Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (4th Edition)

Published by Pearson
ISBN 10: 0133942651
ISBN 13: 978-0-13394-265-1

Chapter 31 - Electromagnetic Fields and Waves - Exercises and Problems - Page 901: 15


(a) $\lambda = 10.0~nm$ (b) $f = 3.00\times 10^{16}~Hz$ (c) $B_0 = 6.67\times 10^{-8}~T$

Work Step by Step

We can write the general equation for an electric field: $E = E_0~cos(kx-\omega t)$ We can write the equation for this electric field: $E_y = (20.0~V/m)~cos[(6.28\times 10^8)x-\omega t]$ (a) We can find the wavelength: $\lambda = \frac{2\pi}{k}$ $\lambda = \frac{2\pi}{6.28\times 10^8}$ $\lambda = 1.00\times 10^{-8}~m$ $\lambda = 10.0~nm$ (b) We can find the frequency: $f = \frac{c}{\lambda}$ $f = \frac{3.0\times 10^8~m/s}{1.00\times 10^{-8}~m}$ $f = 3.00\times 10^{16}~Hz$ (c) We can find the magnetic field amplitude: $B_0 = \frac{E_0}{c}$ $B_0 = \frac{20.0~V/m}{3.0\times 10^8~m/s}$ $B_0 = 6.67\times 10^{-8}~T$
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