The bar magnet and its field

A bar magnet has a north pole and a south pole. Its field looks exactly like the field of a current-carrying solenoid: a bar magnet behaves like a coil of tiny currents (from its electrons).

Its strength is the magnetic moment m, a vector pointing from S to N inside the magnet. Unit: J/T (or A m²).

There are no single poles. Cut a magnet in half and you get two smaller magnets, each with its own N and S. A separate north pole (a magnetic monopole) has never been found.

Magnetic field lines:

• Outside the magnet they go from N to S; inside they go from S to N. So every line is a closed loop.
• They never cross.
• Crowded lines mean a strong field.

Compare electric field lines, which start and end on charges. Magnetic lines have nowhere to start or end, because there are no magnetic charges.

Gauss's law for magnetism: the net magnetic flux through any closed surface is zero. Every line that goes in also comes out.

Far from a short magnet, the field looks like an electric dipole's, with µ₀/4π in place of k:

• Axial line: B = (µ₀/4π) × 2m / r³, along m.
• Equatorial line: B = (µ₀/4π) × m / r³, half as much, and opposite to m.

Example: m = 1 J/T, 10 cm away on the equatorial line: B = 10⁻⁷ × 1 / (0.1)³ = 10⁻⁴ T. On the axis it would be 2 × 10⁻⁴ T.