Project Plan: Relativistic E&M

Sources: In terms of sources, this project is fairly simple. The main source will be Chapter 12 of Griffiths’ Introduction to Electrodynamics, 3rd ed. This will provide a framework for deriving the transformation equations.

Process/Timeline: There are five main steps involved in this project:

1) 4/7-4/14: Derive the transformation equations. This will be a proof-based step, and I need to refresh myself on some of the concepts of mechanical relativity, so it may take some time.

2) 4/14-4/18: Pick one or two simple scenarios and find their E- and B- fields if they were traveling in a moving reference frame. This will be a computational step. The transformation equations are pretty straightforward, so it should take less time. This is just to have a proof of concept, so it is less important that the system has interesting behavior in a moving reference frame.

3) 4/18-4/24: Make 3D or 2D vector field models of these situations in Mathematica. This portion will be focused on figuring out how to make mathematica do what I want. The goal is to come up with an animation or interactive figure that can be used to view the vector fields when the system is moving at different speeds.

4) 4/24-5/2: Find and model situations that display either representative or unusual behavior when considered in a relativistic reference frame. Once the Mathematica simulation for the first situation has been figured out, the following cases should be easier to take care of. Interesting behavior might include systems that only have an electric field in one reference frame and only a magnetic frame in another. It also may be interesting to consider what happens if a reference frame is moving faster than the speed of light.

5) 5/15/14: Summarize results and write conclusions. This will consist of a final look at the systems considered earlier and suggest possible directions for future exploration.