Electric is Magnetic - Relativistically speaking

DavidFi

I know that electric and magnetic fields are the same phenomena just from a different perspective.
I also know that this is related to the relativistic speed of the electrons flowing in the wires.

I am unable to grasp the picture - how does it happen?

Do you have an explanation?

Thank you.
David.

Bob S

See the electromagnetic relations and transformations at
http://pdg.lbl.gov/2005/reviews/elecrelarpp.pdf
The electric and magnetic transformations (last four lines) show that the non-relativistic transformations of transverse fields are

E_p^prime = E_p + v x B_p
and
B_p^prime = B_p - (1/c²) v x B_p
So you could see the effect in a moving train, if your equipment were sensitive enough.

DavidFi

My problem is with visualizing this phenomenon.

If we will think of a moving train that carries electrically charged material - we get moving charge. From the mathematic I can see the cross product being transverse to the moving direction.

But I can not think of any "reason" (if a "reason" is the correct word) to how this happens?

What causes the transverse force?

from the mathematics we could calculate the "lifting" force on a electrically charged ball standing near the moving train but I do see any possible explanation for a force in the up direction.

Do you see one?

Thank you.
David

DaleSpam

Hi DavidFi, welcome to PF. The best page I have found for explaining this point is "Purcell Simplified".

Mentz114

DavidFI:
Suppose I had a 'cathode ray tube', where electrons fly through an electric field, get deflected and hit the screen in a certain place. I don't see any magnetic forces on the electrons. An observer in a frame moving wrt to my lab will see the electrons hitting the same spot on the screen. They will calculate that the electrons were deflected by an electric and a magnetic field. The magnetic field seems to spring up solely to ensure that both observers can explain why the electrons hit that particular spot.

How this happens is not explained by mainstream theory ( not that I know of ).

DavidFi

OK, Purcell shows my mistakes one by one without shame :-)

1) There is no UP force caused by the moving charge of the train.
The magnetic field lines are up , the current flow is in the same plan as the force perpendicular to the UP pointing magnetic filed lines.

2) A wire is equivalent to 2 trains (not one)
- First train with positive charge, moving
- Second train with negative charge "standing still" - just keeping the net charge of the wire 0 in the lab frame of reference.

Thank you for fixing my mistakes.
Sorry for the confusion

David.

DaleSpam

No problem, it is a powerful concept once you see it laid out that way.

DavidFi

I am looking for a simulation tool that could simulate this type of phenomena

Just for grasping the principle a little better

Could you recommend one?
Thank you.
David.

DavidFi

Could it be that there is no simulator that could simulate Relativistic phenomena?

DaleSpam

I don't know of any dedicated simulation tool for this. I always just use Mathematica.

DavidFi

I found a few mechanical relativistic simulators:
http://www.adamauton.com/warp/links.html

My be I/we could change one of them ...?
but in what way?