Problem 11. Suppose a capacitor consists of two parallel metal plates with area A, and the gap between them is h. The gap is small compared to the dimensions of the plates. Since the plates are metal, the charges on each plate are free to move, and will tend to cluster themselves more densely near the edges due to the mutual repulsion of the other charges in the same plate. However, it turns out that if the gap is small, this is a small effect, so we can get away with assuming uniform charge density on each plate. Find the field between the plates when the charges on the plates are q and -q. Use: E = 2πkσ.
Instruction:
- Draw a diagram of the metal plates and draw field lines.
- Draw a Gaussian surface you will use to calculate the electric flux.
- By using Gauss's law, find the field between the plates.
- Draw a different Gaussian surface and show that Gauss's law is valid with the electric field you find in this problem. (Show that Gauss's law is correct in a different Gaussian surface.)