Problem 5 (20 points, continued on next page)
A plane electromagnetic wave varies sinusoidally as it travels through vacuum in the +z
direction. The magnetic field has its maximum value ($B_{max}$) at the origin at $r = 0$. At the
origin at t = 0, the magnetic field points in the +x direction.
(5a) Write a symbolic vector expression for the magnetic field as a function of time for a
plane wave in terms of $B_{max}$, the wavenumber, the angular frequency, and the coordinates.
Pay attention to the initial conditions described above.
(5b) Write a symbolic expression using $B_{max}$ and constants of nature for the average power
per unit area delivered by this electromagnetic wave.
Problem 5 (20 points, continued from the previous page)
A plane electromagnetic wave varies sinusoidally as it travels through vacuum in the +z
direction. The magnetic field has its maximum value ($B_{max}$) at the origin at t = 0. At the
origin at t = 0, the magnetic field points in the +x direction.
The frequency of the electromagnetic wave is 100 MHz. The amplitude $B_{max} = 2.0 \times 10^{-7}$ T.
(5c) Calculate the wavelength.
(5d) Calculate the amplitude of the electric field at the origin at t = 0.
(5e) Give the vector direction of the electric field at the origin at t = 0.
$\hat{i} + \hat{j}$
$\hat{i} - \hat{j}$
$\hat{i} + \hat{k}$
$\hat{i} - \hat{k}$