Electric fields on a two-dimensional spherical surface

Previous works have addressed the effects of geometry on Maxwell's equations. Global solutions have been found for radiation solutions, electro-magnetic fields with no charges. For electro-magnetic fields from charges, mostly local solutions have been researched. We present a look at the effects of geometry on E-fields and address the common misconception of E-field termination. First, an alternative procedure of the classical theory is presented through the introduction of time to the formulation. We then use this formulation to examine the generation of an E-field on a two-sphere. We find that it is not possible to establish a static E-field on a spherical surface and, therefore, no global solutions can be found for a point source. We next use a two-sphere to formulate a way of using classical electrostatics on a limited portion of the confined space. This results in an E-field that is modified by the geometry of the 2D space. We give corresponding equations for the 3D case and apply the results to a cosmological model.