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arXiv · 0705.2081

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

A. M. Stewart
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Abstract

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

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A. M. Stewart. 2007-05-15. On an identity for the volume integral of the square of a vector field. https://doi.org/10.1119/1.2426352

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