TITLE:
Complementing the Lagrangian Density of the E. M. Field and the Surface Integral of the p-v Vector Product
AUTHORS:
Mirwais Rashid
KEYWORDS:
Electromagnetic Field, Parallel-Vertical Product, Surface Integral
JOURNAL NAME:
Applied Mathematics,
Vol.2 No.2,
February
25,
2011
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.