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A proof is given of the vector identity proposed by Gubarev, Stodolsky andZakarov that relates the volume integral of the square of a 3-vector field tonon-local integrals of the curl and divergence of the field. The identity isapplied to the case of the magnetic vector potential and magnetic field of arotating charged shell. The latter provides a straightforward exercise in theuse of the addition theorem of spherical harmonics.

On an identity for the volume integral of the square of a vector field