Write a computer program to implement the finite difference method. The program can be in any computer language that is available within the school. Set up the code to find the potential for a parallel plate capacitor in the box shown below, all dimensions are in mm.

A number of points are shown with origin at the bottom left of the dielectric. The top plate is 6mm long with 2mm between the plate and the outer box. The horizontal side wall is 12mm and the vertical side wall is 6mm. There is a potential of 10V on the upper plate and 0V on the box. Between the plate and the box is a dielectric as shown in the diagram this has a dielectric constant of 9. Using your programme:  

1. Calculate the potential at points P,Q,R,S 

2. Calculate the electric field at P,Q,R,S 

3. Draw a contour map showing the potential 

4. Calculate the capacitance of the structure using your finite difference data and compare with that of a parallel plate capacitor of the same size if the fields outside the dielectric are neglected. You can calculate the capacitance per unit length. 

5. Calculate the capacitance of the structure using your finite difference program if the dielectric were not there. 

6. If the structure were a parallel plate transmission line extending into the page, what is the velocity of the electromagnetic wave along the line? Do this using your finite difference data as well as using the simple parallel plate assumption.  

Assessment –A report is required with a description of how you tackled the problem and the answers to the six questions. It should be self-contained with a good description of the methods you used. Your computer code should be included as an appendix. 

Solution includes MATLAB program and a report