The interval of propagation in Maxwell’s theory is lightlike. If we assume that the interval is timelike, instead, by introducing a fundamental length, a rich new theory emerges. In this article it is shown that by varying the interval with respect to the fundamental length, the Lienard-Wiechert (LW) potential automatically emerges.Then by varying the fundamental length in the expression for the moment of LW potential about the interval of propagation, the total field of a single point charge moving with arbitrary velocity and acceleration also emerges.They have exactly the same form as in Maxwell’s theory but are finite everywhere, have finite self-effects and obey the Lorenz gauge condition.This is accomplished without using Maxwell’s eqs at all. Only the interval of propagation is used.The Lorentz force, the field Lagrangian density, the energy stress tensor, all have the same form, are finite everywhere and have finite self effects.This shows that there exist at least one consistent theory different from Maxwell’s theory which gives the same results while eliminating the infinities of Maxwell’s theory in a Lorentz covariant way.