How to Calculate Electric Field and Potential for a Uniformly Charged Sheet?

[akashkhan25]

Homework Statement

A sheet of uniform charge density σ n dimensions a x a . find the electric field n potential on an axis passing through the midpoint of the sheet and perpendicular to the sheet as a function of distance h from the midpoint

Homework Equations

The Attempt at a Solution

 

[Bhumble]

Do you have a specific question or post your attempt at solving so we can see where your problem is?

 

[akashkhan25]

Well I tried finding the potential due to a strip element on the sheet and then integrating it but have a problem with the integration as when i plug in h$$\rightarrow$$0 I don't get $$\sigma/2\epsilon_{o}$$

 

[Bhumble]

E is not a constant function of h. Break this down into three piece-wise functions.
E where h > 0, E where h = 0, and E where h < 0.

Use Gauss' Law with a pill box to get E above and E below. For E at h = 0 ask yourself what is the E field at a point charge? Is E continuous?