12.1 Magnetic Fields

A magnetic field is a vector field. At each point it has a size and a direction, and it tells you the magnetic force on moving charges, currents or magnetic materials placed there. The unit of magnetic field is the tesla (T). Earth's field at the surface is about 5 × 10⁻⁵ T; a strong fridge magnet is around 0.01 T.

Every magnetic field comes from magnetic dipoles: objects with a north pole and a south pole. There are no magnetic monopoles, meaning a lone north or south pole. Break a bar magnet in half and you don't get a separate north and south; you get two smaller magnets, each with both poles.

Like poles repel and opposite poles attract. A dipole's field gets weaker as you move away from it.

Magnetic field lines always form closed loops. Outside a bar magnet, they leave the north pole, curve around and enter the south pole. Inside the magnet, they run from south back to north, closing the loop. This is a big difference from electric field lines, which start and stop on charges.

As with electric fields, lines are closer together where the field is stronger (near the poles), and they never cross. A vector field map shows the same thing with arrows.

A compass needle is a small dipole. In a magnetic field, it turns until it lines up with the field, with its north end pointing along the field direction. Moving a compass around a magnet traces out the field lines.

Earth's field is roughly the field of a giant bar magnet. A compass's north end points toward Earth's geographic north, so the magnetic pole up there is actually a south magnetic pole: it attracts the compass's north end.

Magnetic dipoles come from charges moving in circles or spinning. In materials, that's the motion and spin of electrons in atoms. Each atom can act like a tiny dipole. In most materials, these atomic dipoles point in random directions and cancel out.

Both permanent magnets and temporarily magnetized objects get their magnetism the same way: many atomic dipoles lining up in the same direction.

What a material is made of decides how it reacts when you put it in a magnetic field.

• Ferromagnetic materials (iron, nickel, cobalt) have regions called domains, where huge numbers of atomic dipoles already point the same way. An outside field makes the domains line up, and they can stay lined up after the field is removed, making a permanent magnet. That's why a paper clip sticks to a magnet and can become a weak magnet itself.
• Paramagnetic materials (aluminum, titanium, magnesium) are weakly attracted. Their atomic dipoles line up a little with an outside field, but the alignment disappears when the field is removed.
• Diamagnetism is present in all materials: their electrons respond with a weak alignment opposite to the outside field, so they're very slightly repelled. It's usually hidden by the stronger effects above.
• Magnetic permeability measures how strongly a material becomes magnetized in an outside field. Empty space has a fixed value, the vacuum permeability μ₀ = 4π × 10⁻⁷ T·m/A. A material's permeability isn't a constant; it can change with temperature, orientation and the strength of the outside field.