# Dielectric lens

1. May 6, 2012

### humanist rho

1. The problem statement, all variables and given/known data

In the figure the left surface of a dielectric lens is that of a circular
cylinder, and the right surface is a plane. If E1 at point P(r,45,z) in
region 1 is $$5\hat{a}_{r}-3\hat{a}_{\phi }$$, what must be the dielectric
constant of the lens if the electric field in the 3rd region is parallel to
the x axis?

2. Relevant equations

3. The attempt at a solution

The coordinate systems are confusing me.

First region
Tangential componet $$E_{1t}=-3\hat{a}_{\phi }$$

Normal component $$E_{1n}=5\hat{a}_{r}$$
(boundary is charge free,i think)

second region

Tangential componet $$E_{2t}=-3\hat{a}_{\phi }$$

Normal component $$E_{2n}=\dfrac{5}{\varepsilon _{r}}\hat{a}_{r}$$

Now what to do ?