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 585: 32

Answer

40 degrees north of west.

Work Step by Step

See diagram. The magnetic field caused by the current in the wire points to the west at the location of the compass, by the right hand rule. Calculate the strength of this field. $$B_{wire}=\frac{\mu_oI}{2\pi r}$$ $$ =\frac{4\pi\times10^{-7}(48A)}{2\pi(0.18m)}=5.33\times10^{-5}T $$ The horizontal component of the Earth’s magnetic field that affects the compass needle is pointing due north, and its strength is given. Find the direction of the net field, which is the direction that the compass needle will point. $$\theta=tan^{-1}\frac{B_{Earth}}{B_{wire}}=\frac{0.45\times10^{-4}T }{5.33\times10^{-5}T }=40^{\circ}$$ The compass needle points 40 degrees north of west.
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