Electric Field Calculation for Coaxial Plates with Holes

[superkraken]

Homework Statement

two infinitely large plates are at a distance d from each other .they carry a unifor surface charge of densities X and -X.the plates have round coaxial holes of radius R.with d<<R.find the electric field through the axis of the holes(taking them as circles) as a function of distance l from them.[/B]

Homework Equations

The Attempt at a Solution

i think i should find the field due to both the plates and subtaract the field due to the hole.i don't exactly know how to do that if that's how it done.

 

[Khashishi]

Ok then. Show what you get for the field of the plates (without hole).
Then show what you get for the hole. Since you are on axis, you only need to consider one component of the field. What can you say about the direction of the field? Just do an integration over the surfaces of the holes, summing over the nonzero component.

 

[superkraken]

ok but what do i integrate from where to where?if i take a small area of width dx and at a distance dr from tthe center .the answer is pretty confusing

 

[Khashishi]

Integrate over the surface area of the circle. Thanks to symmetry, you can do this as a 1D integral.