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: 8

Answer

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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 current needed is given by $$I=\dfrac{2\pi d B}{\mu_0}$$ At point $d=0.01\;\rm m$; $$I=\dfrac{2\pi (0.01) B}{4\pi \times 10^{-7}}$$ $$I=\dfrac{ B}{200 \times 10^{-7}}$$ Using the data in Table 32.1, to find the currents needed, $$I_1=\dfrac{ B_{\rm Earth's \;surface}}{200 \times 10^{-7}}=\dfrac{ (5\times 10^{-5})}{200 \times 10^{-7}}=\color{red}{\bf 2.5}\;\rm A$$ $$I_2=\dfrac{ B_{\rm Refrigerator\;magnet}}{200 \times 10^{-7}}=\dfrac{ (5\times 10^{-3})}{200 \times 10^{-7}}=\color{red}{\bf 250}\;\rm A$$ $$(I_3)_{\rm minimun}=\dfrac{ B_{\rm Lab\;magnet}}{200 \times 10^{-7}}=\dfrac{ (0.1)}{200 \times 10^{-7}}=\color{red}{\bf 5000}\;\rm A$$ $$(I_3)_{\rm maximum}=\dfrac{ B_{\rm Lab\;magnet}}{200 \times 10^{-7}}=\dfrac{ (1)}{200 \times 10^{-7}}=\color{red}{\bf 50,000}\;\rm A$$ $$I_4=\dfrac{ B_{\rm superconducting \;magnet}}{200 \times 10^{-7}}=\dfrac{ (10)}{200 \times 10^{-7}}=\color{red}{\bf 500,000}\;\rm A$$
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