### Project Summary

In this project I will be solving the Laplace equation in 2D numerically in order to calculate the Voltage/Potential Field in a pre-defined region. After finding said region, the end goal is to produce a visualization of Voltage, Electric field, Flux field, and charge density as a function of position.

### Scenario:

As specified in the project prompt, there exists within a defined region of 20x20cm where the absolute center 0,0 corresponds to the centroid of the system. In the region, a square conductor with a voltage of 10 volts as well as a ring with specified thickness contains a voltage of 3 volts.

Figure 1: Square conductor and ring conductor with specified voltages within the system. Res = 300 Figure 2: example of matrix of conductors Res = 50 to see voltage values of each cell in matrix. Figure 3: Voltage potential distribution using iterative laplace algorithm after 20,000 iterations. Figure 4: magnitude of E field with respect to the voltage field previously produced. Figure 5: magnitude of D field with respect to the electric field previously produced. Figure 6: Outer perimeter/Surface Area to be dotted with D field to produce charge density. Figure 7 a & b: Charge distribution at two angles with respect to the D field previously produced.