Bar Magnet & Dipole Field

A bar magnet is a permanent magnet with two opposite POLES at its ends — by convention North (N) and South (S).

Magnetic field lines emerge from N, curve around, and enter S externally. Inside the magnet they go S → N (closed loops, no monopoles).

Magnetic dipole moment: m = NIA (for a current loop equivalent) or m = qm × 2L for a magnetic-charge bar magnet.

Field along the AXIAL line (on the magnet's axis, distance r ≫ L): B_axial = (μ₀/4π)·(2m/r³).

Field along the EQUATORIAL line (perpendicular bisector, distance r ≫ L): B_equatorial = (μ₀/4π)·(m/r³). Half the axial field.

Like poles repel, unlike attract — force ∝ 1/r⁴ for short bar magnets along axial line.

Cutting a bar magnet in half produces TWO smaller bar magnets, each with its own N and S — NO isolated monopoles.

Earth itself acts as a giant bar magnet (approximately) — used in compass navigation.