Maxwell’s Equations: The Great Discovery in Electromagnetism


By Robert Hazen, Ph.D.George Mason University

The three great discoveries of the 19th century linked electricity and magnetism, these seemingly unrelated phenomenon. First, Hans Oersted showed that electricity flowing in coils of wire produced magnetic effects. Michael Faraday demonstrated how a moving magnetic field can produce electricity through electromagnetic induction. And, finally, James Maxwell’s equations connecting electricity and magnetism led to a new discovery about the natural world.

An image of a coil electromagnetic circuit.
The relationship between magnetism and electricity was discovered through experiments, but James Maxwell quantified this relationship through his equations. (Image: Aris-Tect Group/Shutterstock)

Magnets and Electricity

Magnetic forces seem to be an attribute of a few odd materials—iron, the mineral magnetite, several other solids, but not very many. And these incorporate the north and the south magnetic poles, something that’s intrinsic to those materials. All magnets have these two poles. Magnets are always physical objects. They have seemingly permanent properties.

Electrical forces, on the other hand, appear all around us, whenever an object accumulates a surplus or a deficiency of electrons—a positive or a negative charge, if you will. Electrically charged objects will typically be either positive or negative depending on that surplus or deficiency of electrons. These electric charges seem quite transient. You can charge up an object, the object can lose its charge, and we see these phenomena all around us.

Learn more about electricity.

Both Attractive and Repulsive

But of course, there are also some very important similarities between these two forces. These forces set electricity and magnetism apart from, for example, gravity. In each case the force can be either attractive or repulsive; that’s very different from gravity, which is always only attractive. In each case, like poles or like charges repel each other, whereas opposite poles or opposite charges attract each other.

Well, in any event, whatever the nature of electricity and magnetism, Newton’s clear definition of a force allows—this phenomenon that allows a mass to accelerate—both electricity and magnetism to be studied by scientists who wanted to understand the nature of the everyday phenomenon in our world. So, electricity and magnetism, of course, were intensely studied in the 17th, 18th, and into the 19th century.

This is a transcript from the video series The Joy of ScienceWatch it now, on Wondrium.

Modern Energy

The technological importance of the early discoveries in electromagnetism, was huge. Michael Faraday’s discovery of electromagnetic induction provided an easy way to achieve a previously difficult conversion. Gravitational potential energy, for example, or heat, can be converted into electrical energy by this process. You have to just put an electrical generator in the way, and that takes the one kind of energy and converts it to a different kind of energy.

Before this, people had to build their industries next to sources of energy. But electrical energy can be transferred from many, many miles just over a system of wires. In the 19th century, each household had to manage its own fuel supply. Usually, you had wood coal. Rural electrification in America transformed society. For the first time families all over America were linked physically by an energy source.

The Four Equations of James Clerk Maxwell

A drawing of an early induction coil.
The discoveries in electromagnetism made it possible to create machines for the creation and transfer of electricity, such as induction coils. (Image: Kogo/Public domain)

In 1871, physicist James Clerk Maxwell was appointed to be the first professor of experimental physics at Cambridge, and he also started the Cavendish Laboratory.

Maxwell set down an elegant mathematical formulation of electricity and magnetism in the 1860s. These were the four equations, Maxwell’s equations, of electromagnetism. These equations are very complex mathematically, but we can describe these four equations in everyday words.

The first equation is just a restatement of Coulomb’s law, that a force exists between any two electrical charged objects. The force is proportional to the charges, and it is inversely proportional to the square of the distance between the charges. The second equation describes the magnetic phenomenon and says that every magnet always has two poles, a north pole and a south pole.

The third equation says that changing an electric field produces magnetic effects. And the symmetrical fourth equation says that changing magnetic fields produces electricity.

Learn more about electromagnetism.

Electromagnetism and Light

One of the great wonders of mathematics, one of the things that makes mathematics so powerful in science, is that it can lead to unexpected insights. Sets of equations can be manipulated through algebra and other sorts of mathematical processes and you can certainly learn new things about the natural world that you never suspected.

This is what happened to Maxwell. He manipulated his four equations and found that one possible mathematical solution to the way electricity and magnetism works is a wave. And because constants are built into this equation, he found that this wave had some very special properties. Indeed, the most distinctive property is that the wave had to travel at 186,000 miles per second, the speed of light.

As a result, from very esoteric sort of mathematical reasoning in describing these phenomena of electricity and magnetism, Maxwell discovered the nature of light. Light is an electromagnetic property. This was an astonishing discovery that transformed the future of science.

Common Questions about Maxwell’s Equations

Q: What appears to be the difference between magnetism and electricity?

Magnetism is limited to a few physical materials. They have seemingly permanent properties. On the other hand, electricity appears all around us is many forms, but appears to be transient, in that electrical charge can be removed or changed from positive to negative.

Q: What is the common feature of electricity and magnetism?

In both electricity and magnetism, the force can be either attractive or repulsive, unlike say gravity, which is always only attractive. In each case, like poles or like charges repel each other, whereas opposite poles or opposite charges attract each other.

Q: What did Maxwell discover while working on his four equations of electromagnetism?

James Maxwell manipulated his four equations and found that one possible mathematical solution to the way electricity and magnetism works is a wave. The most distinctive property of this wave was that it traveled at 186,000 miles per second, the speed of light. This meant that light was an electromagnetic wave.

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