Question

When we applied Gauss's Law to find the electric field of an infinite sheet of charge, we also treated the sheet as if it was very thin, like a sheet of paper. But if the sheet has an appreciable thickness, we can investigate the field within the sheet as well. Here are two views of a thick sheet of charge with my suggestion for a Gaussian surface, viewed both head-on and at an angle so you can see the distances: The sheet extends out infinitely to the left and right, as well as into and out of the page. Since it is infinite, we must use charge density instead of total charge to describe it. The charge is throughout the entire volume of this thick sheet, so we use volume charge density: p = charge/volume. Apply Gauss's Law to determine the electric field as a function of y within this thick sheet of charge. Determine the voltage V as a function of y, setting the reference point to be V = 0 at y = 30. Bonus +3: Check to see if the electric field is continuous at the boundaries y = +d and y = -d. You will need to determine the field outside the sheet in order to do this. It might help to graph E vs. y to get a sense of what's going on.

Answer 1