​ If Coulomb’s law involved 1\r^3. (instead of 1\r^2 ), Gauss law be still true? ​

Question

If Coulomb’s law involved \(\frac{1}{r^3}\). (instead of \(\frac{1}{r^2}\)), Gauss law be still true?

Answer 1

The surface area in space varies as r² so that field varies as\(\frac{1}{r^2}\). Hence \(\frac{1}{r^2}\) dependence is essential.