By the assumption of spherical symmetry, the integrand is a constant which can be taken out of the integral. The result is 4 π π r 2 r ^ ^ ⋅ ⋅ E ( r ) = Q ε ε 0 where r̂ is a unit vector pointing radially away from the charge. Again by spherical symmetry, E points in the radial direction, and so we get E ( r ) = Q 4 π π ε ε 0 r ^ ^ r 2 which is essentially equivalent to Coulomb's law. Thus the inverse-square law dependence of the electric field in Coulomb's law follows from Gauss's law.