Question

If coulombs law involved 1/r³ dependence, where r is distance between two point charges would gausss law be true? Why?

Answer 1

NO the gauss law is not valid because gauss theorm is based on inverse square dependence of electric field on the distance
$$\begin{gathered} letuscheckthethevalidityofgausslaw \\ E.ds=\frac{kq}{r^3}\times 4\pi r^2(takingachargeqinsideasphere) \\ =\frac{q\times 4\pi }{4\pi {\xi }_{0}r}=\frac{q}{{\xi }_{0}r} \\ henceabovewecanseethatgausslawisinvalid. \end{gathered}$$