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Lorentz Force & Newton's 3rd Law

  1. Feb 12, 2015 #1

    I have been wondering this for a while and have only recently thought to ask here.

    The Lorentz force is the interaction of a moving charge in a magnetic field, it doesn't seem to have any sort of physical force applied to it, only the magnetic interaction.
    I was wondering, if there is a force being generated by the field on the moving charge, then where is the equal and opposite force as stated in newtons 3rd law or does it not have one?

    Thank you very much.
  2. jcsd
  3. Feb 12, 2015 #2

    Simon Bridge

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    It is important not to mix up models, in this case the force and interaction picture seems to have got mixed up.

    Force picture:
    - a moving charge experiences a force from the electromagnetic field.
    The reaction force is experienced by whatever generated the field.... i.e. another charge.
    We don't always deal with that for the same reason we don't always bother with the reaction of the Earth to, say, a bouncing ball.

    Interaction picture:
    - a moving charge experiences an electromagnetic interaction.
    ... this is a different model. To get an interaction, it must absorb or emit a virtual photon.
    The concept of "force" is not invoked as part of the model here, only conservation and symmetry arguments.
    So discussion of forces in this model is irrelevant.

    However, we can ask how the appearance of the third law comes about from fundamental interactions - which is, I suspect, where you are headed.
    It happens due to the photon interaction involving two charged bodies - one loses the photon and the other gains it.

    Newton's laws of motion are an emergent phenomena arsing from many fundamental interactions - they only work on average.
  4. Feb 12, 2015 #3


    Staff: Mentor

    Newton's third law doesn't apply to fields. However, it does generalize to the conservation of momentum, which applies to fields. The change in the momentum of the charge is associated with an equal and opposite change in the momentum of the field.
  5. Feb 13, 2015 #4
    Hey Guys, thanks for responding.

    Conservation of momentum is what I was primarily concerned about.

    So there is a reaction force that acts on the object that generated the field.

    The two charges example makes sense, but where would the reaction force act on a magnetic field generated by a coil of wire?

    The electron charges are spinning in the coils which generates the magnetic field, when the field interacts with another charge outside the coils, does the reaction force try and stretch the coil radius outwards in all directions?

    Thank you kindly.
  6. Feb 13, 2015 #5

    Simon Bridge

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    com of coil.
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