Practice portal › Magnetism and Matter › Bar Magnet and Dipole in a Field
Asked in RS Academy GUJCET booklet · Field of a bar magnet and earth's field
Idea: use the exact axial field of a real magnet rather than the short-dipole shortcut. For a bar magnet of half-length l and moment m, the field on the axis at distance r from the centre is
B=(μ₀)/(4π)(2mr)/((r²-l²)²).
When r l the l² is negligible and this becomes (μ₀)/(4π)(2m)/(r³), the familiar inverse-cube law.
But close to the magnet, where r is comparable with l, the (r²-l²)² matters and the field falls off more steeply than 1/(r³).
The word 'always' is what decides the question: no single power of r works at every point on the axis.
So the field is not necessarily proportional to 1/(r³) at all points.
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