The general form of Gauss’s law describes how a charge creates an electric field in a material, as well as in vacuum. It is where ) = 1)0 is the permittivity of the material.
(a) A sheet with charge Q uniformly distributed over its area A is surrounded by a dielectric. Show that the sheet creates a uniform electric field at nearby points, with magnitude E = Q /2A).
(b) Two large sheets of area A, carrying opposite charges of equal magnitude Q, are a small distance d apart. Show that they create uniform electric field in the space between them, with magnitude E = Q /A).
(c) Assume that the negative plate is at zero potential. Show that the positive plate is at potential Qd/A).
(d) Show that the capacitance of the pair of plates is A)/d = 1A)0/d.