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

A proof is given of the vector identity proposed by Gubarev, Stodolsky, and Zakarov that relates the volume integral of the square of a three-vector field to nonlocal integrals of the curl and divergence of the field. The identity is applied to the vector potential and magnetic field of a rotating charged shell. The latter provides a straightforward application of the use of the addition theorem of spherical harmonics.