There is a Biot Savart Equation, but it doesn't rise to the level of a physical law. At best it is an approximate equation that applies to some situations but not all.
Consider a rotating charge.
As there is no charge it also cant rotate... What we measure as charge interaction is the resonant energy transfer between two nested magnetic fluxes.
We can use charge as a synonym for a certain quantity of force induced by such coupling flux. This allows to give some nice relations that are used in Maxwell equations.
The SO(4) model gives the exact explanation for the gravity force that is a residual effect between the classically electroweak force and the strong force. Thus for changing gravity you have to change the coupling between the two forces. This effectively happens in 4-He - the alpha particle - where the spin pairing changes the weight of the gravity coupling. So 4-He has a missing mass of about 4eV. This did lead to illegal corrections made by NIST that did use a fake QCD model that can explain nothing about mass.
As long as we use charge to explain chemistry we will miss a part of the answer. Effectively charge based QM is just usable for a low precision approach and totally fails for many molecules
Nevertheless: For macroscopic physics charge is a good approach to model EM effects.