How electricity and magnetism came together

Many of the greatest breakthroughs in physics to date simplify our understanding of the natural world, instead of complicating it. 

A case in point is the work for which James Clerk Maxwell is famous. His eponymous equations unified electricity, magnetism, and eventually optics under the banner of electromagnetism. With it, Maxwell provided a mathematical basis for many of today’s important technologies, including wireless communication and power generation.

Maxwell’s equations are a powerful example of how physicists bring disparate laws, formulations, and theories under a single framework, making them more useful for application and research. Today, we’re diving into the unification of magnetism and electricity, what that meant for physicists, and how Maxwell’s equations birthed a new technological age.

A brief history of electricity and magnetism

By the 1800s, humans had already long known about electricity and magnetism. Pieces of magnetite, for example, were used in Ancient India to remove arrows from people’s bodies and electric fish were prescribed to cure headaches in ancient Rome (neither are recommended today).

Our story, however, will start in 1820, when a Danish scientist named Hans Christian Ørsted discovered that electric currents impacted nearby compass needles. This implied a direct relationship between electricity and magnetism. A few months later, Ørsted published findings showing that electric currents produce circular magnetic fields as they flow through wires.

Ørsted’s papers led to an increased interest in electrodynamics, the classical study of electric charge and currents. Many researchers started experimenting and theorizing, building off each other’s work and independently discovering similar phenomena.

Three are particularly important to Maxwell’s story: Carl Friedrich Gauss, André-Marie Ampère, and Michael Faraday.

Carl Friedrich Gauss

Today, many physicists know Gauss as the namesake of a Gaussian distribution, which appears in statistics and probability theory.  

But Gauss was also fascinated by magnetism. Together with his colleague Johann Mayer, he established an international working group that measured the Earth’s magnetic field and found that it had two magnetic poles.  

Gauss mathematically proved that magnetic monopoles couldn’t exist in classical physics. Every magnet has both a North and South pole. If you cut a magnet in half, you end up with two magnets, each with its own North and South pole.

Gauss also formulated the law that describes how electric charges create an electric field.  

These two discoveries by Gauss became foundational for Maxwell’s famous equations for electromagnetism.

André-Marie Ampère

You may recognize the name Ampère as the namesake for amperes (or amps), a unit of measurement for electric current.

Ampère discovered that two parallel wires can attract or repel each other depending on the direction of electricity flowing through them. This led to Ampère's law, which relates to the circulation of a magnetic field around a closed loop to an electric current passing through the loop.

Michael Faraday

Finally, English scientist Michael Faraday was also experimenting after hearing of Ørsted’s discoveries.

Faraday had long been interested in electricity and chemistry, but he is also known for developing one of the most important inventions in history: the homopolar motor. The first electric generator, this simple motor worked by a phenomenon he called electromagnetic rotation.

Faraday was an experimentalist at heart, but he developed his theories of “lines of force” based on his experiments and observations, describing the way he visualized magnetic field lines produced by the phenomena he studied. Once again, these ideas would go on to become an important foundation on which Maxwell’s equations were built.

The work of these three scientists, alongside countless others, led to an unwieldly number of theories, laws, and experimental results. They needed simplification and summary. They needed to be brought together into something much more usable.

Enter James Clerk Maxwell.

Shedding some light on electricity and magnetism

Educated at the University of Edinburgh and Cambridge, Maxwell had experimented with magnetism and electricity. But it was his interest in light that gave him the additional insight that would help push his equations beyond electromagnetism.

For Maxwell, bringing together these disparate ideas, and doing so concisely, was incredibly important. “The first process therefore in the effectual study of the science must be one of simplification and reduction of the results of previous investigations to a form in which the mind can grasp them,” he wrote in a paper called On Faraday’s Lines of Force.

In 1860, Maxwell moved to King’s College in London, where Faraday also lectured, and published a four-part series of papers that transformed physics. In them, he detailed 20 partial differential equations that describe how electric and magnetic fields are generated by electric charges and currents.

Essentially, Maxwell’s papers brought together four laws:

1. Gauss’s law detailing the distribution of electric charge to an electric field
2. Gauss’s law for magnetism, which showed that magnetic monopoles don’t exist
3. Faraday’s law of induction, which described how a changing magnetic field can induce an electric current
4. Ampère's circuital law, relating the circulation of a magnetic field around a closed loop to the electric current

This was a substantial feat unto itself, but within these papers were two important breakthroughs that led to more than further simplification, it led to a whole new discovery. Through his work, Maxwell made an important tweak to Ampère's law to include displacement current, outlining that magnetic fields affect electrical ones and vice versa.

He also discovered that electromagnetic fields travel at the speed of light, a coincidence he could not ignore. Through that, he realized that light itself was electromagnetic and that all three were results of the same phenomenon.

What do we mean by “unified electricity and magnetism?”

So what does it mean to unify electricity and magnetism? It means that physicists have created a mathematical framework and rigorous description for how electricity and magnetism work, one that proves they are two sides of the same coin.  

This was Maxwell’s triumph, and it was a gamechanger.  

Today, it is known as classical electromagnetism, to distinguish it from the quantum version of electrodynamics that would come about during the twentieth century, long after Maxwell’s death. But he laid the groundwork, and it remains one of the greatest achievements in modern physics. By distilling the findings of people like Faraday and Ampère into those twenty equations, he created a series of mathematical descriptions for electromagnetic waves. These equations were then used by inventors, engineers, and innovators as the theoretical foundation for modern technologies like radio waves, power generators, radar, and more. They also were used by physicists like Albert Einstein, who developed special relativity and kickstarted the next era of physics.

Today, physicists at Perimeter Institute and around the world are pursuing similar projects. There are other unifications that may yet be achieved. The most famous example is a theory of everything that would unite gravity and quantum mechanics. That could have an enormous impact on our world, much like Maxwell’s work changed his world over 150 years ago.