Infinite planes and electric feilds

[EV33]

Homework Statement

I have a conceptual question.

If there are two parallel infinite planes with charge densities of -sigma and +sigma, would the E field between them really be constant?

Homework Equations

E=sigma/(2*epsilon_0)

(K*q_0*Q)/r^2

The Attempt at a Solution

There is an example in my book that asks for the E field in between the two planes, and it is solved under the assumption that the E field remains the same regardless of the distance from either plane as long as it is within the two planes.

Is this done for simplicity or is it done that way because that is how it is in reality?

Because when I look at it I think of the electric field and electric force as varying with r.

 

[ehild]

The electric field between two infinite parallel plate with homogeneous surface charge density is constant everywhere between the planes. In reality, the area of the planes are finite, but this is a good approximation if the distance of the planes is much less then the length and width of the planes, and not to close at the edges.

This can be proved matematicaly, using Coulomb's law, but the proof needs integration. I do not know what level of maths are you familiar with.
If those planes are of metal, than you know that the electric field must be perpendicular to them, so the electric field lines are parallel between the plates.
Moreover, there are q/epsilon field lines originating from a charge q. If the charge density on the surface is even, we have the same number of field lines per unit area throughout the planes - that is the field is homogeneous and normal to the planes everywhere between them.

 

[EV33]

oh ok that is kind of what I thought.

Thank you very much. That helps a lot.