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In electromagnetic statics, the standard procedure to determine the electricscalar potential or magnetic vector potential in a bounded space is to solvePoisson's equation subject to certain boundary conditions. On the other hand,as a direct generalization of Coulomb's law or Biot-Savart law, the staticelectromagnetic potentials may also be obtained by directly integrating theelectric charge or current distributions over the region (either volume orsurface) where they are spread out. What is the relation between these twoformalisms? In this article, we prove that they are in fact equivalent to eachother in mathematics. Examples are also presented to explicitly show thevalidity of this equivalence.

Equivalence of Two Methods to Solve Static Electromagnetic Potentials