On Variational Principles for Electromagnetic Theory

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Abstract
New variational principles for electromagnetic theory are established. A functional consisting of the field vectors is defined through the use of a convolution, and it is shown that the variation of this functional subject to appropriate constraints is completely equivalent to Maxwell's equations, Ohm's law, and the constitutive equations, together with appropriate boundary and initial conditions. The present formulation does not have the defects of the classical variational principle for electromagnetic theory since it does not require the introduction of scalar and vector potentials and a priori knowledge of the field vectors at the final stage. Two variational formulations for the electric and magnetic field vectors alone are also presented.

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