Question

A plane wave traveling along the x-axis in a polystyrene-filled region with 𝜀𝑟 = 2.54 has an electric field given by 𝐸𝑦=𝐸0cos(𝜔𝑡−𝑘𝑥). The frequency is 2.4 GHz, and 𝐸0= 5.0 V/m.

Find the following:

1.1.1. The amplitude and direction of the magnetic field;

1.1.2. The phase velocity;

1.1.3. The wavelength; and

1.1.4. The phase shift between the positions 𝑥1=0.1𝑚 and 𝑥2=0.15𝑚

Answer 1

$H=\sqrt{\frac{\epsilon}{\mu_0}}E=7.1~\frac{kA}m,$

$v=\frac{\omega}k=1.8\cdot 10^8~\frac ms,$

$\lambda=\frac c {\nu}=0.125~m,$

$p=\int_{x_1}^{x_2}Edx=0.23~m.$