Length contraction and magnetic field

[Per Oni]

Some days ago there was a discussion on pf whether eath’s magnetic field was rotating. That got me to think again about magnetism and relativity and I found this article: http://en.wikibooks.org/wiki/Special_Relativity/Simultaneity,_time_dilation_and_length_contraction

Including this section:

If Jim is moving relative to the wire at the same velocity as the negative charges he sees the wire contracted relative to Bill:

Bill should see the space between the charges that are moving along the wire to be contracted by the same amount but the requirement for electrical neutrality means that the moving charges will be spread out to match those in the frame of the fixed charges in the wire.
This means that Jim sees the negative charges spread out so that:

To me there are several points which need clarifying. In the 1st sentence:” ….he sees the wire contracted relative to Bill……” should be: …he sees the +ve ions contracted relative to Bill….. Second and much more interesting why should there be electrical neutrality? Ok I do know that a neutral wire contains the same amount of +ve and –ve charges but I can easily add or subtract some electrons so that there’s no neutrality. Alternatively I can redistribute some electrons so that locally the neutrality is disturbed.
Further more in Jim’s rest frame he sees the +ve charges moving. To obtain “electrical neutrality” does he see the +ve ions spread out?
To conclude: to me, in the way things are explained here there’s no difference between Jim moving with the electrons looking at Bill or Bill moving with +ve ions looking at Jim. Both have to come to the same conclusion regarding magnetic forces.

 

[Per Oni]

In a nut shell: This theory says that Bill experiences no extra force because the electrons are increasing their mutual distance and that as a result of their velocity Bill sees this distance again contracted. So all electrons are moving a little sideways. Where do they end up? At the back of this current carrying circuit?

Does anybody have any idea?

 

[Per Oni]

Look at this problem from a different perspective. In a way that is not immediately related.

Compare an oscillating electrical dipole consisting of a pair of opposite charges oscillating round a fixed point, and a radiating electrical dipole antenna. If you look at electro magnetic equations and pictures then both look very similar.

But why should they be similar? Where are the +ve oscillating charges in the antenna? Conventional theory says (unless I am mistaken) that in a normal good conductor only the –ve charges are moving and accelerating and the +ve ions are static except for thermal movements.

Is it therefore a fair statement to say that in an antenna there exist an electronic mirror image which is an exact opposite in velocity, acceleration and charge to the electrons? But in order to behave/radiate in a manner as the electrons these +ve images have to be real.
What do you think?

 

[Mentz114]

But why should they be similar? Where are the +ve oscillating charges in the antenna? Conventional theory says (unless I am mistaken) that in a normal good conductor only the –ve charges are moving and accelerating and the +ve ions are static except for thermal movements.

You answered that earlier.

Second and much more interesting why should there be electrical neutrality? Ok I do know that a neutral wire contains the same amount of +ve and –ve charges but I can easily add or subtract some electrons so that there’s no neutrality. Alternatively I can redistribute some electrons so that locally the neutrality is disturbed.

One could argue that a buch of -ve charges moving to my left ia the same as a bunch od +ve charges moving to the right. Choosing a new zero level for potential has this effect.

 

[Per Oni]

One could argue that a buch of -ve charges moving to my left ia the same as a bunch od +ve charges moving to the right. Choosing a new zero level for potential has this effect.

Your answer made me think of another related topic.
The electrical conduction of a p-type material is thought of as electrons jumping into vacant +ve holes. Theory says that –ve charges moving left are in reality +ve charges moving right. This can apparently be proven with the Hall effect probe, where +ve charges are deflected.

The trouble for me is that for a charge to be deflected in a magnetic field this charge has to make a movement. It is not good enough just to think that the +ve charge appears to move. Truth is: no movement no force.
What’s your idea? Are +ve charges really moving?

 

[Per Oni]

Since I wrote #3 I had a look at radiation patterns of various electrical dipoles. Here is a gem: http://www.mathpages.com/HOME/kmath575/kmath575.htm

If you go right to the bottom of that page you can see the pattern of a single oscillating charge which is ofcourse different from a dipole pattern. Also note the comment underneath the pattern.

If you really think that a current causes electrons to spread out have a quick calculation on how far they would have to spread out to deal with the electronic Fermi speed. In a typical electrical current the drift speed is ~10-3. Fermi speed is ~10+6. Ratio ~10+9. Since relativistic length is contracted by a term V^2 we have now a ratio of ~10+18. Under these conditions consider a rod of metal L>>D and look in the directions of D and L.
This thought experiment assumes the electrons have a Fermi speed, however I’ve seen comments in pf stating that electrons don’t have this speed but are in some of a “state”.