- #1

doktorwho

- 181

- 6

## Homework Statement

A very thin plane of length ##2a## is placed in the air at height ##a## above the conducting surface. The plane is charged on its surface and the expression for it's surface charge density (##ρ_s##) is given by ##ρ_s=ρ_{s0}*\frac{x}{a}## and ##ρ_{s0}## is some constant.

a) Determine the surface charge density function inducted on the conducting surface.

The image that goes with this is uploaded.

## Homework Equations

$$ρ_s=ρ_{s0}*\frac{x}{a}$$

## The Attempt at a Solution

I need help in starting to solve the problem. I have some theories as to how i would solve it and i would like a feedback on if it's ok to do so.

I was going to use a theory where we remove the conducting surface and add a mirror image of the object with an opposite charge. So at ##2a## distance from the first plane there is a second plane with a charge density $$ρ_{s2}=-ρ_{s0}*\frac{x}{a}$$. Now all i have to do is calculate the electric field right? I am confused as how I am going to do this.

I know that the electric field of a plane is $$E_p=\frac{ρ_s}{2ε_0}$$ but how will i find the inducted charge and express it in a surface charge density function?[/B]