Exercise 9.3

Consider the following simple model of an electronic capacitor, consisting of two flat metal plates enclosed in a square metal box:

For simplicity let us model the system in two dimensions. Using any of the methods we have studied, write a program to calculate the electrostatic potential in the box on a grid of 100×100 points, where the walls of the box are at voltage zero and the two plates (which are of negligible thickness) are at voltages ±1V as shown. Have your program calculate the value of the potential at each grid point to a precision of 10⁶ volts and then make a density plot of the result.

Hint: Notice that the capacitor plates are at fixed voltage, not fixed charge, so this problem differs from the problem with the two charges in Exercise 9.1. In effect, the capacitor plates are part of the boundary condition in this case: they behave the same way as the walls of the box, with potentials that are fixed at a certain value and cannot change.