EE 430-Principles of Electromagnetic Fields
Principles of Electromagnetic Fields
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EE 430-Principles of Electromagnetic Fields
PROJECT ON MESH RELAXATION METHODS FOR BOUNDARY
VALUE PROBLEMS IN ELECTROSTATICS
Name (Print):
Problem Weight Score
1 20
2 30
3 30
4 20
Total 100
Instructions:
1. The project reports should be uploaded in Canvas by 4 PM on Thursday, March
17. Please include a cover sheet (this page) with you name and assignment questions,
and a brief description of your solution approach (including principal mathematical
expressions) for each of the project assignments. Please include in your report copies
of all codes you developed for this project. Please submit one pdf file containing all
project results including your Matlab codes.
2. You are allowed to use your textbook, your own lecture notes, and MATLAB
function sorEE430S22.m posted in EE 430 Project folder on CANVAS. Please review
pages 93-110 of the textbook, and H.O.s #14 and #15 on solution of partial differen-
tial equations using finite differences before starting your work on this assignment. No
other materials are permitted. You are allowed to discuss project assignments with
your classmates only, but only on conceptual level. The completed project should
be your own work. You are not allowed to share parts of the code or compare final
results.
1. (20%) Find analytical solutions for the electric field ~E and potential V for an
infinite cylinder of radius R uniformly charged with density ρ0. Assume that V=0 at
the axis of the cylinder.
Assuming that z axis is parallel to the axis of the cylinder and that the cylinder
is centered at the point with coordinates x0 = Lx/2 and y0 = Ly/2 in the center
of the two-dimensional domain shown in Figure 1, find values of the potential and
electric field at grid locations. Define positions of grid points as x(ix)=∆x× (ix − 1)
for ix varying from 1 to nx + 1, and y(iy)=∆y × (iy − 1) for iy varying from 1 to
ny+1, where ∆x=Lx/nx and ∆y=Ly/ny. Plot scans of the potential and electric field
magnitude as a function of x at y0 = Ly/2 and as a function of y at x0 = Lx/2. You
1
can use MATLAB functions contour.m, imagesc.m, quiver.m to plot two-dimensional
distributions of the potential and electric field (vector and magnitude). Assume
Lx=Ly=3 cm, R=Lx/6, ρ0=8.85×10−12 C m−3. It is useful to plot both potential
(using contour.m) and electric field vector (using quiver.m) in the same figure, as
illustrated in Figure 2, to visualize the relationship between the equipotential lines and
electric field vector. Look at results for two resolutions nx=ny=20 and nx=ny=100.