Bar magnet and magnetic materials

Bar magnets and magnetic materials

A bar magnet behaves like a magnetic dipole with moment m directed from its south pole to its north pole (inside the magnet). Its field pattern is like that of a solenoid of the same shape. Magnetic field lines form closed loops: outside the magnet they run from N to S, inside from S to N. This is because isolated magnetic poles (monopoles) do not exist.

For a short bar magnet at large distance r:

• Axial line: B = (μ₀/4π)(2m/r³).
• Equatorial line: B = (μ₀/4π)(m/r³), opposite to m.

In a uniform field, a bar magnet feels torque τ = mB sin θ and has potential energy U = –mB cos θ.

Magnetisation and susceptibility: a material placed in a field H gets a magnetisation M = χH, where χ is the magnetic susceptibility. Relative permeability μ_r = 1 + χ, and μ = μ₀μ_r.

Classes of materials:

• Diamagnetic (bismuth, copper, water, superconductors): χ small and negative, μ_r slightly less than 1. They are weakly repelled by a magnet and move from stronger to weaker field regions. A superconductor is a perfect diamagnet (χ = –1); expelling the field is the Meissner effect.
• Paramagnetic (aluminium, sodium, oxygen): χ small and positive. Weakly attracted. χ ∝ 1/T (Curie’s law).
• Ferromagnetic (iron, cobalt, nickel): χ very large and positive, due to domains. Strongly attracted. Above the Curie temperature they become paramagnetic.

Key points

• Field lines of a magnet are closed loops; no magnetic monopoles.
• μ_r = 1 + χ.
• Dia: χ < 0. Para: small χ > 0. Ferro: very large χ > 0.
• Curie’s law for paramagnets: χ ∝ 1/T.

Exam tips

• Classification questions (which material is diamagnetic, etc.) are common.
• Learn behaviour in a non-uniform field: dia moves to weaker field, para and ferro to stronger field.

Common mistakes

• Thinking magnetic field lines start at N and end at S (they continue inside).
• Calling copper or water paramagnetic; both are diamagnetic.
• Believing ferromagnetism exists at all temperatures.