Question:

Which of the following statement(s) is/are correct?

The Gauss law can be used to calculate the field distribution around an electric dipole.

If the electric field between two point charges is zero somewhere, then the sign of the two charges is the same.

The work done by the external force in moving a unit positive charge from point A at potential VA to point B at potential VB is (VB−VA).

If the electric field due to a point charge varies as r⁻⁵ instead of r⁻², then the Gauss law will still be valid.

Solution:

If field due to a point charge varies as r⁻⁵, then E = cr⁻⁵ where c is a constant. ∫E.ds = cr⁻⁵ × 4πr² = 4πcr⁻³ ≠ qenclosed/ε₀
Hence, gauss law is invalid and option A is wrong.
Electric field due to a dipole is not symmetric and hence a gaussian surface cannot be used to find the electric field due to a dipole using Gauss Law. Hence, option B is wrong.
Electric field on the line joining the charges are opposite in direction if they are of the same sign only. Hence, option C is correct.
By definition of potential, work done by external force to move a unit positive charge from point A to point B is W = q(VB−VA) = VB−VA
Hence, option D is correct