Magnetism caused by special relativity?

1. Oct 21, 2011

Per Oni

Hi all.

Some time ago I was talking here about relativity and magnetic fields and how they relate. Someone gave this formula: B’ = γ (Bo – V x E / C^2). See: http://en.wikipedia.org/wiki/Classical_electromagnetism_and_special_relativity

Now my argument (contrary to popular believe) is that this formula shows me that a magnetic field is not caused by SR. What it does show is that a magnetic field is acted upon by SR as (say) time and length are acted upon.

As an example what the result of this thought is consider how a magnetic field round a conductor might be explained, using the above formula. We know that the average electron drift Vd is negligible compared with C (ie γ~0), therefore this formula becomes: B’= - Vd X E / C^2. Expanding: E = λ / 2πr εo and I=λ x Vd and C^2=1/εo μo, we get B= I μo / 2πr, which is the correct result.
If you want to see how length contraction might affect this results you have to add a γ of 1 + Vd^2 / 2 C^2 = ~ E-21. This is a one followed by 21 zero’s and is therefore immeasurable small, however for high velocity electrons it needs to be taken in account.

As you can see, my above calculation is far more straight forward and simple then the torturous procedure you would have to follow when having to explain the causes via length contraction of the drift electrons. See http://en.wikipedia.org/wiki/Classical_electromagnetism_and_special_relativity In addition, following that road might well be wrong in the first place.

Note that I have not shown what causes a magnetic field, all I have shown (I hope) is how it is not caused by SR.