Exercise 7.1: Verification

1. Assume that the source of the potential is a point charge of $1\mu C$ at the origin. We know that the potential is going to be given by:
   

   $$V(x,y)=\frac{1\mu C}{\sqrt{x^2+y^2}}$$ (78)

   
   
   Choose a reasonable value of $\Delta$ and compare the values of $V(x,y)$ given by (79) in the center of one, and the average of $V$ in the four neighboring points (obtained also with Eq.(79)). Repeat for 5 different cells at different distances from the origin. Does the relative agreement depend on the distance of the cell to the origin?

2. Repeat part 1 with smaller values of $\Delta$. Are the results in better agreement?