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Magnetic field of straight wire, charges travels at relativistic speed

  1. Dec 25, 2013 #1

    nos

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    Hi there,

    Is it true that the magnetic field of a straight wire is the same when the charges are moving at low speeds (v <<c) as when they are moving at relativistic speeds (v~c). The extra relativistic factor the magnetic field gets from the moving charges cancels upon integrating. According to my calculation, magnetic field has the same value, relativity or not.

    I could provide you with my calculation if needed ;)

    I presumably expected a different value.

    Thanks, nos
     
  2. jcsd
  3. Dec 25, 2013 #2
    If they're moving faster then the current density is higher so the magnetic field will be stronger.
     
  4. Dec 25, 2013 #3

    nos

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    Ah I see now. Of course, the formula for B-field stays the same, but the current for slowly particles is lower than current produced by fast particles, thus a different value for B-field.

    Actually my question should have been: Is it true that the formula stays the same taking relativity into account.

    Thank you.
     
    Last edited: Dec 25, 2013
  5. Dec 25, 2013 #4
    Yes.

    The general form of your question is: "are Maxwell's equations invariant under a Lorentz transform?", to which the answer is yes. This fact is very interesting, as well as very historically relevant as Maxwell's equations predate Einstin's formulation of special relativity; they were a major factor in the formulation of special relativity in the first place.
     
  6. Dec 25, 2013 #5

    bhobba

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    Science Advisor
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