About Coulomb's law, it only works for a small test charge.

I am not perceptive of this part.

Does it works for a conductive sphere? I found many questions in my book employing this law to calculate the answer where it involves not only a small test charge but also a sphere.

does it? i've never seen anything about that. can you post a link?

 

I always seen it as an electrostatic version of newtons laws of gravity, in that they can work for large charges and spheres.

You can add the vectors of individual point charges, so you can scale up Coulomb's law. You can assume a charge density and integrate over the volume of the charge — each differential volume element will obey Coulomb's law, because it is essentially a point. You can also use a point approximation if the separation distance is significantly larger than the size of the particle.

 

There are examples of the particle-size correction in physics calculations, where e.g. a proton or nucleus is initially treated as a point particle and then a correction is made for its finite size.

IIRC for a spherical object applying gausses law to calculate the electric field (and therefore force) it simplifies to the coulomb interaction anyway.

Well where it gets more complicated with insulating spherical shells and conducting spheres and such you can always take a Gaussian surface to calculate the charge or electric field using electric flux.