There's so much more to electric fields than you were taught
The first time you learn about the concept of an electric field, it's always in the context of a charged particle sitting at rest, described by Coulomb's law. But that's only the beginning.
For one thing, the electric field produced by a moving charge—especially one that's moving close to the speed of light—can be very different. Not to mention the fields sourced by accelerating charges, which are even more intricate.
In this video, we'll discover why. We'll start by reviewing the basics: the ordinary Coulomb field of a charge sitting at rest. We'll develop the geometric intuition behind Gauss's law, and see how it captures the relation between the field and the charges that sourced it.
From there, we'll allow our charge to start moving—at first with constant velocity. And we'll see, by analogy with relativistic length contraction, that the field of a charge moving close to the speed of light is "squished" along its direction of motion.
And finally, we'll study the most fascinating variety of field—the field produced by an accelerating charge. By applying the principle of causality, we'll discover that an accelerating charged particle must radiate electromagnetic waves that communicate the change in its state of motion to the rest of the universe.