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Correct derivation of magnetism from SR

  1. Sep 25, 2006 #1

    Hans de Vries

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    The correct derivation of magnetism as a relativistic side effect
    of electrostatics:

    http://chip-architect.com/physics/Magnetism_from_SR.pdf


    I've claimed quite a few times here that Purcell's derivation is not
    correct. Making claims is one thing. Better is to pinpoint exactly
    what is wrong, and then, of course, provide the right derivation.

    Two mistakes which cancel plus an omission eventually produce the
    required result. We’ll discuss the mistakes and then give the correct
    derivation, which, surprisingly (for me as well), turns out to be even
    simpler. (for the case of the charge moving parallel to the wire)

    Also derived is the case where the charge is moving perpendicular
    to the wire. Furthermore, the required charge density is derived, for
    the electrons in a current carrying wire, in order to be electrically
    neutral in the rest-frame.

    To be self consistent, the paper does derive the relativistic EM
    potential and the relativistic electrostatic field for a point particle
    from the classical EM wave equations in a way which is both short
    and simple.

    I spend a lot of effort to make the paper understandable and clear.


    Regards, Hans.

    P.S: An online presentation of Purcell's derivation is available here:
    http://physics.weber.edu/schroeder/mrr/MRRhandout.pdf#search="purcell simplified"
    from Dan Schroeder (The one from Peskin & Schroeder)
     
    Last edited: Sep 25, 2006
  2. jcsd
  3. Sep 25, 2006 #2

    CarlB

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    Allow me to be the first on PF to compliment your paper.

    And this paragraph from page 5 got past the syntax checker, corrections are in bold:

    Carl
     
  4. Sep 25, 2006 #3

    Hans de Vries

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    Thanks, Carl

    You'll find that the corrected spelling is already uploaded. It's 4:30 AM where
    I'm currently. Time to sleep :^)


    Regards, Hans
     
  5. Sep 25, 2006 #4

    pervect

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    A few comments: It's a bit circular to use Maxwell's equations and then claim that one has 'derived' the magnetic field. Maxwell's equations already assume the existence of a magnetic field. So the title of the paper doesn't exactly represent what's being done. (I'm not sure I have a fix for this concern, but I don't think the title as-is is quite right, I'm just not sure what would be better offhand).

    I would also stop short of claiming that Purcell is wrong, though from my brief glance I would agree that your deriation is better, and that Purcell's derivation would be correct only for very low velocities while your derivation does not suffer from that limitation.

    One other comment. We seem to agree that the positive and negative charge densities per unit length must be the same in the rest frame of the wire in order for the wire to be uncharged.

    Yet your diagram in figure 3 (left) does not seem to reflect this. Shouldn't it be the same as the diagram in figure 1 (left)? This removes some of the apparent "conflict" with Purcell - the diagrams are not really so dissimilar as all that..
     
    Last edited: Sep 25, 2006
  6. Sep 25, 2006 #5

    Hans de Vries

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    With the very low velocities you probably mean slower as the electron
    drift in the wire. Where it really goes wrong is the intermediate result:

    [tex] F_{elec} =\frac{v^2\ Q_L}{2\pi\epsilon_o c^2 y}\ Q [/tex]

    Here the force is proportional to v2 while v is the speed of the
    test-charge relative to the wire. The force should of course be
    linear in v. The derivation gets rid of one v by combining it with QL
    into current I. However, the speed which defines the current in
    the wire is another v: The relative speed between the electrons and
    the ions...

    Ah, this is (was) a copy/paste error. The comment in the image belongs
    to another one. A corrected version is already uploaded. Thanks.


    Regards, Hans
     
  7. Sep 26, 2006 #6

    Hans de Vries

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    Hmmm, in Dan Schroeder's presentation of the derivation:

    http://physics.weber.edu/schroeder/mrr/MRRhandout.pdf#search="purcell simplified"

    The test-charge is always at rest with the positive ions, and thus at rest
    with the wire...... consequently there is only one sort of v here. So it's
    hard to mix them up..


    Regards, Hans
     
    Last edited: Sep 26, 2006
  8. Oct 18, 2006 #7

    Hans de Vries

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    The simplest, and the full derivation of Magnetism
    as a Relativistic side effect of ElectroStatics


    http://chip-architect.com/physics/Magnetism_from_SR.pdf


    Some rework is done. We now start directly with the derivation, which is further simplified, and critics on the Purcell derivation are limited to the abstract and more to the point.


    Regards, Hans.
     
    Last edited: Oct 18, 2006
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