From: mustafa@seas.smu.edu (Mustafa Kocaturk)
Subject: Re: Magnetic question (again!)
Summary: Magnetism is a relativistic effect of charges in motion
Cc: mustafa@seas.smu.edu
Organization: SMU - School of Engineering & Applied Science - Dallas
Date: Fri, 18 Dec 1992 22:26:41 GMT

In article <1992Dec17.183821.13124@topaz.ucq.edu.au> freeman_l@topaz.ucq.edu.au writes:

[ ... introductory text clipped for brevity ... ]

>That leads me to the following conclusions-:
>
>A magnetic field must somehow provide a frame of reference for a charged
>particle.
>Not only that, but the field/particle system must also be aware" of time,
>because it can distinguish between fast motion and slow motion.
>
>A magnetic field can move around in space. This seems at first thought to be
>a pretty obvious statement, but.... WHAT is actaually moving? Has a magnetic
>field got some fine internal structure, like the Classical lines of Force,
>so that you can say: THIS bit of the magnetic field is now over HERE!

  I am not quite sure what is meant by "fine internal structure".
  I suspect that the finite speed of "electromagnetic" interaction
  is being implied.  Or is it the particle nature of the force ?
  Actually the two must be tightly related.  I will use the finite
  speed ( < c ) property to explain how magnetic fields arise.

  A magnetic field is nothing but a relativistic effect.
  It is easy to understand the electrostatic force
  that exists between two stationary charges.  When one of them
  moves with respect to the other, the electrostatic force it exerts
  on the other cannot change with zero delay.
  The interaction propagates with the speed of light.
  With no reference to magnetic fields,
  I will call this situation an "electrodynamic field".

  Owing to the finite propagation velocity of the electric
  (Coulomb) force, a snapshot of the lines of force will
  therefore exhibit a concavity towards the direction that their
  source is moving.

  The situation becomes easier to understand when two like point
  charges are moving with the same velocity.  A stationary observer
  will see that the force lines emanating from both charges are concave
  towards their common direction of motion.  This means that during
  the snapshot, the force between the charges as measured by the
  stationary observer will be smaller in magnitude, and given by

	   q q
	    1 2
     f = k ---- cos(angle between force lines and the line drawn
             2               through the charges)
	    r

  To put it in words, both charges will be experiencing delayed
  electric forces, namely, they will be "escaping from" each other's
  repulsion!  Furthermore, the distance r that the force travels
  is greater than the distance between the charges.  The force
  will have a component along the direction of travel, but it will
  be cancelled out because of the even symmetry along that direction,
  leaving only the component along the straight line passing
  through the charges.  A similar logic will show that unlike charges
  travelling with the same velocity will experience a smaller attraction
  towards each other than they would if they were stationary.

  For the sake of clarification, I am exploiting this model to
  assert that the difference between this electrodynamic force and the
  electrostatic force equals the magnetic force, without any claim to
  mathematical rigor.

  Magnetism is therefore nothing but an abstraction derived from this
  relativistic effect arising from motion of charges relative to the
  observer who is measuring the forces.  All magnetism laws like the
  Biot-Savart law and Lenz's law deal with an abstraction called the
  magnetic field vector, besides charges, velocities and distances.
  Constants like the permittivity and magnetic permeability of the
  medium (epsilon and mu, respectively) provide adjustment between
  the speed of light and the system of units.  Note that epsilon times
  mu gives the speed of light to the power minus two.  Two are actually
  sufficient to determine the third, thanks to James Clerk Maxwell.
  
  Another related quantity is the electrostatic vector potential,
  which is used to handle this relativistic effect arising from the
  motion of charges within the framework of vector calculus and
  classical dynamics.

  In the two-point-charge example discussed above, the magnetic force
  can not overcome the electric force, since the charges cannot travel
  faster than light.
>
>It's hard to put these concepts into words, but I hope
>that you'll get the gist of what I'm saying.

  I agree that it is hard to explain relativity in electromagnetics
  in a few words.  One ought to do thought experiments.

>
>Leo Freeman
>Physics Dept.
>Uviversity of Central Queensland,
>Rockhampton, QLD, Australia.
>

Yours respectfully,

-- 
Mustafa Kocaturk   mustafa@seas.smu.edu  EE Dept., Room 305A, Caruth Bldg.
Home: 214-706-5954  Office: 214-768-1475  SMU Box 753190, Dallas, TX 75275
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