Getting electric potential from charge density over whole sp

[Thomas Rothe]

Homework Statement

Let’s say I have got a charge density $\rho (x,y,z) = \cfrac{C}{x^2}$ with C a specific constant. I want to know the potential on every point in space. How can I get an expression of the electric potential in terms of position?

Homework Equations

Gauss law/coulomb's law probably

The Attempt at a Solution

favorite
Let’s say I have got a charge density ρ(x,y,z)=Cx2'>ρ(x,y,z)=Cx2ρ(x,y,z)=Cx2 with C a specific constant. I want to know the potential on every point in space. How can I get an expression of the electric potential in terms of position?

Plotting the charge density we get of course infinite amount of planes with the same charge density each, along the x-axis. With this picture in mind we might guess that there are just x-components of the electric fields perpendicular to the planes, because of symmetry.

I think that this could be a key point (if I was right) in calculating the potential (or electric field) but I just can’t come up with a specific expression for that since I would have to consider all planes with specific charge density. Neither Gauss Law, Coulomb’s law or any other definition of potential/electric fields seems to be applicable.

Is there a simple way to calculate such a potential? (It actually doesn’t seems to be that hard)

 

[kuruman]

Hi Thomas Rothe and welcome to PF.

Please use legible code for your equations, preferably LaTeX.
I would try to solve the Poisson equation, $\nabla^2 \varphi=\rho(x,y,z)$. Is $\rho(x,y,z)=C/x^2$? I can't tell for sure.