# Inclined plate capacitor grid/ mesh

You can calculate the electric potential over every point in a defined space by solving Laplace's equation. To do this in a computer program you set up an 2-d array/ matrix and loop the internal points applying the following formula:

$$\phi(x,y)= \frac{\phi(x_{i-1},y_j)+\phi(x_{i+1},y_j)+\phi(x_i,y_{j-1})+\phi(x_i,_{j+1})}{4}$$

Meaning that the electric potential at $\phi(x,y)$ is just the average of the 4 neighbouring points. Included in the array are areas of constant potential i.e. the algorithm does not alter them. These are the boundary conditions (the outer points of the grid/ matrix, set to 0) and the two plates (at a user defined location, set to -1 and 1). Now with the grid set up as it is currently: evenly spaced in both x and y direction, only a parallel plate capacitor can be modelled. If i try to put the plate at an incline it will just look like a stair case.

My question is, how can i set this up in terms of a computer program in order to calculate the electric potential over all points with one plate rotated at an arbitrary angle $\theta$?

Thanks.