Poisson's equation in electrostatics governs the electric potential φ in the presence of a charge density p(x,y) and is given by the following:

where ∈o is the permittivity of empty space. Consider the figure below. We have two square charges (20 cm x 20 cm) of charge density +1 C/m2 and -1 C/m2 located 20 cm from the edges. Write a Python program to solve this equation on an 1x1 meter square box, where all four of the boundaries are kept at φ = 0. Note that this is a Boundary Value Problem PDE and the drawing below isn't drawn to scale. Setup your 2D grid with a spacing of a = 1cm between each point, set ∈o = 1, and continue the iteration until your solution for the electric potential changes by less than 10-4 V. You can use either the relaxation method, the overrelaxation method or the Gauss-Seidel method to solve this system. Note: This calculation might take your computer a couple of minutes depending on which method you choose and on your computer specs. On my mid-range, 3 year old laptop, this takes about 30 seconds or so.