}(T \cdot m)/A)}$$ $$\approx5\times10^{15}J$$
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