Physics: Principles with Applications (7th Edition)

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

Chapter 20 - Magnetism - Problems - Page 586: 48

Answer

To maximize the magnetic field, the wire should be short and with a large radius.

Work Step by Step

$B=\frac{\mu_0NI}{l_s}$ $I=\frac{V}{R}$ and $R=\rho \frac{l_w}{A_w}$, so $B=\frac{\mu_0NVA_w}{l_w\rho l_s}$ $V=\frac{m_{Cu}}{\rho_{Cu}}=l_wA_w$ $A_w=\frac{m_{Cu}}{\rho_{Cu}l_w}$ $N=\frac{l_w}{2\pi r_s}$ By substituting, we have: $B=\frac{\mu_0Vl_wm_{Cu}}{\rho_{Cu}\rho_{RCu}l_w^2l_s2\pi r_s}$ Therefore, to maximize the magnetic field, the wire should be short and with a large radius.
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