Electric Field and Uniformly Charged Planes (conceptual)

[dimpledur]

Homework Statement

I am pursuing conceptual help regarding electric field due to uniformly charged planes.

Homework Equations

$$E=\frac{\sigma}{2\epsilon}$$

The Attempt at a Solution

I understand that a capictor has plates that are +/-Q. However, how would you calculate the elctric field between the plates if the plates are not equal in charge? Would the electric field between the plates still be uniform?

$$E=\frac{\sigma _1}{2\epsilon} + \frac{\sigma _2}{2\epsilon}$$

 

[Mandeep Deka]

There's a simple way to find that out!
Consider an arbitrary charge distribution on the two plates, of the capacitor. Find out the expression for the net electric field, at any point on the interior of a plate. What should it be equal to?

 

[dimpledur]

The force on a test charge q, due to plate Q1, would be:

F= (kqQ1)/r^2

F=[kq(sigma1)A]/r^2

therefore, E=[kq(sigma)A]/(r^2*q) =[k(sigma1)A]/r^2

If there was an addition plate with charge Q2, we would have E=[k(sigma1)A]/r^2

Therefore, the electric field due to the two plates would be:
E=[k(sigma1)A]/r^2 + [k(sigma1)A]/r^2

 

[dimpledur]

Does that look correct?