How Magnets Attract: Field Lines, Domains and the Physics Kids Feel

A magnet is made of a billion tiny magnets

Every atom of iron behaves like an unimaginably small magnet, because its electrons spin in a way that gives the atom a tiny magnetic moment. In an ordinary piece of iron, these atomic moments point in random directions and cancel out, so the metal shows no overall magnetism. Inside a permanent magnet, though, huge numbers of neighbouring atoms lock together into regions called domains, each domain acting like one large, unified compass needle. When most of a material's domains are aligned in the same direction, their individual fields add up instead of cancelling, and the whole object becomes a magnet with a real north and south pole.

Field lines: mapping an invisible push and pull

A magnet doesn't need to touch something to affect it — it fills the space around it with a magnetic field, usually drawn as looping lines that leave the north pole, curve through the surrounding space, and re-enter at the south pole. Field lines are a bookkeeping device, not physical threads, but they capture two real facts at once: their direction shows which way a compass needle would point at that spot, and how close together they are shows how strong the field is there. Near the poles, where the lines bunch up tightly, the field is strong and the pull on a paperclip is fierce; further out, where the lines spread apart, the pull fades quickly.

Induced magnetism: the paperclip becomes a magnet too

A paperclip has no magnetism of its own sitting on a table. The moment a real magnet gets close, though, its field pushes the paperclip's own domains into alignment — the paperclip becomes a temporary induced magnet, with its near end taking on the opposite pole to the magnet facing it. Opposite poles attract, so the paperclip is pulled straight toward the source. This is why a magnet attracts a paperclip even though the paperclip started out with no field of its own — the attraction is always toward whichever pole is inducing the alignment, which is why it never matters which end of the magnet you use.

F(dipole)  ∝  1 / r⁴     (force between two small magnetic dipoles)

compare:
F(gravity)         ∝  1 / r²     (Newton, point masses)
F(electric charge) ∝  1 / r²     (Coulomb, point charges)

a magnet's pull fades MUCH faster with distance than gravity does

This is the physics behind the classic "how close does the paperclip need to be" experiment: because dipole-dipole attraction falls off so steeply with distance, a magnet that can fling a paperclip across a centimetre of table can be almost undetectable a few centimetres further away. It also explains why a stack of paperclips can hang in a chain from a single magnet — the paperclip touching the magnet becomes strongly induced and magnetises the next one down the line, each link a little weaker than the one above it, until the chain gets too long and the weakest link falls off.

Only some metals play along

Not everything metallic responds. Only ferromagnetic elements — iron, nickel, cobalt, and a handful of alloys and rare-earth compounds built from them — have the atomic structure that lets domains form and align strongly. That is precisely why steel paperclips (mostly iron) snap toward a magnet while aluminium foil, copper wire and most coins barely notice one at all: their atoms are magnetic individually, but nothing locks their moments into a large, coordinated domain the way iron's crystal structure does.

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