Suppose a moving proton traverses a uniform magnetic field with constant velocity. Note that because the proton is moving, it is generating its own magnetic field.
Is the magnetic force experienced by the proton completely explained by the Lorentz force law, i.e., F = q (v x B)?
Or, is the proton also experiencing an additional magnetic force arising from the interaction of its own magnetic field with the external field? If that is incorrect, is the Lorentz force law actually just describing the result of proton field-external field interactions, such that any and all magnetic force on the proton is explained by the Lorentz force?
Answer
Magnetic fields do not interact with magnetic fields; they simply superpose. Instead, magnetic fields interact with charged particles.
It is reasonable to ask whether a moving charged particle feels its own magnetic field, just as it is reasonable to ask whether a stationary (or moving) charged particle feels its own electric field.
The answer in the case of stationary or uniformly-moving charged particle is that these electric and magnetic self-forces are observed to be zero. For a point particle, its electrical and magnetic fields become infinitely large near the particle, but they can be understood as acting on the particle in a symmetric way such that there is no net force in any direction.
In the case of an accelerating charged particle, things are more complicated. Then the Lorentz force due to external fields is not the whole story. An accelerating charge radiates electromagnetic waves that carry energy, momentum, and angular momentum away to infinity. The energy in these waves must come from the kinetic energy of the particle, so there must be a backreaction force on the particle slowing it down, in order to conserve energy. This backreaction can be understood as the self-force, where the accelerating particle’s own field exerts a nonzero force on it.
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