Electricity and magnetism/Magnetism/Coulomb's law in electrodynamics

To calculate the forces between moving charges we need generalized Coulomb's law: If a charge is eternally stationary in an inertial frame of reference, then the force it exerts on a moving charge is the same as the electrostatic force it would exert on that charge if it were stationary at the same position. If a charge is eternally immobile in an inertial frame of reference, the electric field of which it is the source has had time to propagate throughout space and establish itself there. If a charge is accelerated, there is no inertial frame of reference in which it is eternally stationary. The Coulomb field of which it is the source in its rest frame at a given moment takes time to propagate. At a later time, it is the source of another Coulomb field, in another rest frame. This is why accelerated charges are the source of electromagnetic waves that propagate throughout space. Light is produced by accelerated electrical charges: File:Field-disturbance-propagation.gif An immobile electric charge is not a source of light because no waves propagate in the electric field it establishes around it. Generalized Coulomb's law makes it possible to calculate the electric force field of any system of charges in uniform rectilinear motion relative to each other. To calculate the force exerted by all the charges, we calculate the sum of the forces exerted separately by each charge. To calculate the force exerted by a charge, we consider the frame of reference where it is at rest and calculate the Coulomb force. The Lorentz transformation then makes it possible to calculate this force in any frame of reference. (Animation: Coulomb field produced by a charge in uniform rectilinear motion)