Let F 1 and F 2 be the instantaneous forces that act on a particle with charge q when it moves through a magnetic field B(r) with velocities 1 and 2 , respectively Without choosing a coordinate system, show that B(r) can be determined from the observables 1 F 1 and 2 F 2 if 1 and 2 are appropriately oriented

Question: Let F 1 and F 2 be the instantaneous forces that act on a particle with charge q when it moves through a magnetic field

Let F₁ and F₂ be the instantaneous forces that act on a particle with charge q when it moves through a magnetic field B(r) with velocities υ₁ and υ₂, respectively. Without choosing a coordinate system, show that B(r) can be determined from the observables υ₁ × F₁ and υ₂ × F₂ if υ1 and υ₂ are appropriately oriented.

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