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Physical interpretation of the Lorentz force

Coulomb's law is only valid for point charges at rest. In fact, the electromagnetic force between two point charges depends not only on the distance but also on the relative velocity. For small relative velocities and very small accelerations, instead of the Coulomb force, the Weber force can be applied. The sum of the Weber forces of all charge carriers in a closed DC loop on a single test charge produces - regardless of the shape of the current loop - the Lorentz force.

The interpretation of magnetism by means of a modified Coulomb law was first proposed by Carl Friedrich Gauss. In 1835, Gauss assumed that each segment of a DC loop contains an equal number of negative and positive point charges that move at different speeds. If Coulomb's law were completely correct, no force should act between any two short segments of such current loops. However, around 1825, André-Marie Ampère demonstrated experimentally that this is not the case. Ampère also formulated a force law. Based on this law, Gauss concluded that the electromagnetic force between two point charges depends not only on the distance but also on the relative velocity.

The Weber force is a central force and complies with Newton's third law. This demonstrates not only the conservation of momentum but also that the conservation of energy and the conservation of angular momentum apply. Weber electrodynamics is only a quasistatic approximation, i.e. it should not be used for higher velocities and accelerations. However, the Weber force illustrates that the Lorentz force can be traced back to central forces between numerous point-like charge carriers.