Reddit mentions of The Classical Theory of Fields: Volume 2 (Course of Theoretical Physics Series)

Griffiths E&M is a common E&M textbook for physics undergrad. It's common enough that you should be able to find the solutions online. A good contrasting approach is Landau. He typically takes a more elegant or straight forward approach to solve problems and doesn't have many (if any?) brute force problems.

c is called the speed of light, but really it's the speed limit of the universe. Landau and Lifshitz give a beautiful explanation in their famous textbook series (not for the inexperienced) as to why it makes sense for there to be a "speed limit."

> However, experiment shows that instantaneous interactions do not exist in nature. Thus a mechanics based on the assumption of instantaneous propagation of interactions contains within itself a certain inaccuracy. In actuality, if any change takes place in one of the interacting bodies, it will influence the other bodies only after the lapse of a certain interval of time. It is only after this time interval that processes caused by the initial change begin to take place in the second body. Dividing the distance between the two bodies by this time interval, we obtain the velocity of propagation of the interaction.

> We note that this velocity should, strictly speaking, be called the maximum velocity of propagation of interaction. It determines only that interval of time after which a change occurring in one body begins to manifest itself in another. It is clear that the existence of a maximum velocity of propagation of interactions implies, at the same time, that motions of bodies with greater velocity than this are in general impossible in nature. For if such a motion could occur, then by means of it one could realize an interaction with a velocity exceeding
the maximum possible velocity of propagation of interactions.

Basically, if there wasn't a universal speed limit, then interactions could occur instantaneously over any distance. Events in distant galaxies billions of light-years away could affect us immediately. This is not how we observe nature to work, so their must be a speed limit. Now, everyone must agree on that speed limit all the time, or else it's not really a speed limit. Working out the full implications of that gives us special relativity.

Now the question is, why should light travel exactly at that speed limit? Because it's massless. To quote L&L again:

> Experiment shows that the so-called principle of relativity is valid. According to this principle all the laws of nature are identical in all inertial systems of reference. In other words, the equations expressing the laws of nature are invariant with respect to transformations of coordinates and time from one inertial system to another. This means that the equation describing any law of nature, when written in terms of coordinates and time in different inertial reference systems, has one and the same form.

When he talks about "inertial reference systems" he's talking about a system of stuff all moving together at constant velocity. So no matter where you are, and no matter how fast you're moving, physics looks the same everywhere. Another way to put it is that there's no way to say whether I'm standing still and you're moving, or you're standing still and I'm moving. Physics looks identical in either case, so one statement is as good as the other.

What does this have to do with massless particles moving at the speed of light? If something is moving at less than the speed of light, then it must have a co-moving reference frame. That is, there is some vantage point (some speed and direction of motion) in which that thing is at rest. But if we were able to get into the co-moving reference frame of a massless particle, then we would see it have no mass and no momentum, hence no energy at all. It wouldn't be there! So some observers would say there is a particle, and others would say there's not. There would be a disagreement about physical observables based on reference frame, which contradicts the principle of relativity. Now it is possible for a massless particle to move at exactly the universal speed limit because everyone always agrees on that speed, so no matter what reference frame you're in, you'll always see it moving exactly at that speed limit. This also implies that a massive particle can never move at the universal speed limit.

Edit: fixed some typos.