3. An electric field associated with a uniform plane wave propagating in air is
$\vec{E}(z,t) = 1000 \cos(\pi \times 10^8 t - \beta z)\hat{a}_x \left[\frac{V}{m}\right]$
If this wave is normally incident on a glass medium ($\epsilon_g = 5\epsilon_0$, $\mu_g = \mu_0$)
and $\sigma_g = 0$), determine the following:
3.1. the wave number, $\beta$, in air and in glass.
3.2. the reflection and transmission coefficients $\Gamma$ and $\tau$, respectively.
3.3. the reflected and transmitted electric and magnetic fields.
HINT: $\beta = \omega \sqrt{\mu \epsilon}$
$\epsilon_0 = \frac{10^{-9}}{36\pi} \left[\frac{F}{m}\right]$, $\mu_0 = 4\pi \times 10^{-7} \left[\frac{H}{m}\right]$, $\eta = \sqrt{\frac{\mu}{\epsilon}}$
$\Gamma = \frac{\eta_2-\eta_1}{\eta_2+\eta_1}$, $\tau = \frac{2\eta_2}{\eta_2+\eta_1}$, $\vec{E}_r = \Gamma \vec{E}_i$, $\vec{E}_t = \tau \vec{E}_i$
4. A slab of a uniform density $\rho_v = 25 \left[\frac{mC}{m^3}\right]$ extends to infinity in
