Question

Why coulomb's law is only applicable to stationary charges?

Answer 1

When charges are in motion they produce both a electric and magnetic field. Coulomb's law can only explain electric field and ignores magnetic field.

Answer 2

for moving charges we have to consider magnetic force along with electric force.

We use Lorentz force whenever charge is moving.

Answer 3

What if they are both stationary with respect to the same inertial reference frame? Or does Newton's law not apply here?

Answer 4

then there is only electric force. and we apply coulombs law.

or, you can apply lorentz force law where you have to put magnetic field equal to zero.