The four-dimensional space-time of special relativity is augmented with a fifth dimension to take into account the gauge transformation of the electromagnetic potentials. And in doing this, a new field is introduced purely from dimensional consideration. It will be shown in this paper that this field plays an especially important role inside the electron. It gives rise naturally to the Poincare stress needed for maintaining dynamical equilibrium within an extensive electron, it also reflects the dielectric constant and permeability of the medium within. It thus appears feasible to adopt a fluid structure for the extensive electron, and stable solution for the motion of the fluid particiea has been obtained in general. The electrodynamics within the electron has also been obtained, and no physical solution with spherical symmetry exists. Axially symmetrical solution probably exists, which will be discussed in a subsequent paper.