Two conducting planes, one grounded one has a surface charge

[SU403RUNFAST]

Homework Statement

The plane with surface charge sigma lies in x-z plane at y=0, parallel to it at y=a there is a grounded plane. What is the field just above the bottom plane, find the potential between the planes

Homework Equations

discontinuity E=sigma/epsilon, V=Qd/Aepsilon take the gradient I can find V, what is E

The Attempt at a Solution

I know that for an infinite plane just above or below the E field is sigma over epsilon naught. The sigma in this question on the top plane is sigmacos(lambdax) so it depends on x, is sinusoidal. is E sigma/epsilon and i just plug in the sigma given? Or do i do the method of images

 

[Sturk200]

Homework Statement

The plane with surface charge sigma lies in x-z plane at y=0, parallel to it at y=a there is a grounded plane. What is the field just above the bottom plane, find the potential between the planes

Homework Equations

discontinuity E=sigma/epsilon, V=Qd/Aepsilon take the gradient I can find V, what is E

The Attempt at a Solution

I know that for an infinite plane just above or below the E field is sigma over epsilon naught. The sigma in this question on the top plane is sigmacos(lambdax) so it depends on x, is sinusoidal. is E sigma/epsilon and i just plug in the sigma given? Or do i do the method of images

Isn't the field just above or below an infinite plane sigma over two epsilon naught?

Gauss says E * a is sigma*a over epsilon naught. But we have to close the pillbox on both sides of the sheet, so E * a is actually 2Ea. The sigma*a/(2a*eps0) = E, and the field is sig over two E naught. Outside a conductor the two would drop out, I believe. But if it's just a sheet...

 

[TSny]

I know that for an infinite plane just above or below the E field is sigma over epsilon naught.

Yes, at any point just outside the surface of any conductor, the electric field is perpendicular to the surface and has a magnitude ##|E| = |\sigma|/\epsilon_0## (assuming electrostatic conditions).

The sigma in this question on the top plane is sigmacos(lambdax) so it depends on x, is sinusoidal. is E sigma/epsilon and i just plug in the sigma given?

Did you mean to say that this is ##\sigma## on the top surface of the plane at ##y = 0##? If so, I would agree.

EDIT: However, I don't think the bottom plane can have such a space-varying charge density if the plane is a conductor. Are you sure both planes are conductors? Also, are they infinite planes?