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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

          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

3. An electric field associated with a uniform plane wave propagating in air is
E⃗(z,t) = 1000 cos(π× 10^8 t - β z)âx [(V)/(m)]
If this wave is normally incident on a glass medium (= 5ϵ0, = μ0)
and = 0), determine the following:
3.1. the wave number, β, in air and in glass.
3.2. the reflection and transmission coefficients Γ and τ, respectively.
3.3. the reflected and transmitted electric and magnetic fields.
HINT: β = ω√(μϵ)
ϵ0 = (10^-9)/(36π)[(F)/(m)], μ0 = 4π× 10^-7[(H)/(m)], η = √((μ)/(ϵ))
Γ = (η2-η1)/(η2+η1), τ = (2η2)/(η2+η1), E⃗r = ΓE⃗i, E⃗t = τE⃗i
4. A slab of a uniform density = 25 [(mC)/(m^3)] extends to infinity in

Added by Casey M.

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