Consider a point charge q in three-dimensional space. symmetry requires the electric field to point directly away from the charge in all directions. to find e(r), the magnitude of the field at distance r from the charge, the logical gaussian surface is a sphere centered at the charge. the electric field is normal to this surface, so the dot product of the electric field and an infinitesimal surface element involves cos(0)=1. the flux integral is therefore reduced to ∫e(r)da=e(r)a(r), where e(r) is the magnitude of the electric field on the gaussian surface, and a(r) is the area of the surface.