Magnetic field of straight wire, charges travels at relativistic speed

[nos]

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

 

[mikeph]

If they're moving faster then the current density is higher so the magnetic field will be stronger.

 

[nos]

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.

 

[mikeph]

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.

 

[bhobba]

It is also interesting to note that Coulombs Law and SR is enough all by themselves to derive Maxwell's equations:
http://richardhaskell.com/files/Special Relativity and Maxwells Equations.pdf

Thanks
Bill