Magnetic Fields and Flux Density

Magnetic field — a region in which a magnetic material, a current-carrying conductor, or a moving charge experiences a force.

Field lines run from north to south outside a magnet, and south to north inside it. They never cross, and closer lines mean a stronger field.

Fields produced by currents

A long straight wire — the field lines are concentric circles around the wire. Point the right thumb along the conventional current and the fingers curl in the direction of the field.

A flat coil — the circular fields of each part of the loop reinforce at the centre, giving a field through the middle of the loop.

A solenoid — the field inside is strong and nearly uniform, running along the axis, and outside it looks like the field of a bar magnet. Curl the right hand's fingers in the direction of the current and the thumb points to the north end.

Magnetic flux density (B) — the strength of a magnetic field, defined through the force it exerts on a current-carrying conductor. Measured in teslas (T), where one tesla is one newton per amp per metre.

One tesla is a very strong field — the Earth's field is around 5 × 10⁻⁵ T, a fridge magnet a few times 10⁻³ T, and an MRI scanner 1 to 3 T. Laboratory electromagnets reach a few tens of teslas.

Example: the name "flux density" is a clue, not decoration. B is the amount of magnetic flux passing through unit area, Φ = BA, which is exactly what "density of flux" means. Keeping that in mind makes flux linkage and induction far less arbitrary when you reach them.

Permanent magnets are not the only source — every magnetic field ultimately comes from moving charge, whether that is a current in a wire or the motion of electrons within atoms. There is no magnetic equivalent of an isolated charge: cutting a bar magnet in half gives two complete magnets, never a separate north pole.