16.2 Plane Electromagnetic Waves

The wave equation was obtained by (1) finding the E field produced by the changing B field, (2) finding the B field produced by the changing E field, and combining the two results. Which of Maxwell’s equations was the basis of step (1) and which of step (2)?

What conclusions did our analysis of Maxwell’s equations lead to about these properties of a plane electromagnetic wave:
(a) the relative directions of wave propagation, of the E field, and of B field,
(b) the speed of travel of the wave and how the speed depends on frequency, and
(c) the relative magnitudes of the E and B fields.

Under what conditions might wires in a circuit where the current flows in only one direction emit electromagnetic waves?

If the Sun suddenly turned off, we would not know it until its light stopped coming. How long would that be, given that the Sun is $1.496 \times 10^{11} \text{m}$ away?

An electromagnetic wave has a frequency of 12 MHz. What is its wavelength in vacuum?

The electric field of an electromagnetic wave traveling in vacuum is described by the following wave function: $\overset{\rightarrow}{\mathbf{E}} = \left(5.00 \text{V}/\text{m}\right)$
$\text{cos} \left[k x - \left(6.00 \times 10^{9} \left( \text{s}\right)^{−1}\right) t + 0.40\right] \hat{\mathbf{j}}$ where k is the wavenumber in rad/m, x is in m, t is in s.
Find the following quantities:
(a) amplitude
(b) frequency
(c) wavelength
(d) the direction of the travel of the wave
(e) the associated magnetic field wave

The following represents an electromagnetic wave traveling in the direction of the positive y-axis: $\begin{matrix}E_{x} = E_{0} \text{cos} \left(k y - \omega t\right) ; E_{y} = 0 ; E_{z} = 0 \\ B_{x} = 0 ; B_{y} = 0 ; B_{z} = B_{0} \text{cos} \left(k y - \omega t\right)\end{matrix}$.
The wave is passing through a wide tube of circular cross-section of radius R whose axis is along the x-axis. Find the expression for the displacement current through the tube.