1984E2. Two large, parallel conducting plates are joined by a wire, as shown above, so that they are at the same potential. Between the plates, at a distance a from the upper plate and a distance b from the lower plate, is a thin, uniformly charged sheet whose charge per unit area is σ The electric fields between the plates above and below the sheet have magnitudes E1 and E2, respectively.
a. Determine the ratio E1/E2 so that the potential difference between the outer plates is zero.
b. The Gaussian surface in the diagram immediately below has faces of area A parallel to the charged sheet. By applying Gauss's law to this surface, develop a relationship among E1,E2, a, and any appropriate fundamental constants.
c. By applying Gauss's law to an appropriately chosen Gaussian surface, show that the sum of the induced charge densities, σ1 and σ2, on the inner surfaces of the conducting plates equals −σ. Indicate clearly on the diagram below, the Gaussian surface you used.
d. Develop an expression for the potential difference V between the charged sheet and the conducting plates in terms of σ,a,b, and any appropriate fundamental constants.