MATLAB02
ELEC 3310
Instructions
A cuboid parallel-plate capacitor has dimensions 0.3 mm × 0.3 m × 0.3 m
(height, length, width). Use the numerical Laplace’s equation to find the capac-
itance, C, of this structure if the relative permittivity is ϵr = 2.2. Compare this
with the analytical equation for the capacitance of a parallel plate capacitor.
Include in your report a plot of the voltage as a function of the 2-dimensional
space, and the surface charge density as a function of the distance along the plate
that you choose to calculate it on. Plots should be titled, labelled, with print
large enough to read. This was not mentioned in class but shall be mentioned
here: you can substantially descrease the error in C if you sum ρs along ρs(2 :
end− 1, end). It is written in the lecture notes on this topic.
Do not screenshot your plot(s). Export them from MATLAB in any of the
many ways available. Do not screenshot your code; copy and pasting usually
holds the formatting from MATLAB to Microsoft Word. I would rather see
poorly formatted copy and paste than a screenshot of your desktop. If you use
LATEX, see: https://www.overleaf.com/learn/latex/Questions/How_can_
I_include_MATLAB_code_in_my_LaTeX_document%3F.
1 The Report
Write a brief report describing your solution. The report should contain the
following sections:
1. Introduction: Describe the project and explain to the reader what you are
about to show them. Describe Laplace’s equation for a voltage field, and
its numerical implementation. You do not need to re-derive them, just
show them and explain what they are.
2. Analytical Calculations and Numerical Results: Briefly describe the an-
alytical calculation of the requested quantity. Show here the requested
plots from the output of your code and describe them.
3. Conclusion: Compare the analytical and numerical solution for C. Include
a percent error of your analytically and numerically calculated values.
Explain why these values may not be 100% equivalent and any way or
situation that you think they would be better.
1
4. Appendix: Your complete MATLAB code.
The final report does not need to be long, but it should be professional in
appearance and thorough. In other words, this report is not graded by word
count, it is graded by the quality of the content. Figures should have captions
describing the figure, axes should be labeled, illustrations should be drawn in a
computer program. The use of LATEX is highly recommended (you have access
to a free LATEX editor at overleaf.com through the University), but not required.
Grading Rubric
Category Points
Introduction/description 6
Analytical Calculations and
Numerical Results
6
Comparison/discussion 6
Overall quality of report 6
Code included in Appendix 6
Total 30