Transient front and initial conditions in Maxwell’s theory

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Abstract
Through investigating the transient front, initial conditions are obtained from the time domain electromagnetic problem involving objects with edges or vertices. These conditions are required so that Maxwell’s divergence equations are satisfied away from a radiating surface. Via a simple example, it is demonstrated that when such idealized geometries are considered, the time dependence of the source in such a problem cannot be chosen arbitrarily under Maxwell’s theory.