In my job as a spacecraft engineer, I am very familiar with understanding gravity and how it drives the motion of objects. However, I came to realize that I don't have a deep understanding of any of the other 3 fundamental forces of nature (electromagnetism and the strong/weak nuclear forces). I decided it would be useful for me to start off the year by reading Feynman's introduction to electromagnetism. Because most things in nature have a net-neutral charge, we don't often have an appeciation for just how strong the electromagnetic force is. Feynman states that if you were standing at arm's length from another person and you each possessed just one percent more electrons than protons, the repulsive force would be enough to lift a "weight" equal to that of the entire earth.
From this chapter, I have several main takeaways. First, the force on a charge q moving at velocity v (which we know from experiment) is given by
where E and B are the electric and magnetic fields. Clearly, in order to resolve the force on a charge, we must have knowledge of these two fields. This is where the four Maxwell equations come into play.
One confusion I had initially is that Maxwell's equations appear to be overdetermined in the sense that they provide 8 equations (two scalar equations and two 3D vector equations) for 6 unknowns. After some research I discovered that it can be shown that any system satisfying the 3rd and 4th equations above also satisfies the 1st and 2nd equations.
The fascinating thing about the electromagnetic field to me is that charged particles and each of the two fields are in a constant dance with one another. What I mean by this is that the positions of charges dictate what the electric and magnetic fields look like which dictates the positions of charged particles which dictate what the electric and magnetic fields look like. edit: I am realizing a couple days after writing this that this is no different than how gravity works