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.

Determine the magnitude E(r) by applying Gauss's law.