Question: Let j (r) be an arbitrary current distribution. (a) Show that the components of the magnetic dipole moment m = 1/ 2 d 3

Let j (r) be an arbitrary current distribution.

(a) Show that the components of the magnetic dipole moment m = 1/ 2 ∫ d³ r r × j are invariant to a rigid shift of the origin of coordinates.
(b) Show that the components of the Cartesian magnetic quadrupole moment

m = fdr (r = j);rj

are invariant to a rigid shift of the origin only if the magnetic moment vanishes.

m = fdr (r = j);rj

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