Section 5.6 · Home exercises · 3 of 7
Home exercise 5.6.3: From \vec H to \vec E, then the power
About the home exercises of Section 5.6
Home exercises 5.6.1–5.6.3 belong to the lecture, Home exercises 5.6.4–5.6.7 to the exercise lecture.
From to , then the power
#In free space (, no sources) the magnetic field phasor of a wave is
- Find the frequency (use ).
- Find from the phasor form of Ampère's law, , and check that it satisfies the Helmholtz equation.
- Find the time-average Poynting vector and the power crossing of the plane const.
Strategy
In free space fixes . Ampère's law with no current gives , and then from Eq. (5.6.27).
a)
, so and ().
b)
Only is present:
Helmholtz: , so .
c)
and are in phase, so
Answer
Check
, and points along , the direction in which travels.
Remark
The ratio and the right-handed triad formed by , and the direction of travel are general properties of plane waves in free space, the subject of Section 6.1.