UPSC Combined Geo-Scientist, Mains · 2017 · Mains Paper II

Q1(i). Units of magnetic moment

Question

Show that magnetic dipole moment has unit A m², equivalent to J T⁻¹, where T is tesla.

1 A m²=1 J T⁻¹.

A current loop has magnetic moment μ=IAn̂, so its SI unit is ampere times square metre.
Its energy in a uniform magnetic field is U=-μ· B, requiring [μ]=J/T.
From the magnetic force on a wire, F=BIl, one tesla is N/(A m). Therefore J/T=(N m)/(N/(A m))=A m².
Torque gives the same dimensional check: τ=μ× B, with torque in N m.

The full model answer

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