Derivation of the Biot-Savart Law from Coulomb's Law?

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The title says it all--I'm working through The Feynmann Lectures, and came across the assertion that a magnetic field can be thought of as a relativistic-transformation of an electric field (and vice-versa). This makes sense to me, since the magnetic field of a moving point-charge can easily be transformed away by working in the reference frame of the charge. The electric field seems more (classically) invariant, but I imagine length-contraction/time dilation play a role there. I was wondering if there is a possible derivation of the Biot-Savart Law by calculating the Lorentz transformation of the Coulomb force field, or something along those lines?
 

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