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We know that work done by Lorentz Force $q(\vec{v}\times\vec{B})$ is $0$ on moving charge in magnetic field as velocity is always perpendicular to the force. This means that kinetic energy remains constant, however, I think that like electric and gravitational fields have a potential associated to the position of an object in them, a magnetic field should too, right? But then moving through a magnetic field will not be able to always maintain constant KE as sum of mechanical energies has to be constant, and "moving" through magnetic field will change its position in the field, hence its "magnetic potential" will change. But that does not happen.

Am I interpreting magnetic field's effects and relation to potential incorrectly? What is the correct interpretation?

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  • $\begingroup$ „ This means that kinetic energy remains constant“ is a wrong assumption. See the free-electron-laser, where the electrons slow down, describing a zig-zag-trajectory and emitting photons. For the mechanism behind see Detect reaction force to Lorentz force $\endgroup$
    – HolgerFiedler
    Commented Aug 14, 2023 at 4:32
  • $\begingroup$ @HolgerFiedler thanks, i was just assuming the ideal case where the charge doesnt decay into other particles like photons $\endgroup$
    – AltercatingCurrent
    Commented Aug 14, 2023 at 10:04
  • $\begingroup$ The electron doesn’t decay, simply it’s kinetic energy get converted into the emission of photons until stand still. $\endgroup$
    – HolgerFiedler
    Commented Aug 14, 2023 at 10:53

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You're making an assumption that there's a well defined "potential energy" associated with any field based on your position in it.

This is only true of conservative force fields — the magnetic field is not conservative.

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