How Are Electricity and Magnetism Connected? From Ørsted’s Compass to Maxwell’s Light

Rub a balloon and it sticks to a wall. Hold a magnet near a fridge and it clicks into place. For most of history these looked like unrelated tricks. Today they are understood as two faces of one force, electromagnetism, which also turns out to be the explanation of light. This post follows how that unification happened, with the experiments that forced it, and the characters in our Electromagnetism collection who embody each step.

How was the link between electricity and magnetism discovered?

In the spring of 1820, Hans Christian Ørsted, a professor at the University of Copenhagen, held a compass beside a wire connected to a battery during a lecture demonstration. When the current flowed, the needle swung. As the Niels Bohr Institute’s history notes, the effect appeared not when the needle pointed toward the wire, as he had expected, but when needle and wire were parallel (Niels Bohr Institute^[1]). An electric current makes a magnetic field.

Can magnetism make electricity?

If currents make magnetism, can magnets make currents? Michael Faraday showed in 1831 that they can, but only when something changes. Moving a magnet near a coil, or switching a nearby current on and off, drives a current in the coil; a steady magnetic field does nothing (Britannica^[2]). This is electromagnetic induction, the principle behind every generator, transformer and wireless charger. In modern form, Faraday’s law says the induced voltage around a loop equals minus the rate of change of magnetic flux through it:

ℰ = −dΦ_B/dt

Feynman’s chapter on the laws of induction develops it from both sides, moving wires and changing fields (Feynman Lectures II-17^[3]).

What does the minus sign mean? Lenz’s law

In 1834 Heinrich Lenz gave the rule for the direction of the induced current: it always flows so as to oppose the change that caused it (Britannica^[4]). That minus sign is energy conservation in disguise. If the induced current helped the change, a magnet would be pulled along for free while the wire heated up. Drop a strong magnet down a copper pipe and you can watch Lenz’s law: it drifts down slowly, braked by eddy currents in a pipe that is not even magnetic. MacLatchy, Backman and Bogan turned this into a quantitative student experiment in 1993 (Am. J. Phys.^[5]). That pipe is our sticker Lenzor: Change the flux. I push back.

What are Maxwell’s equations?

By the 1860s, the laws of electricity and magnetism were known piece by piece: charges make electric fields; there are no magnetic charges; changing magnetic fields make electric fields (Faraday); currents make magnetic fields (Ampère). James Clerk Maxwell noticed that Ampère’s law, as written, contradicted conservation of charge where charge piles up, as on a capacitor plate. He fixed it by adding a term: a changing electric field also makes a magnetic field. His 1865 paper, “A Dynamical Theory of the Electromagnetic Field,” set out the complete theory (Phil. Trans.^[6]).

The tidy four-line vector form taught today is not how Maxwell wrote it; Oliver Heaviside and others condensed it later. Our Maxwell sticker carries the modern version and the missing term.

Why is light an electromagnetic wave?

With Maxwell’s extra term, a changing electric field makes a changing magnetic field, which makes a changing electric field, and the disturbance carries itself through empty space as a wave. Maxwell could compute its speed from two constants measured on a laboratory bench with coils and capacitors:

c = 1 / √(μ₀ε₀)

The answer matched the measured speed of light. Maxwell concluded that light is an electromagnetic disturbance (Phil. Trans.^[6]). In the late 1880s Heinrich Hertz generated and detected such waves with electric sparks, the beginning of radio (Britannica^[7]). That light is a wave of fields with a direction also explains polarisation: Étienne-Louis Malus discovered in 1809 that reflected light is polarised (Britannica^[8]), and the cos² rule for polarisers that carries his name is our sticker Diagonix. Why the speed of light then became a cosmic speed limit is the subject of Why Is the Speed of Light the Limit?

Is magnetism just electricity in motion?

In a deep sense, yes. Whether a force looks electric or magnetic depends on how you are moving. Feynman shows that a charge moving beside a current-carrying wire feels a magnetic force in one frame, and that in the charge’s own frame the same effect appears as an electric force, because relativity changes the densities of the moving charges in the wire (Feynman Lectures II-13^[9]). Electric and magnetic fields are two parts of one electromagnetic field. That is why Einstein’s 1905 relativity paper was titled “On the Electrodynamics of Moving Bodies” (Ann. Phys.^[10]).

