Problem 6.1.4: Power flow of a linear and a circular wave

Problem 6.1.4

Power flow of a linear and a circular wave

Two $1$ -GHz uniform plane waves travel towards $+ z$ in free space:

(i) E_{1} (ii) E_{2} = 100 cos (ω t - β z) a_{x} V/m, = 100 [cos (ω t - β z) a_{x} + sin (ω t - β z) a_{y}] V/m .

For each wave find $β$ , the magnetic field $H (z, t)$ , the instantaneous Poynting vector $P (z, t)$ and its time average $P_{a v}$ . Show that for the circularly polarised wave $P$ is constant in time and space. What is the polarisation of (ii)?

Adapted from: D. K. Cheng, Field and Wave Electromagnetics, 2nd ed., Problem P.8-17.

Try it yourself first.