While I did succeed in creating a model that allowed the user to view the field at different speeds, it only managed to show the direction and relative magnitude compared to the rest of the current fields. If I were to continue with this project, I would attempt to improve it in several ways.
-First, I would try to find a way to make Mathematica account for the absolute magnitude of the fields so that the uniform fields would appear to change as the speed was varied. This might be accomplished by using equipotential surfaces rather than vector fields.
-Second, I would write code such that the user could simply input (or maybe copy and paste) a particular E-field equation for a rest frame, and the program would interpret the equation and produce the vector plots with sliders as shown in my model.
-Third, I would model more discrete situations rather than infinite distributions of charge or current so that the changes in field would be more visible.
-Fourth, I might consider a different type of plot, since Mathematica seems to deal with this kind of plot poorly. For instance, a static plot of E versus v and B versus v at a single point in space might better show the changing relative magnitudes of the fields.
That being said, this project was successful in several regards. It emphasizes the interplay of electric and magnetic behaviors when considered in moving reference frames, and at least in the case of the point charge, it allows for an examination of the changing shape of the fields at different speeds. It also sets up the framework for being able to model more complex systems by providing a proof-of-concept using simpler cases. Therefore, this project successfully modeled the fundamentals of relativistic electromagnetism, and provides a good foundation for a more in-depth exploration.
On a personal level, I was really hoping someone would do a project on relativistic E and M and I’m glad you did. I think that in the intro courses, modern, and 240 we see and learn about relative frames and Maxwell’s equations but never get a real visual understanding of what exactly happens when you combine these concepts. So thank you for doing this!
First, I really liked how you established the basic fields of each configuration. I thought it was especially interesting, as you said, to confirm that the relative strength of field vectors did not change as you increased the speed. Due to the nature of my project, I especially liked seeing your data for the wire. In my project, I completely disregarded the properties of the electric field from the wire and it was refreshing to be reminded how intertwined they are with the magnetic field, especially when one is being caused by the other. Another really interesting point you made was emphasizing how the electric field of a discrete point charge flattens out in the x direction.
I share your struggles with Mathematica; I found it incredibly difficult to set up a manipulation of a 3D model. However, I do think that there were ways to make a manipulation of velocity, even if you had to show it as a 2D graph: perhaps the magnetic and electric field at a specific point? You could then have generalized that property and applied it to the rest of the space. I also would have liked to see you involve Maxwell’s equations, if even a little. Finally, I think for the capacitor models you could have spaced out the vectors a little bit to make them more visible individually. Overall, great job.