Visualization of Maxwell’s wave equation in 3-D

Introduction

Maxwell equation unifies and explains all electromagnetic phenomena. In fact,
his equations are credited as being the greatest contribution towards our modern
society. These equations influenced the creation of TVs, phones, transformers,
electric motors, wireless and fiber optic communications. Also, Albert Einstein
used Maxwell’s equation to derive and prove his theory of Relativity.
In a quote taken from Feynman Lecture of Physics stated that “From a long
view of the history of mankind-seen from, say, ten thousand years from now-there
can be little doubt that the most significant event of the 19th century will
be judged as Maxwell’s discovery of the laws of electrodynamics. The American
Civil War will pale into provincial insignificance in comparison with the important
scientific even to the same decade.”

Maxwell equations

Historically, Maxwell used his equation to calculate the speed of light to be
3x10^6 m/s, which was experimentally validated to be correct, and had stated
that his equations will allow for wireless communication, that too was validated
by Hertz with the discovery of the radio wave.

Maxwell equation for time harmonics fields

Maxwell equations for time-harmonics fields

For this project, the time was considered as being the z axis, and thus kz in
the equation above was the phase shift.

For communication purposes, the magnetic and magnetic fields become polarized.
The main objective of this project is to visualize the electromagnetic wave
propagating and to view how polarization changes the electric and magnetic field.

Design

The purpose of this project is to visualize Maxwell electromagnetic waves in
three dimensions. Since there are an infinite amount of situations of electromagnetic
waves propagation, the main focus of this design is to visualize the electromagnetic
wave propagation of linear, circular, and elliptical polarization.

Objective

- Write a small Matlab program that simulates the propagation of electromagnetic
fields for linear polarization, circular polarization and elliptical polarization

- Create a quick time movie to visualize electromagnetic wave propagation by
using Capvte and adobe Premiere

- Create a web page to publish the results

Movie