# Charged wire inside a linear dielectric

1. May 10, 2014

### jennyjones

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

see attachment 2

2. Relevant equations

a.

3. The attempt at a solution

see atachment 1

i am stuck at problem a. the question is to write down the boundary conditions for that the E field has to satisfy infinetly far away from the wire and at the boundary of the dielectric z = 0.

I'm not sure how to do this, any help is welcome

thanks

Jenny

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2. May 10, 2014

### rdijkgraaf

Dat mag niet. Groetjes B. N.

3. May 10, 2014

### vanhees71

You have the following equations, valid everywhere
$$\vec{\nabla} \times \vec{E}=0, \quad \vec{\nabla} \cdot \vec{D}=\rho, \quad \vec{D}=\epsilon \vec{E}.$$
$$\epsilon=\Theta(z)+\epsilon_{r} \Theta(-z).$$
$$\vec{e}_z \times [\vec{E}(x,y,0^+)-\vec{E}(x,y,0^-)]=0,$$
because $\vec{e}_z$ is the normal vector of the dielectric's boundary surface.
$$\vec{e}_z [\vec{D}(x,y,0^+)-\vec{D}(x,y,0^-)] = \sigma.$$
Here $\sigma$ is the surface charge density on the surface of the dielectric.