[ScienceLover (OP)]

Would Gauss’s law remain valid if Coulomb’s law were replaced by an inverse cube law?suitable example.
Coulomb’s law and Gauss’s law are equivalent statements?  ?

[Pmb]

Would Gauss’s law remain valid if Coulomb’s law were replaced by an inverse cube law?[/quite]
No.

suitable example.
Coulomb’s law and Gauss’s law are equivalent statements?  ?

That's true. But Coulomb's law is an inverse square law and because of that they are equivalent because Coulomb's law is an inverse square law. If it wasn't then that would not longer be true. If you were to follow the derivation of Gauss's law you'd see this. Gauss's law is more appropriately called Gauss's theorem because it can be derived.

[ScienceLover (OP)]

Thanks for the great response, can you give an example please for
Would Gauss’s law remain valid if Coulomb’s law were replaced by an inverse cube law?like  comparison when its valid and why not valid?

[Atomic-S]

Consider a point charge, a spherical shell around it at one radius, and another shell around it at a much larger radius. The flux density at the surfaces varies as the inverse of the square of the two radii. However, the area of the shells varies as the square of the radii, so that the total flux for both shells is the same. Thus, we have conservation of flux going into the space between them and coming out again.  If, however, the elecrtic field varied inversely as the cube of the radii, the amount of flux from the outer shell would total less than that through the inner shell, so that the divergence of the field (in places where charge is not) could no longer be zero, and flux would not be conserved. By the way, this sort of situation somewhat resembled that of the strong force inside atomic nuclei.

[Pmb]

Thanks for the great response, can you give an example please for
Would Gauss’s law remain valid if Coulomb’s law were replaced by an inverse cube law?like  comparison when its valid and why not valid?

Choose your own since it would never work under any circumstance. I.e. it's always invalid for a 1/r^3 force.