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3.) (30 pts) A plane wave traveling in air (free space), is written as $\vec{E}_i = \hat{y}20e^{-j(\sqrt{3}x+z)}$ is incident on a planar surface of dielectric material with $\epsilon_r = 4$ and occupies the half- space, $z \ge 0$. Hint: for this problem, use the general expression $\vec{E} = \vec{E}_0e^{-jk\cdot\vec{r}}$, where $\vec{k} = \hat{x}k_x + \hat{y}k_y + \hat{z}k_z = k\hat{k}$, $\vec{r} = \hat{x}x + \hat{y}y + \hat{z}z$, and determine values for $k_x$, $k_y$, and $k_z$ (some of which can be equal to zero) using the above expression. Determine the following: a. the polarization of the incident wave (perpendicular, parallel or otherwise), b. the angles of incidence and transmission (expressed in degrees) c. the frequency, in Hz, of the incident field d. the time-domain expression for the incident electric and magnetic fields e. the phasor expression for the transmitted electric and magnetic fields f. the average power density carried by the wave into the dielectric medium

          3.) (30 pts) A plane wave traveling in air (free space), is written as
$\vec{E}_i = \hat{y}20e^{-j(\sqrt{3}x+z)}$
is incident on a planar surface of dielectric material with $\epsilon_r = 4$ and occupies the half-
space, $z \ge 0$. Hint: for this problem, use the general expression $\vec{E} = \vec{E}_0e^{-jk\cdot\vec{r}}$, where
$\vec{k} = \hat{x}k_x + \hat{y}k_y + \hat{z}k_z = k\hat{k}$, $\vec{r} = \hat{x}x + \hat{y}y + \hat{z}z$, and determine values for $k_x$, $k_y$, and $k_z$
(some of which can be equal to zero) using the above expression.
Determine the following:
a. the polarization of the incident wave (perpendicular, parallel or otherwise),
b. the angles of incidence and transmission (expressed in degrees)
c. the frequency, in Hz, of the incident field
d. the time-domain expression for the incident electric and magnetic fields
e. the phasor expression for the transmitted electric and magnetic
fields
f. the average power density carried by the wave into the
dielectric medium

3.) (30 pts) A plane wave traveling in air (free space), is written as
E⃗i = ŷ20e^-j(√(3)x+z)
is incident on a planar surface of dielectric material with = 4 and occupies the half-
space, z ≥ 0. Hint: for this problem, use the general expression E⃗ = E⃗0e^-jk·r⃗, where
k⃗ = x̂kx + ŷky + ẑkz = kk̂, r⃗ = x̂x + ŷy + ẑz, and determine values for kx, ky, and kz
(some of which can be equal to zero) using the above expression.
Determine the following:
a. the polarization of the incident wave (perpendicular, parallel or otherwise),
b. the angles of incidence and transmission (expressed in degrees)
c. the frequency, in Hz, of the incident field
d. the time-domain expression for the incident electric and magnetic fields
e. the phasor expression for the transmitted electric and magnetic
fields
f. the average power density carried by the wave into the
dielectric medium

Added by Bryan B.

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