Needs to use the Gauss Seidel method in 3D to solve the given equation. Would prefer it written in python, but can translate if need be.

2. Poisson's Equation Given is the Poisson equation in three dimensions and Cartesian coordinates For the charge density function consider a sphere with radius R - 1. In this case the density function is given by (x, y, z) For the numerical and analytical considerations described below, you can set co 1. a) Solve the given problem by writing a code based on Gauss-Seidel iteration. For the domain use -10s S10 -10s y S10 -10s z 10 and use 100 grid points in each direction so that the total number of points in your volume is 1000000 b) After obtaining the potential as function of z, y, and z, make a plot showing z, y 0,2 0) versus r. Compare your graph with the exact analytical result for the case that we are outside of the sphere. Hints: i) The analytical result for the potential outside of the sphere is V(r)-g/ (4#01+Vo u here Vo is a constant. u) In order to find good agreement between numerical and analytical results, you need a laryer number of iterations. Good agreement can be found for 10000 iterations. 2. Poisson's Equation Given is the Poisson equation in three dimensions and Cartesian coordinates For the charge density function consider a sphere with radius R - 1. In this case the density function is given by (x, y, z) For the numerical and analytical considerations described below, you can set co 1. a) Solve the given problem by writing a code based on Gauss-Seidel iteration. For the domain use -10s S10 -10s y S10 -10s z 10 and use 100 grid points in each direction so that the total number of points in your volume is 1000000 b) After obtaining the potential as function of z, y, and z, make a plot showing z, y 0,2 0) versus r. Compare your graph with the exact analytical result for the case that we are outside of the sphere. Hints: i) The analytical result for the potential outside of the sphere is V(r)-g/ (4#01+Vo u here Vo is a constant. u) In order to find good agreement between numerical and analytical results, you need a laryer number of iterations. Good agreement can be found for 10000 iterations