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2012•Sri Lankan Journal of PhysicsOpen access

Longitudinal and transverse components of a vector field

Alexander Stewart

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Abstract

A unified account, from a pedagogical perspective, is given of the longitudinal and transverse projective delta functions proposed by Belinfante and of their relation to the Helmholtz theorem for the decomposition of a vector field into its longitudinal and transverse components. It is argued that the results are applicable to fields that are time-dependent as well as fields that are time-independent. Keywords: Classical electromagnetism; Helmholtz's theorem; transverse; longitudinalDOI: http://dx.doi.org/10.4038/sljp.v12i0.3504Sri Lankan Journal of Physics, Vol. 12 (2011) 33-42

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A unified account, from a pedagogical perspective, is given of the longitudinal and transverse projective delta functions proposed by Belinfante and of their relation to the Helmholtz theorem for the decomposition of a vector field into its longitudinal and transverse components. It is argued that the results are applicable to fields that are time-dependent as well as fields that are time-independent. Keywords: Classical electromagnetism; Helmholtz's theorem; transverse; longitudinalDOI: http://dx.doi.org/10.4038/sljp.v12i0.3504Sri Lankan Journal of Physics, Vol. 12 (2011) 33-42

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Available abstract

A unified account, from a pedagogical perspective, is given of the longitudinal and transverse projective delta functions proposed by Belinfante and of their relation to the Helmholtz theorem for the decomposition of a vector field into its longitudinal and transverse components. It is argued that the results are applicable to fields that are time-dependent as well as fields that are time-independent. Keywords: Classical electromagnetism; Helmholtz's theorem; transverse; longitudinalDOI: http://dx.doi.org/10.4038/sljp.v12i0.3504Sri Lankan Journal of Physics, Vol. 12 (2011) 33-42

Key concepts: Transverse plane, Longitudinal field, Helmholtz free energy, Field (mathematics), Vector field, Physics, Mathematical analysis, Pure mathematics

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