In this problem, you can show from Coulomb's law that the constant of proportionality in Gauss's law must be 1/ϵ0. Imagine a sphere with its center at a point charge q.
(a) Write an expression for the electric flux in terms of the field strength E and the radius r of the sphere.
(b) Use Gauss's law in the form ΦE = cq (where c is the constant of proportionality) and the electric field strength given by Coulomb's law to show that c = 1/ϵ0.