Section 6.3 · Further exercises · 1 of 10
Exercise 6.3.1: A medium with \varepsilon_r=\mu_r
Ten further exercises at normal incidence, in the spirit of the problems, the home exercises and the worked examples of this section, each group of five graded from easy to harder. They use only the toolbox at the head of this subsection.
A medium with
#A uniform plane wave of frequency GHz and amplitude V/m travels in air along and falls normally on the plane face of a thick lossless medium. Find , , the transmitted and amplitudes, the fraction of the power reflected and the wavelength in the medium when the medium has (a) , (b) , , (c) , . What do the three media have in common, and what tells them apart at the interface?
Reflection is decided by alone, the wavelength by alone. In air rad/m and cm.
, so and : nothing is reflected. V/m, mA/m, the same as in air. But rad/m: cm and the wave slows to m/s.
: , . V/m, mA/m, , cm.
: , . V/m, mA/m, , cm.
In (b) and (c) gives and , so in both . At : (b) : mA/m , (c) mA/m .
(b) and (c) have the same refractive index and reflect the same power, but with opposite signs of : the dielectric gives a minimum of at the face, the magnetic medium a maximum. Medium (a) has the index yet is invisible at normal incidence because its impedance is that of air. Ferrite tiles used as microwave absorbers are designed this way, with and large losses, so that the wave enters without reflection and is then absorbed. Section 6.4 shows that the trick fails at oblique incidence.
cf. Problem 6.3.1