Exercise 7.4: Poisson's equation

Laplace's equation holds for charge free regions. If there is a charge distribution inside the region we must use Poisson's equation (74) instead.

1. Generalize the difference equation for the Poisson's equation, and modify your program accordingly.

2. Consider a square of linear dimension $L=25cm$ fixed at 10V. assume that each interior cell has a uniform charge density $\rho$ such that $\frac{1}{4}A\rho/\epsilon _0 = 3V/cm^2$. Compute thte potential distribution for this case. Compare the equipotential lines with thos found in Exercise 7.3.

3. Find the potential distribution of the charge distribution of part 1. is restricted to a square of side $L=5cm$ in the center.