A 3-D Tensorial Integral Formulation of Scattering Containing Intriguing Relations

We investigate the role of the electric field and its normal derivative in 3-D electromagnetic scattering theory. We present an alternative integral equation formulation that uses the electric field and its normal derivative as the boundary unknowns. In particular, we extend a traditional formulation that is used in 2-D scattering theory to three-dimensions. We uncover several intriguing relationships involving closed surface integrals of the field and/or its derivative. In order not to obscure the physical/geometric awareness, the derivation is made from a tensor calculus perspective.