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

WIRED | 8/6/2019 | Rhett Allain
Level 3
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If you hang around with physics people long enough, eventually someone brings up Maxwell's equations. Maybe it will be part of a joke, or maybe it will be on a T-shirt or as 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.

There are four of these equations, and I'll go over each one and give a conceptual explanation. But let me go ahead and say that Maxwell's equations are sort of a big deal in physics. They are 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 these equations together even though many others contributed.

#### Equations - Calculus - Skills - Ways - Equations

Now for the equations. Don't worry, you won't need to refresh your calculus skills. Also, let me point out that there are two different ways to write these equations. In one method, they are written as integrals. In the other method they are shown as spatial derivatives. I'll start off with both versions of the equation, but you don't really need to understand the calculus notation.

The short version is that Gauss's Law describes the electric field pattern due to electric charges. What is a field? I like this description:

#### Energy - Field - Things - Galaxy

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):

#### Charges

If you take two electric charges,...