1. A long coaxial cable of length $l$ has an inner conductor (radius a)
and an outer conductor (radius b). There are z-monochromatic
waves traveling between the conductors in z-direction of the form:
$\vec{E}(s, \phi, z, t) = \frac{A}{s}cos(kz - \omega t)\hat{\phi}$ and $\vec{B}(s, \phi, z, t) = \frac{A}{cs}cos(kz - \omega t)\hat{s}$.
(a) Calculate the Poynting vector in between the conductors.
(b) Calculate the electromagnetic momentum stored in the fields in be-
tween the conductors. momentum density
3. Water ice is transparent in the visible spectrum and has a refractive index
of $n_{\lambda=500nm} = 1.3$.
(a) What is the Brewster angle for an ice cube surrounded by air (n = 1).
(b) Now you immerse the ice cube in olive oil ($n_{\lambda=500nm} = 1.5$). Calculate
the critical angle above you would get total internal reflection.
(c) Now you take the ice cube out of the olive oil. You want to cut a
prism with one angle being the Brewster angle (the other two being
equal, isosceles triangle) out of the ice cube. Sketch the beam path
for a laser beam ($\lambda = 500nm$) hitting the prism so that there is no
reflection at the prism surface.
(d) Add a second red laser beam with the same incident angle to your
sketch.