Where does electromagnetism show up in everyday life?

Power grids and motors

Transformers use induction to raise and lower AC voltages, which makes long-distance transmission practical. Nikola Tesla’s polyphase AC motor, patented in 1888 as US Patent 381,968, uses alternating currents out of step with each other to make a magnetic field rotate by itself (US Patent 381,968^[11]). See our Tesla sticker for the AC/DC story told fairly.

Faraday cages and cars in thunderstorms

Charge on a conductor spreads over its outer surface, leaving the field inside an enclosed cavity at zero. Faraday tested this by building a large foil-covered cube and sitting inside while its outside was charged until sparks flew; he recorded the experiment in his Experimental Researches in Electricity (Faraday, Project Gutenberg^[12]). The US National Weather Service notes that the outer metal shell of a hard-topped car protects people inside from lightning with the windows closed (NWS^[13]). The tyres have nothing to do with it. That is our Faraday sticker.

Particle accelerators

A charge moving across a magnetic field curves in a circle, and its lap frequency does not depend on its speed. Ernest Lawrence built the cyclotron on that fact and won the 1939 Nobel Prize “for the invention and development of the cyclotron” (NobelPrize.org^[14]). That is Gyrolla: Bigger circle. Same lap time.

Quantum electromagnetism

At low temperatures and high magnetic fields, a thin layer of electrons shows a Hall resistance quantised in exact steps of h/e², the quantum Hall effect, discovered by Klaus von Klitzing (NobelPrize.org^[15]). More on that cold frontier in What Happens at Absolute Zero?

Key terms in plain English

• Electric field: the influence a charge exerts on other charges around it.
• Magnetic field: the influence that moving charges and magnets exert on other moving charges and magnets.
• Magnetic flux (Φ_B): how much magnetic field passes through a loop. Changing it induces a voltage (Feynman Lectures^[3]).
• Induction: producing a voltage by changing magnetic flux, discovered by Faraday in 1831 (Britannica^[2]).
• Eddy currents: swirling currents induced in a conductor by a changing field; they cause magnetic braking.
• Electromagnetic wave: a self-sustaining wave of electric and magnetic fields travelling at c (Phil. Trans.^[6]).
• Polarisation: the direction in which a light wave’s electric field oscillates (Britannica^[8]).

How does a generator work?

A generator is Faraday’s law with a motor driving it. A coil spins in a magnetic field, or a magnet spins inside a coil, so the flux through the coil changes continuously and a voltage is induced. Because the flux rises and falls as the coil turns, the voltage naturally alternates, which is one reason alternating current became the standard for power. Lenz’s law shows up as a mechanical cost: the induced current produces a magnetic force that resists the rotation, so the more current you draw, the harder the turbine must push. Energy is conserved; the work done turning the shaft becomes the electrical energy delivered (Britannica^[4]).

What is the electromagnetic spectrum?

Once light was understood as an electromagnetic wave, it became clear that visible light is just one narrow band of a much wider family, distinguished only by wavelength. Radio waves, microwaves, infrared, visible light, ultraviolet, X-rays and gamma rays are all the same kind of wave. Hertz’s spark experiments showed that waves far longer than visible light obey the same rules (Britannica^[7]). Every phone call, Wi-Fi signal and microwave oven depends on that insight, which began with a twitching compass needle in Copenhagen.

Is electromagnetism the strongest force?

Between two protons, electromagnetism is far stronger than gravity, but weaker than the strong nuclear force at nuclear distances, which is why nuclei hold together despite electric repulsion. That contest is the subject of What Holds the Nucleus Together? On the scale of everyday objects, electromagnetism dominates almost everything you touch: friction, chemistry, the solidity of a table and the light you read by.

