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

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

2007-05-15

arxiv.org/abs/0705.2081v3

American Journal of Physics, 75 (6) 561-564 (2007)

Physics

Classical Physics

Based upon the paper in Am. J. Phys., but contains also a derivation of the central result that is valid for the scalar produc

Scientific paper

10.1119/1.2426352

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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