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