# Formulating Lorentz's force law

1. Mar 5, 2006

### antoon

How did sir Hendric Antoon Lorentz got to his formula:
F= B v q

Was i just experimental? or is this something witch follows out of the maxwell equesions or wath?

2. Mar 6, 2006

### dextercioby

You mean

$$\vec{F}=q \vec{v}\times\vec{B}$$

,surely. I dunno the answer to the first question, but i do for the second. It follows in relativistic electrodynamics as a motion equation for a relativistic electrically charged particle in an electromagnetic field. Such equation can be derived as the Euler-Lagrange equation for the action obtained by adding the action for a free particle and the interaction term.

Daniel.

3. Mar 6, 2006

### Galileo

Without invoking the action principle, yeah it's a fundamental axiom of the theory of EM and its justification is certainly experimental. Turns out that in relativity, Maxwell's equations don't need changing, but the Lorentz force law does.