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I want to make sure I'm understanding this correctly:

My understanding is that magnetic force can do no work because it can never change the speed of an object -- instead it can only cause acceleration by changing the direction of velocity. So, for example, if there's a positively charged particle next to a wire conducting a current, from the frame of reference where the particle is moving with the electrons in the wire and the positive charges inside the wire are at rest, a magnetic force would cause the particle to be pushed away from the wire (whereas, from the rest frame of the particle, it would be an electric force, since magnetic forces can't cause changes in speed, only in the direction of motion). The magnetic force vector would be perpendicular to the flow of current in the wire and the parallel motion of the particle next to the wire, but it would point in the same direction the particle is pushed towards. Hence, it's perpendicular to the particle's original direction of motion, was which parallel with the current vector, but in the same direction the particle is moving in after the repulsive force acted on it.

Is that correct, or am I misunderstanding something?

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  • $\begingroup$ Your analysis about the magnetic force only applies in your first frame of reference, in which case the magnetic force indeed remains always perpendicular to the particle velocity. In the second frame of reference, as you've identified, the force points along displacement because the nature of the force is electric and not magnetic. $\endgroup$
    – DanDan面
    Commented Feb 16, 2023 at 1:17
  • $\begingroup$ @DanDan0101 Do you mean the magnetic force vector (in the first frame of reference), is perpendicular to BOTH the displacement vector AND the current vector? If that's the case, how could it have any effect on the particle at all? Like, how could it cause the particle to change direction to somewhere it's not pointing? $\endgroup$
    – Mikayla Eckel Cifrese
    Commented Feb 16, 2023 at 1:41
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    $\begingroup$ The velocity is continuous in time. If it's initially parallel to the wire, then after a moment while magnetism applies, the velocity is still mostly parallel to the wire, only slightly rotated outward; and the magnetic force also rotates slightly, so that they're always perpendicular. $\endgroup$
    – mr_e_man
    Commented Feb 16, 2023 at 3:08

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