Problem #$1(4$pts each $20$ pts total$)$:

a$)$ vec$(E)(z,t)=E_0[hat(x)cos(t+kz)+$hat$(y)cos(t+kz-\frac{}{2})]$ is$...$

Linearly polarized in the hat$(x)$ direction

Left$-$handed circularly polarized

Right$-$handed circularly polarized

Linearly polarized in both the hat$(x)$ and hat$(y)$ directions

b$)$ The skin depth $({}_s)$ of a medium

Is characterized by electric and magnetic fields that have uniform properties at all points across an infinite plane.

Characterizes how deep an electromagnetic wave can penetrate into a conducting medium.

Describes the locus traced by the tip of the $E$ vector at a given point in space as a function of time.

c$)$ The equation: vec$(E)(z,t)=$hat$(x)Acos(t+k_{y}y-k_{z}z-\frac{}{8})$ expresses a wave with which of the following properties?

An hat$(x)-$polarized plane wave with the amplitude of $A,$ propagating toward $+x$ and $-z$ directions

An hat$(x)-$polarized plane wave with the amplitude of $A,$ propagating toward $-y$ and $+z$ directions

An hat$(z)-$polarized plane wave with the amplitude of $A,$ propagating toward $+x$ and $-z$ directions

An hat$(y)-$polarized plane wave with the amplitude of $A,$ propagating toward $-x$ and $+z$ directions

d$)($Fill in the blank$)$ The normal component of the electric flux is $q,$ across the boundary between any two media?

Discontinuous by the amount of surface current density

Continuous

Discontinuous by the amount of surface charge density

$0$

Equal to $2\mathrm{.}71828$

e$)$ A plane wave in air is normally incident onto a perfect electrical conductor $($PEC$).$ At the boundary between the air and PEC, what is the reflection coefficient?

$=0$

$=1$

$=-1$

$=\frac{1}{e}$

f$)($Bonus: $3$ pts$)$ True or False: Magnetic field inside PEC is always zero.