I have two earthed metal plates, separated by a distance $d$ with a plane of charge density $\sigma$ placed a distance $a$ from the lower plate. I want to derive expressions for the strength of the electric field in the regions between the plane and the top plate and the plane and the bottom plate.
I'm not sure how to apply Gauss's Law to the given situation. I think the best Gaussian surface to use would be a cylinder(?), and then somehow integrate over the two regions. But this would suggest that the electric field between the charged plane and the bottom surface was independent of the total separation, $d$ of the two earthed plates, which I don't think is correct. I don't yet fully understand Gauss's Law, and need more practice with it.
Please can someone point me in the correct direction, and give me a hint as to what I should be looking to integrate?
With very many thanks,