###### By Laura J. Bottomley, NC State University

## The easiest way to get a magnetic field is to pick up a magnet, which generates a permanent electric field. We can’t see the field without help. But, when you pour iron filings over the magnet, they will line up along the lines of the magnetic field. The lines start on one side of the magnet and end on the other. What does this tell us about magnetic charges?

### Magnetic Charges Are a Myth

All magnets have two poles, which we call north and south. We can’t have a particle that has only one pole; they come in pairs. The phenomenon that shows up in these field lines—that they both start and end on the magnet—shows us a very interesting way that magnetism differs from electricity. It is that magnetic charges, as opposed to electric charges, don’t exist.

The field lines of an electric field can begin on a single charge and radiate outward, in essence not terminating. Magnetic field lines can’t do that. This means the universe is asymmetric, and that tends to bother scientists. To an engineer, it means that we cannot build systems that carry magnetic currents in the same way we build systems to carry electric currents.

This article comes directly from content in the video seriesElectrical Engineering for Everyone. Watch it now, on Wondrium.

### Learning the Language of Math

The tool that we use to model the behavior of electromagnetic energy is mathematical equations. One of the things that puts some people off about engineering in general, and electrical engineering specifically, is our tendency to speak in math. And when we say “speak in math,” we really mean it.

Mathematics is a language, very much like any other. The most important thing to realize about it is that, just like a native English speaker has to learn Spanish, we all have to learn to speak math at some point in our lives.

Let’s illustrate a set of electrical and magnetic phenomena that underlie all of electrical engineering. They illustrate four very famous equations, now called Maxwell’s equations. Maxwell’s four equations are actually two pairs: the first pair about fields, and the second pair about charges.

### Maxwell’s Equations

First, a magnetic field changing over space yields an electric field that changes over time, plus some electric current. This part of the equation that has the upside-down delta stands for the magnetic field varying in all three dimensions of space. The part that stands for the electric field varying only in time is written by del/dt.

To understand something varying in time but not in space, imagine a time-lapse video showing a seed sprouting, growing, and getting leaves. It’s varying in time, but not in space because it isn’t traveling. By contrast, something varying in space but not time is like taking a picture of a field of sunflowers. They won’t all be blooming the same amount. They will vary over the space of the field, but they won’t vary in time because the picture is a snapshot of a moment in time.

Second, a magnetic field changing over time produces an electric field that changes over space. This is something that Michael Faraday first noticed in 1831. Third, electric charges give rise to an electric field that varies over space. The field is strongest near the electric charge and gets weaker as the distance increases. Each charge creates an electric field. Because the charges are the same polarity, the fields oppose each other, which causes a force to be generated between them.

Finally, there is no such thing as a magnetic charge. While electrons carry an electric charge, no one has ever found anything that carries a magnetic charge.

### The Neat Duality of Maxwell’s Equations

So, the outcome of all this is that changing electric fields cause changing magnetic fields, and changing magnetic fields causes electric fields and current. And the reverse is also true. Changing current causes magnetic fields.

The lack of magnetic charges, and thus the lack of magnetic current, is the only thing that keeps these phenomena from being completely mirrored. This duality of Maxwell’s equations is pretty neat. One of the things they predict is that a motor can be a generator and vice versa.

### Common Questions about Why We Don’t Have Magnetic Charges

**Q: What does pouring iron filings over a magnet teach us?**The result of pouring iron filings over a magnet is that they will line up along the lines of the magnetic field of that magnet. The lines start from one side and end on the other. The fact that magnetic poles come in pairs tells us that, unlike electrical charges, there is no such thing as a magnetic charge, and in this way, the universe is asymmetrical.

**Q: What do each of Maxwell’s equations tell us?**The first pair of Maxwell’s equations tell us that a magnetic field changing over space yields an electric field changing over time. The second pair address electrical and magnetic charges; namely the fact that electrical charges give rise to electrical fields, and that there is no such thing as a magnetic charge.

**Q: Why are Maxwell’s equations important to electrical engineering?**Maxwell’s equations address the electrical and magnetic phenomena that are the very essence of electrical engineering. They illustrate such phenomena in mathematical language and tell us about the relationship between electrical fields and magnetic fields, electrical fields and electrical charges, and the non-existence of magnetic charges.