ABSTRACT
As in many other disciplines, there exists set of differential equations that fixes the setting of electromagnetism. Maxwell equations govern the relation among electric and magnetic fields. One of the reasons for the difficulty may lie in the fact that Maxwell equations do not explicitly exhibit current to be a continuous flow. In this chapter, the authors prove that electric current is a continuous flow. The continuous-part is shown by the equation of continuity as with fluid flows. The authors show the flow-part by reducing the Maxwell equations to two partial DEs and one wave equation satisfied by shift which appears as an auxiliary term by slightly modifying argument. Since both fluid and electric current are flows, it is natural to apply differential forms rather than treating the 2- and 3-dimensional flows separately. The authors give a rather transparent treatment by an efficient use of differential forms which has been applied successfully in reference in fluid dynamics.
