 If the Gaussian surface uniformly encloses an insulated, symmetrical charge arrangement, the formula can be simplified to

where formula_32 represents the angle between the electric field vector and the area vector.If all of the electric field lines cross the surface at 90°, the formula can be further simplified to

Because the surface area of a sphere is formula_34, the electric field a distance formula_35 away from a uniform, spherical charge arrangement is

where formula_38 is Coulomb's constant (formula_39).This formula applies to the electric field due to a point charge, outside of a conducting sphere or shell, outside of a uniformly charged insulating sphere, or between the plates of a spherical capacitor.