Magnetic Fields

Hold two magnets close and you can feel it: an invisible springiness in the empty air between them, pushing your hands apart or dragging them together, though nothing is touching. Slide a paperclip across the table towards a magnet and, at some invisible line, it suddenly springs into life and skates across to stick. Somewhere out there, all around the magnet, the space itself has become active.

That active region is the magnetic field: the area around a magnet (or, as you'll see later, around a wire carrying an electric current) where it can exert a force on a magnetic material or on another magnet. Step outside the field and nothing happens; step inside it and the magnet reaches out and pushes or pulls, across the gap, without ever touching. On the magnets page you met this field as "the invisible thing that grabs the paperclip." This page is about mapping it — working out its exact shape, its direction, and where it is strong or weak.

Drawing the invisible: field lines

You can't see a field, but you can make it reveal itself. Lay a bar magnet under a sheet of paper, sprinkle iron filings on top, and tap the paper. The filings don't scatter randomly — each tiny sliver turns into a miniature magnet and lines up, and together they snap into a set of sweeping curves that arc from one end of the magnet round to the other. We draw those curves as magnetic field lines: a simple, powerful map of the field.

A field line does two jobs at once. Its direction (we draw an arrow on it) tells you which way the field points — the way the force would push the North pole of a tiny test magnet placed there. And how crowded together the lines are tells you how strong the field is: bunched-up lines mean a strong field, widely-spaced lines mean a weak one. Near the poles the lines are packed tight, so that is where a magnet is strongest — exactly where the biggest clump of paperclips grabs on.

The four rules for drawing field lines

Every field-line diagram obeys the same four rules — they are worth memorising:

Outside the magnet, lines run from North to South. Each line leaves the North pole and curves round to enter the South pole. (Inside the magnet they run the other way, S back to N, so every line is a closed loop.)
Field lines never cross. At any point the field can only push one way, so two lines can never meet or touch.
Closer lines mean a stronger field. Where the lines are packed together the field is strong; where they spread apart it is weak.
The field is strongest at the poles — that's where the lines are most tightly bunched — and fades away the further out you go.

"Crowded lines" is a picture, but scientists also put a number on it. The strength of a magnetic field is called its magnetic flux density, written B, and it is measured in tesla (symbol \text{T}), named after the inventor Nikola Tesla.

A tesla is a huge field, so everyday magnets are quoted in thousandths of a tesla (millitesla, \text{mT}). The Earth's field where you are standing is only about 0.00005\ \text{T} — tiny, yet enough to swing a compass needle right round. A fridge magnet is roughly 5\ \text{mT}, a scrapyard crane magnet a few hundred millitesla, and the giant magnets inside a hospital MRI scanner reach 1.5\ \text{T} — thirty thousand times the Earth's field, and strong enough to yank a steel oxygen cylinder clean across the room.

A bar magnet's field

Here is the classic pattern — the same shape the iron filings make. The looping arrows are the field lines, leaving the red North pole and curving round to the blue South pole. Notice how they crowd together at the two ends (strong field) and spread out over the middle of the magnet (weak field).

Now the interesting part. Sitting in the field is a small plotting compass — its needle is drawn with a red North end. Drag the slider to carry the compass around the magnet and watch its needle: everywhere it goes, the needle swings to lie along the field line running through that spot, its red end pointing the way the arrow points. Park it off the North pole and the needle points away; carry it over the top and the needle flips to point back towards the South pole. The compass is reading the field's direction, point by point.

The compass: a tiny magnet that reads the field

Why does a compass line up with the field at all? Because a compass needle is itself a tiny bar magnet, balanced on a pin so it can spin freely. Drop it into a magnetic field and the field grabs its two poles — pulling the needle's North one way and its South the other — and twists it until it settles pointing along the field line, just like a weathervane settles into the wind.

This gives you a beautifully simple way to plot a field by hand, no iron filings needed. Put a plotting compass on the paper near the magnet and pencil a dot at each end of the needle. Move the compass so its tail sits where the head was, and mark the new head. Keep leap-frogging the compass across the page, join up your dots, and you have traced one field line — an arrow-straight recipe for drawing the invisible.

