# Electrodynamics: Electrostatic field potencial in Cartesian coordinates

1. Jan 23, 2013

### C12H17

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

It's given that absolute permitivity is a coordinate function: ε (x, y, z) = Asin(x)cos(y), where A=const

2. Relevant equations

We need to find an electrostatic field potential function $\varphi$ in Cartesian coordinate system.

3. The attempt at a solution

I tired to solve, but I don't know if it's ok. Check, please?

$\vec{D}$=ε$\vec{E}$ and $\vec{E}$= - grad$\varphi$
div$\vec{D}$=ρ
ρ=$\frac{dDx}{dx}$+$\frac{dDy}{dy}$+$\frac{dDz}{dz}$
$\vec{E}$=$\vec{x}$0εEx+$\vec{y}$0εEy+$\vec{z}$0εEz
Dx=εEx
Dy=εEy
Dz=εEz
then
ρ=d Asin(x)cos(y)E x / dx + dAsin(x)cos(y)E y /dy + d Asin(x)cos(y)Ez / dz=Asin(x)sin(y)$\frac{dE}{dx}$+Acos(x)cos(y)$\frac{dE}{dy}$+Asin(x)cos(y)$\frac{dE}{dz}$=Asin(x)sin(y) d $\varphi$2 /dx2 +Acos(x)cos(y) d $\varphi$2 / dy2 + Asin(x)cos(y) d $\varphi$ 2/ dz2

and now i dont know. ;D

Last edited: Jan 23, 2013
2. Jan 27, 2013

### rude man

You're not given any charge distribution, any boundary conditions?

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