information:classification, structural:expansion, information:filtering, linguistic:voice_change
Lorentz force law as the definition of E and B

This is valid, even for particles approaching the speed of light (that is, magnitude of v, | v | ≈ c). So the two vector fields E and B are thereby defined throughout space and time, and these are called the "electric field" and "magnetic field". The fields are defined everywhere in space and time with respect to what force a test charge would receive regardless of whether a charge is present to experience the force.