Take the 2-minute tour ×  Well, there's already a question like
this here so that my question could be considered duplicate, but
I'll try to make my point clear. Is there a way to derive Biot-
Savart law from the Lorentz' Force law or just from Maxwell's
Equations? The point is that we usually defined based on
experiments that the force felt by a moving charge on the
presence of a magnetic field is $F = qv\times B$, now can this
be used in some way to obtain Biot-Savart law like we obtain the
equation for the electric field directly from Coulomb's Force
law?  And I wanted to know that because as pointed out in the
question I've mentioned, although Maxwell's Equations can be
considered more fundamental, those equations are obtained after
we know Coulomb's and Biot-Savart's laws, so if we start with
Maxwell's Equations to obtain Biot-Savart's having use it to
find Maxwell's Equations then I think we'll fall into a circular
argument. In that case, without recoursing to Maxwell's
Equations the only way to obtain B