On the Unification of Electrostatics and Magnetostatics via Maxwell's Equations

It has been widely accepted that Maxwell's equations have provided unification of electricity, magnetism and light. This paper asserts that the equations for the time-independent case have not unified electrostatics and magnetostatics so far. They only remain separated as two distinct sets of equations along with their solutions of Coulomb's and Biot-Savart laws for electric and magnetic fields respectively. Using the single electric field-impulse instead of traditional fields and/or potentials, we present the unification of both electrostatics and magnetostatics via single second-order equation. Such second-order equation is readily extendable to wave equation for electrodynamics. The wave equation or its first-order field-impulse equations would find usefulness in applications of classical/quantum electromagnetics and facilitate computational electromagnetics.