Solution of Maxwell's equations by matrix formulation

摘要

The usual approach in solving Maxwell's equations with given current distribution is by means of finding the vector potential function due to the current source. This approach is generally intensive, for it contains vector differential operations in addition to the integration. This paper presents the detailed derivation of useful formulas for finding electromagnetic fields, such that the complicated vector differential operations are replaced by the simple vector algebraic operations. The resulting solutions are exact, and can be explicitly written in matrix formulation such that both the current source and the resulting fields may be conveniently expressed in terms of any desired coordinate systems. If the fields in the near or far region are of primary interest, this formulation only requires a matrix multiplication, whenever the radiation vector is determined.