Magnetism: Moving Charges and Aligned Spins

One force wearing two faces#

Rub a balloon on your hair and it sticks to a wall; that is electricity. Hold a magnet near a paperclip and it leaps across a gap; that is magnetism. For centuries these looked like two unrelated mysteries. They are not. Electricity and magnetism are two aspects of a single electromagnetic force, and the bridge between them is deceptively simple: magnetism is what moving electric charge produces.

This is the first misconception worth demolishing. Magnetism is not a separate force that happens to live inside certain rocks. A charge sitting perfectly still makes an electric field and nothing more. Set that same charge moving — as a current in a wire, or as the ceaseless motion of electrons inside an atom — and a magnetic field appears around it. Stop the motion and the magnetic field vanishes. There is no magnetism without moving charge.

The unification runs even deeper than "currents make fields." Whether a field looks electric or magnetic depends on how you are moving relative to the charges. A row of charges that looks purely electric to someone standing still looks partly magnetic to someone gliding past, because in their frame the charges are moving. James Clerk Maxwell stitched the two together in the 1860s into one set of equations, and Einstein later showed that relativity makes the pairing inevitable: the electric and magnetic fields are two components of one thing.

A current is a magnet#

The cleanest demonstration is a straight wire. Send a current $I$ through it and the wire becomes wrapped in circular magnetic field lines. The strength at distance $r$ is

$$B = \frac{\mu_0 I}{2\pi r}$$

where $\mu_0$ is the permeability of free space. Double the current and you double the field; move twice as far away and the field halves. The direction follows the right-hand rule: point your right thumb along the current, and your fingers curl the way the field lines circle the wire. Reverse the current and the field reverses with it.

Now bend that wire into a loop, then stack many loops into a coil — a solenoid. Inside the coil the field of every turn points the same way, so the contributions add. A tightly wound solenoid carrying current has a field almost identical to a bar magnet's: a north pole at one end, a south at the other, and closed field lines looping from one to the other outside. This is not an analogy — it is why an electromagnet works, and why an electric motor spins. Feed current through coils and you have made a magnet you can switch on, off, and reverse at will.

The mirror image of this is the force a field exerts back on a moving charge. A charge $q$ moving with velocity $\vec{v}$ through a field $\vec{B}$ feels the Lorentz force

$$\vec{F} = q\,\vec{v} \times \vec{B}$$

The cross product means the force is perpendicular to both the motion and the field — which is exactly why a current-carrying wire in a magnetic field gets pushed sideways, the effect that turns motors and drives loudspeakers. These same moving fields, oscillating together and racing off through space, are the electromagnetic waves we call light.

Where do permanent magnets get their motion?#

If magnetism needs moving charge, what is moving inside a cold, static bar magnet on your desk? The answer lives inside its atoms. Every electron carries an intrinsic property called spin, and both that spin and the electron's orbital motion act like tiny current loops — each electron is a minuscule magnet. In most materials these atomic magnets point every which way and cancel out. In a few, they cooperate.

Domains: why only a few metals are magnetic#

Here is the second big misconception: not all metals are magnetic. Copper, aluminium, gold, and lead are barely magnetic at all. Only ferromagnetic materials — chiefly iron, nickel, and cobalt, plus some of their alloys — are strongly magnetic. What sets them apart is that their atomic magnetic moments spontaneously line up with their neighbours, forming microscopic regions called domains in which trillions of atomic magnets all point the same way.

In an unmagnetized piece of iron the domains themselves point in random directions, so their fields cancel and the lump shows no net magnetism. Apply an external field and the domains that already point the right way grow at the expense of the others, and the rest rotate into line. Once most domains agree, their fields add into a strong bulk magnetization — the iron has become a magnet.

Crucially, this alignment can be undone. Heating or hammering the magnet shakes the domains and lets them tumble back into random orientations, wiping out the net field — which is why a dropped magnet weakens. Every ferromagnet has a Curie temperature above which thermal jostling overwhelms the alignment entirely and the material stops being magnetic. Iron's is about 770 °C. This is also the difference between a permanent magnet and a temporary one: "hard" magnetic materials hold their domain alignment stubbornly, while "soft" iron follows an applied field and relaxes the moment it is removed.

No such thing as half a magnet#

The third misconception is the seductive idea of a single pole — a north without a south. It never happens. Because magnetic field lines always close into complete loops, poles come strictly in pairs. Take a bar magnet and cut it in half hoping to isolate its north end, and you do not get a lone north; you get two smaller complete magnets, each with its own fresh north and south. Cut again and you get four dipoles. Keep going down to a single atom and you still have a dipole.

This is a deep structural fact. An electric charge can be isolated — a lone electron carries negative charge with no positive partner nearby. But no experiment has ever found an isolated magnetic monopole. Some theories beyond the Standard Model predict they might exist somewhere in the universe, and physicists have searched hard, but none has ever been seen. As far as every magnet you will ever handle is concerned, magnetism comes only in dipoles.

That closed-loop, dipole structure scales all the way up. The planet beneath you is a magnet because of currents churning in its molten core, giving it a north and south pole and a field that shelters life — the story of Earth's magnetic field. And when certain metals are cooled until their electrical resistance vanishes, they expel magnetic fields entirely, a striking quantum twist explored in superconductivity.

The one idea to keep#

Strip away the details and a single thread ties it all together. Moving charge makes magnetic fields; magnetic fields push moving charge; and the fields themselves are inseparable from the electric ones. A wire, a spinning electron, and the Earth's liquid core are all doing the same fundamental thing. Magnetism was never a force apart — it is electricity in motion, seen from the side.