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Complementing the Lagrangian Density of the E. M. Field and the Surface Integral of the p-v Vector Product
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Applied Mathematics·Volume 02 (2011)·Pages 225–229·Published 25 February 2011·DOI10.4236/am.2011.22024
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Abstract
Considering the Lagrangian density of the electromagnetic field, a 4 × 4 transformation matrix is found which can be used to include two of the symmetrized Maxwell’s equations as one of the Euler-Lagrange equations of the complete Lagrangian density. The 4 × 4 transformation matrix introduces newly defined vector products. In a Theorem the surface integral of one of the newly defined vector products is shown to be reduced to a line integral.
KeywordsElectromagnetic FieldParallel-Vertical ProductSurface Integral
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