# Derivation of Lorentz force law from the Biot-Savart Law [closed]

How to derive the Lorentz force (F=qv X B) law from the definition of the magnetic field and the Biot-Savart Law?

• To me, the force law $\mathbf{F} = q \mathbf{v} \times \mathbf{B}$ is the definition of the magnetic field. What other definition do you have in mind? – d_b Aug 24 '19 at 1:21
• Like we had studied in middle school the magnetic field was defined on the basis of force felt between two magnets just like the electric field was defined on the basis of the force between two electric charges. – Mayank Pande Aug 24 '19 at 1:33
• Biot-Savart worked out the magnitude of the $B$ field at a given distance from a current carrying wire. It was Lenz who worked out out the force between $2$ current carrying loops or wires. In any case, the force between the current loops or wires requires line integrals - there are no line integrals in the Lorentz force. It's possible the opposite might be true - Lenz from Lorentz. – Cinaed Simson Aug 24 '19 at 3:39

This is not possible. The Biot-Savart Law tells how the moving charges that make up steady currents produce the magnetic field $${\bf B}$$. The Lorentz Force Law tells how the magnetic field, in turn, produces a force on a moving charge. The two phenomena are, at this level, independent, and one cannot be derived from the other.