Problem #2: Let region $z > 0$ be composed of a uniform dielectric material for which $\epsilon_r = 3.1$, while the region $z < 0$ is characterized by $\epsilon_r = 5.4$. There is a surface charge density of $\rho_s = 25 \frac{nC}{m^2}$ at the interface (boundary between the two regions). Let $\vec{D_A} = 40\hat{x} + 10\hat{y} + 30\hat{z} \frac{nC}{m^2}$.
A) Find $\vec{D_A}$, $\vec{E_{An}}$, $\vec{E_{At}}$, $\vec{E_A}$, $\theta_A$
B) Find $\vec{D_{Bn}}$, $\vec{D_{Bt}}$, $\vec{D_B}$, $\vec{E_B}$, $\theta_B$
Where $\theta_A$ is the angle between z-axis and $\vec{D}$.