A short timeline of electromagnetism

• 1809: Étienne-Louis Malus discovers polarisation of light by reflection (Britannica^[8]).
• 1820: Hans Christian Ørsted sees a current deflect a compass needle (Niels Bohr Institute^[1]).
• 1831: Michael Faraday discovers electromagnetic induction (Britannica^[2]).
• 1834: Heinrich Lenz states the rule for the direction of induced currents (Britannica^[4]).
• 1865: James Clerk Maxwell publishes his dynamical theory of the electromagnetic field (Phil. Trans.^[6]).
• 1888: Nikola Tesla’s polyphase motor patent is issued (US Patent 381,968^[11]).
• Late 1880s: Heinrich Hertz produces and detects electromagnetic waves (Britannica^[7]).
• 1905: Einstein’s “On the Electrodynamics of Moving Bodies” unites electricity, magnetism and relativity (Ann. Phys.^[10]).
• 1930s: Ernest Lawrence’s cyclotron puts the magnetic force to work accelerating particles (NobelPrize.org^[14]).

The bottom line

Electricity and magnetism are one thing seen from different angles. A current makes a magnetic field, a changing magnetic field makes a current, and together they make light. Relativity then explains why the split between “electric” and “magnetic” depends on who is watching. From the national grid to the screen you are reading this on, it is all one force at work.

FAQ

Who discovered that electricity and magnetism are related?

Hans Christian Ørsted, in 1820, when a current deflected a compass needle (Niels Bohr Institute^[1]).

What is electromagnetic induction?

A changing magnetic flux drives a voltage in a circuit, discovered by Faraday in 1831 (Britannica^[2]).

Why does Lenz’s law have a minus sign?

The induced current opposes the change that made it, which keeps energy conserved (Britannica^[4]).

How did Maxwell know light is electromagnetic?

His equations predicted waves travelling at 1/√(μ₀ε₀), which matched the measured speed of light (Phil. Trans.^[6]).

Shop the Field Work sticker sheet, the Field Lines hoodie, or the full Electromagnetism collection.

References

1. Niels Bohr Institute, “Electromagnetism – the unique discovery”. https://nbi.ku.dk/english/www/hco/oersted/opdagelsen/
2. Encyclopaedia Britannica, “Faraday’s law of induction”. https://www.britannica.com/science/Faradays-law-of-induction
3. Feynman Lectures on Physics, Vol. II, Ch. 17: The Laws of Induction. https://www.feynmanlectures.caltech.edu/II_17.html
4. Encyclopaedia Britannica, “Lenz’s law”. https://www.britannica.com/science/Lenzs-law
5. MacLatchy, Backman & Bogan (1993) A quantitative magnetic braking experiment, Am. J. Phys. 61, 1096. https://doi.org/10.1119/1.17356
6. J. C. Maxwell (1865), “A Dynamical Theory of the Electromagnetic Field,” Phil. Trans. R. Soc. 155, 459. https://doi.org/10.1098/rstl.1865.0008
7. Encyclopaedia Britannica, “Heinrich Hertz”. https://www.britannica.com/biography/Heinrich-Hertz
8. Encyclopaedia Britannica, “Étienne-Louis Malus”. https://www.britannica.com/biography/Etienne-Louis-Malus
9. Feynman Lectures on Physics, Vol. II, Ch. 13: Magnetostatics. https://www.feynmanlectures.caltech.edu/II_13.html
10. A. Einstein (1905), “Zur Elektrodynamik bewegter Körper,” Ann. Phys. 17, 891. https://doi.org/10.1002/andp.19053221004
11. US Patent 381,968, N. Tesla, “Electro-magnetic motor” (1888). https://patents.google.com/patent/US381968A/en
12. M. Faraday, Experimental Researches in Electricity, Vol. 1 (Project Gutenberg). https://www.gutenberg.org/ebooks/14986
13. US National Weather Service, “Lightning and cars”. https://www.weather.gov/safety/lightning-cars
14. NobelPrize.org, The Nobel Prize in Physics 1939 (Lawrence). https://www.nobelprize.org/prizes/physics/1939/summary/
15. NobelPrize.org, The Nobel Prize in Physics 1985 (quantized Hall effect). https://www.nobelprize.org/prizes/physics/1985/summary/

Written by Pixelated Physics. Every factual claim is linked to the source we checked; points that are still debated are labelled open.