If Coulomb's law involved `1/(r^3)` dependence (instead of `1/(r^2)`), would Gauss'law be still true?

If Coulomb's law involved 1//r^3 dependence (instead of 1//r^2 ), would Gauss's law be still true ?

Answer carefully: If Coulomb’s law involved 1//r^3 dependence (instead of 1//r^2 ), would Gauss’s law be still true ?

Answer carefully: (a) Two large conducting spheres carrying charges Q_(1) and Q_(2) are brought close to each other. Is the magnitude of electrostatic force between them exactly given by Q_(1) Q_(2)//4pi epsilon_(0) r_(2) , where r is the distance between their centers? (b) If Coulomb’s law involved 1//r^(3) dependence (instead of 1//r^(2) ), would Gauss’s law be still true ? (c) A small test charge is released at rest at a point in an electrostatic field configuration. Will it travel along the field line passing through that point? (d) What is the work done by the field of a nucleus in a complete circular orbit of the electron? What if the orbit is elliptical? (e) We know that electric field is discontinuous across the surface of a charged conductor. Is electric potential also discontinuous there? (f) What meaning would you give to the capacitance of a single conductor? (g) Guess a possible reason why water has a much greater dielectric constant (= 80) than say, mica (= 6).

If Coulomb's law involved 1/r^3 (instead of 1/r^2) , would Gauss's law still be true?

If Coulomb's law involved 1/r^3 (instead of 1/r^2) , would Gauss's law still be true?

If Coulomb's law involved 1/r^3 instead of 1/r^2 , would Gauss's law still be true?

Gauss's law part-1

Gauss's law part-2