Why Magnets Push and Pull: The Weirdness of Magnetic Force

Why Magnetic Force Is So Weird

Magnets are familiar. You’ve stuck things to refrigerators your whole life. Compasses point north. MRI machines produce images of your brain. Electric motors spin. We take magnetism for granted.

But stop and think about it: what is magnetic force?

Electric force is straightforward—charges attract or repel along the line connecting them. Positive and negative, push and pull. Simple. But magnetic force? A moving charge near a current-carrying wire feels a force that depends on its velocity, acts perpendicular to its motion, and vanishes the moment it stops moving. That’s bizarre.

Why should motion matter? Why perpendicular? Where does this strange sideways push come from?

Here’s the puzzle: classical physics describes electric and magnetic forces with the Lorentz force law, F = q(E + v×B). Electric force just pushes along the field direction. Magnetic force requires velocity and shoves sideways. Maxwell unified these into the electromagnetic field, treating them as aspects of one thing. But that still leaves the question: is magnetism a separate fundamental force, or something else entirely?

The answer is shocking. Magnetism isn’t fundamental at all. It’s electricity viewed from a moving reference frame.

Are There Really Two Kinds of Force?

Let me set up the classical picture first. Electric fields arise from stationary charges. Put a proton over here, it creates a field around it—we can visualize it as coloring space red. Put an electron there, space turns blue. Like colors repel, opposite colors attract. Charged particles feel forces along these field lines.

Magnetic fields arise from moving charges. Current in a wire creates a magnetic field wrapping in circles around it. Another moving charge near that wire feels a force perpendicular to both its velocity and the field direction. Particles spiral in magnetic fields rather than moving straight. Electromagnets work by coiling current-carrying wires so individual electron magnetic fields add up into larger structures with north and south poles.

And permanent magnets? Those come from quantum spin—electrons behaving as if rotating on their axes, each one a tiny magnet. When enough spins align in a material like iron, you get macroscopic magnetism without any current you can see.

So far, so classical. Electric fields from charges at rest, magnetic fields from charges in motion. Two different phenomena, two different field types. Right?

Wrong. There’s only one electromagnetic field. What you call “electric” versus “magnetic” depends on how you’re moving.

Change Your Frame, Change the Force

Here’s where it gets profound. Consider a current-carrying wire—copper atoms locked in a lattice, with free electrons drifting through it. In the lab frame, the wire is electrically neutral: positive protons in the lattice exactly balance moving electrons. A positive test charge sitting still next to the wire feels no force at all.

Now set that test charge moving parallel to the wire, same direction as the drifting electrons. What happens? Suddenly it feels a force—pushed away from the wire. Classical physics calls this “magnetic force.”

But let’s shift reference frames. Jump to the test charge’s frame, where it’s sitting still. Now the wire is moving relative to you. The protons in the lattice are moving backward. The electrons—originally drifting in the wire—are now closer to stationary relative to you.

Here’s the key: special relativity says moving objects contract along their direction of motion. The faster something moves relative to you, the more it’s squished.

The protons, now moving faster in your frame, contract—bunching closer together. The electrons, moving slower, spread apart. In your new reference frame, the positive charge density is higher than the negative charge density. The wire isn’t neutral anymore! It appears positively charged.

And a positive test charge next to a positively charged wire experiences—what? Plain old electric repulsion. Not magnetic force at all.

The “magnetic force” in the lab frame is just electric force in the moving frame. Different observers, measuring the same physical situation, disagree about whether the force is electric or magnetic. But they agree perfectly on the actual motion of charges.

Relativity at a Millimeter Per Second

Here’s the mind-bending part. Electrons in household wires drift at maybe a millimeter per second. Nowhere near the speed of light. Relativistic effects should be unmeasurably tiny at those speeds.

Yet magnetic forces are huge. Motors work. Generators work. Compasses point north. How can relativistic length contraction matter at walking pace?

The answer: electromagnetic forces are extremely strong. Electric and magnetic interactions couple with a strength characterized by the fine structure constant, about 1/137. Gravity is something like 10^36 times weaker. When your baseline force is that enormous, even the tiniest relativistic correction produces measurable effects.

Think about it. A millimeter-per-second drift velocity gives a relativistic correction proportional to (v/c)². That’s roughly 10^-23 or so—absolutely minuscule. But multiply that by an electric force that would otherwise be strong enough to tear atoms apart, and you get… the magnetic force from a current-carrying wire.

This is profoundly weird. Humanity discovered magnets millennia before Einstein. We used compasses, built motors, wrote Maxwell’s equations. And the whole time, we were unknowingly observing relativistic effects. Spacetime geometry shows up in your refrigerator magnets.

The Force That Isn’t Fundamental

So what’s actually going on?

There’s one electromagnetic field. In the mathematical formalism, it’s a tensor—an object that combines electric and magnetic components and transforms consistently between reference frames. When you change reference frames, electric field components mix with magnetic field components. What one observer calls purely electric, another calls partly magnetic. What one sees as magnetic, another sees as electric.

This isn’t some interpretation trick. The same underlying field produces forces that appear different depending on your motion. The electromagnetic field itself is fundamental. The division into E and B is observer-dependent.

Faraday discovered that changing magnetic fields induce electric currents—electromagnetic induction powers our entire civilization. Changing magnetic field produces electric field. From the relativistic view, this makes perfect sense: if electric and magnetic are the same thing viewed from different motion states, then changing your relative motion (accelerating) mixes them dynamically.

Even quantum electrodynamics—our most precise theory, matching experiments to 10 significant figures—describes one electromagnetic interaction, mediated by virtual photon exchange. The electron doesn’t care whether you call the force electric or magnetic. It just responds to the unified field.

Magnetism feels fundamental because we’ve known it forever. But it’s actually emergent—a relativistic correction to electrostatics. The magnetic force you feel when a fridge magnet grips metal is electricity in disguise, twisted by the fact that charges are moving and your reference frame is not the same as theirs.

Every time you pick up a magnet, you’re holding spacetime geometry in your hands. And that, to me, is one of the most beautiful facts in physics.