Write the expressions for the magnetic field of a short bar magnet at a far point on (a) its axial line and (b) its equatorial line. Show the directions on a diagram, and compare them with an electric dipole.

1. 1 · Define the lines. Axial line: through the poles. Equatorial line: through the centre, perpendicular to the axis.
2. 2 · Write the results.
   • Axial: B = (μ₀/4π)(2m/r³), along m.
   • Equatorial: B = (μ₀/4π)(m/r³), opposite to m.
3. 3 · Draw. [Magnet S to N with m; P on the axis with B along m; R on the equatorial line with B opposite to m; r marked]
4. 4 · Compare. Same forms as the electric dipole with 1/ε₀ → μ₀ and p → m; ratio 2 : 1; both ∝ 1/r³.
5. 5 · Real life. A phone's compass reading drops sharply as a magnet moves away, since B ∝ 1/r³.
6. 6 · Close in one line. So, a bar magnet's far field is the field of a magnetic dipole.

Scoring tip: Say 'results only, far point' and give both directions. The directions are where most marks are lost.