Re: [Phys-l] Charged particles moving along parallel paths

[John Denker <jsd@av8n.com>]

On 12/03/2011 03:10 PM, LaMontagne, Bob wrote:

> Is there a purely classical
> response that is satisfactory in a general physics course that will
> not cover relativity until the following semester?

No.

Not so far as I know.  I'd be quite astonished to
learn of a satisfactory answer that does not revolve 
around special relativity.

=====================================

> How do you respond to the student?

Answer:  I quote the following:
 	   
       	Von Stund’ an sollen Raum für sich und Zeit für sich	         
 	völlig zu Schatten herabsinken
 	und nur noch eine Art Union der beiden
 	soll Selbständigkeit bewahren.
 	
                      Hermann Minkowski (1908)

Translation:

 	From now on, space of itself and time of itself
 	shall sink into mere shadows
 	and only a kind of union of the two
 	shall maintain its independence.


To that I would add:

 	From now on, electrostatics of itself and magnetism of itself
 	shall sink into mere shadows
 	and only a kind of union of the two
 	shall maintain its independence.

===========

An even starker version of the student question involves
electrons moving in a wire, such that a current flows but
the wire is electrically neutral.  Now consider an electron
moving parallel to the wire (moving relative to the lab
frame).  The electron is deflected by the magnetic field.

Now consider the same situation in a frame comoving with
the electron.  There cannot be any magnetic effect on the
electron, since its velocity is zero.

This is quite a stark question, because either the electron
is deflected or it is not.  We don't need to determing how
much; we need to distinguish zero from nonzero.

And never mind the wire, consider only the electromagnetic
field at the location of the test charge.  Special relativity 
explains how the electromagnetic field bivector which is
purely in the magnetic direction in the lab frame picks
up a component in the electric direction when we boost
into the frame comoving with the electron.

This is easy to visualize, easy to explain, and easy to
understand in four dimensions ... and not otherwise ...
as far as I can tell.  The pictures can be found here:
 http://www.av8n.com/physics/magnet-relativity.htm
and the equations can be found here:
 http://www.av8n.com/physics/straight-wire.htm