Get to Know Maxwell's Equations—You're Using Them Right Now


If you hang around with physics people long enough, some­one eventually will bring up Maxwell's equations. Maybe as part of a joke, or on a T-shirt or a tattoo. But they'll be somewhere. So even if you aren't a physics major, it won't hurt to get a basic understanding of these iconic equations as well as Gauss Law also.

Maxwell's equations are sort of a big deal in physics. They're how we can model an electromagnetic wave—also known as light. Oh, it's also how most electric generators work and even electric motors. Essentially, you are using Maxwell's equations right now, even if you don't know it. Why are they called "Maxwell's equations"? That's after James Clark Maxwell. He was the 19th-century scientist who sort of put them together, even though many others contributed.

There are four of these equations, and I'll go over each one and give a conceptual explanation. Don't worry, you won't need to refresh your calculus skills. If you do want to follow the math, let me point out that there are two different ways to write these equations, either as integrals or as spatial derivatives. I'll give both versions—but again, if the math looks uninviting, just ignore it.

Gauss' Law
an equation
Rhett Allain

The short version is that Gauss' law describes the electric field pattern due to electric charges. What is the field? I like this description:
It's an energy field created by all living things. It surrounds us, penetrates us, and binds the galaxy together.
Oh, wait. That was Obi Wan's description of the Force in Star Wars Episode IV. But it's not a terrible description of an electric field. Here is another definition (by me):

If you take two electric charges, there is an interaction force between them. The electric field is the force per unit charge on one of those charges. So, it's sort of like a region that describes how an electric charge would feel a force. But is it even real? Well, a field can have both energy and momentum—so it's at least as real as those things.


Gauss Low And Electric Flux

The concept of Gauss Law is based on electric flux in an enclosed surface. But, a zero flux in an enclosed surface doesn't mean zero electric field since the electric flux is proportional to the enclosed charge.


That’s all for electric flux and Gauss’s Law. I hope you enjoyed this tutorial and learned something new. Feel free to ask any questions in the comments section below.