And there is a bigger prize hiding here. If a compass swings to point along any magnetic field, then out in an open field far from any magnet, the fact that it reliably points North can only mean one thing: the whole Earth must be sitting in a magnetic field of its own.

When two fields meet: attract, repel, and neutral points

Bring a second magnet up and the two fields blend into a single new pattern that shows, at a glance, whether the magnets pull or push:

Unlike poles (N facing S) — attract. The field lines leap straight across the gap from the North of one magnet into the South of the other, like elastic threads stretched taut between them. Lines running directly from one to the other pull the magnets together.
Like poles (N facing N) — repel. Now no line can cross the gap — two Norths both throw their lines outward, so the lines bend sharply away from each other and bulge sideways, and the magnets are pushed apart.

Between two like poles there is a special spot dead in the middle where one magnet's field points exactly one way and the other's points exactly the opposite way, so they cancel and the total field is zero. That spot is called a neutral point: a plotting compass placed there is tugged equally both ways and spins about, unable to decide — a little island of "no field" inside a busy diagram.

Permanent magnets and induced magnets

Not everything that behaves magnetically is a magnet all the time. Physicists split them into two kinds:

A permanent magnet produces its own magnetic field all by itself, all the time — a bar magnet, a fridge magnet, a compass needle. It keeps its two poles whether or not any other magnet is near. These are usually made of steel (or special alloys) because steel holds on to its magnetism.
An induced magnet is a piece of magnetic material — most often iron — that becomes a magnet only while it is inside another magnet's field. Bring a magnet near an iron nail and the nail turns into a magnet itself, and can even pick up a second nail. Take the first magnet away and the induced magnetism mostly vanishes, so the nails drop off. Iron is "soft" magnetically: easy to magnetise, but it doesn't keep it.

Here is the key fact examiners love: induced magnetism always causes attraction, never repulsion. When a magnet induces poles in a lump of iron, it always induces the opposite pole in the nearby end — so the two always pull together. That is exactly why a magnet picks up an unmagnetised paperclip no matter which end of the magnet you offer it: the paperclip obligingly grows whichever pole it needs to be attracted.

The Earth is a giant magnet

Deep down, the Earth has a core of hot, churning iron, and its swirling motion makes the whole planet behave like one colossal bar magnet buried at the centre. Its field stretches far out into space and reaches every point on the surface — which is why a compass works anywhere on Earth, in the middle of the ocean or the middle of a desert, with no magnet in sight.

The needle's North end swings to point roughly towards the Earth's geographic North — that's why it's called a "north-seeking pole," and how sailors and explorers have found their way for centuries. This same field does something else vital: high above us it deflects the stream of charged particles blasting out from the Sun (the solar wind), acting like a planet-sized shield. Where that stream leaks in near the poles it lights the sky with the shimmering aurora — the Northern and Southern Lights.

Four traps snare almost everyone with magnetic fields:

Field lines go North → South only outside the magnet. A common slip is to draw them the wrong way, or to draw them starting and stopping in mid-air. Every line is a complete loop: out of the North, round the outside, into the South.
Field lines must never cross. If your diagram has two lines touching or crossing, it's wrong — the field can only point one way at each place.
A compass needle's North actually points to a magnetic South. Unlike poles attract, so the needle's North is pulled towards the pole near the Earth's geographic North — which means that pole is really the South pole of the Earth-magnet. Confusing, but true, and a favourite exam trick.
Field lines are a model, not real objects. There are no actual strings in the air. The field is smooth and continuous everywhere; the lines are just a handy way to draw its direction and strength. You could draw twice as many, or half as many.

The Earth's magnetic field is not fixed — it drifts, weakens, and every so often flips completely over, so that a compass that pointed North would swing round to point South. These geomagnetic reversals have happened hundreds of times in the planet's history, roughly every few hundred thousand years, though never on a tidy schedule. The last full flip was about 780,000 years ago.

How can we possibly know? As molten rock erupts and freezes at the ocean floor, iron minerals inside it lock in the direction of the field at that moment, like a frozen compass. Reading these stripes of rock outward from the mid-ocean ridges reveals band after band of alternating North and South — a tape-recording of every flip the Earth has ever made, written in stone.