At 11:32 AM 1/31/5, Merlyn wrote:
>OK, I've done some more pondering on the whole thing, and I think I may
>have an answer.
>
>Assuming the electric field propagates at c, as the magnetic field is
>proven to do, then there would be a notable "dopplering" of the field
>gradient surrounding a moving charged particle.
>
>This Doppler effect would decrease the force on a charged particle ahead
>of the moving one and increase the force on a particle behind it.
>
>A particle at rest WRT the aether would experience a lesser force, and
>then a greater force, which would average to be no effect at all.
>
>A particle moving relative to the aether however would experience a
>different force, as the effective field gradients would be modified by the
>momentum of the moving particle.
>
>Identicle charged particles moving in the same direction are not
>"attracted" to each other, they are simply repelled less strongly than if
>they were stationary. Surrounding electrostatic pressure takes care of
>the rest.
>
>When the particles pass each other moving in opposite directions, the
>repulsion is enhanced.
>
>Perhaps by doing the math related to this idea, one could determine a
>difference in magnetic field strength between 2 systems with identical
>amperages, but widely different drift speeds.
You have to remember that at a given current I that a higher drift speed
means a lower (current carrying) charge density. You end up with the
exactly same magnetic effects, unless the "drift speed" happens to be very
near c.
A quantitative analysis of all this was done in Purcell, *Electrcity and
Magnetism*, and Shadowitz, *The Electromagnetic Field*. However, it is
based on special relativity, the apparent compression of space associated
with moving objects (by a factor of gamma). This apparent compression of
space containing charge amounts to an increase of apparent charge density
rho. In other words:
rho = rho_0 * (1 - v^2/c^2)^(-1/2)
Starting from this point it is possible to generate ampere's laws, for
parallel wires, etc. Thus magnetism is entirely the result of the relative
motion of charges.
So, differentiating with respect to v, we get
d(rho)/dv = (rho_0/c^2) * v * (1 - v^2/c^2)^(-3/2)
Where at small c the term (1 - v^2/c^2)^(-3/2) can be ignored so:
d(rho)/dv = (rho_0/c^2) * v
and from this, applied separately to the moving charge carriers and
stationary charges of the two wires of interest, it can be shown the net
force is proportional to current squared, etc. This all goes to show that
relativistic effects at small velocities multiplied by a huge charge
densities can produce ordinary world effects.
Another viewpoint is that magnetism is purely the result of the
electrostatic force when retardation is considered, i.e. causality.
Retardation is the effect of the delay of force transmission. The
electrostatic force is transmitted at velocity c. When two bodies are in
motion, the force on body A from body B comes from the location of body B
at an earlier time, the retarded time. There is a complete quantitative
discussion of this and other issues, like relativistic clocks, in
Jefimenko's *Retardation and Relativity* (ISBN 0-917406-21-4). This
concept is extended to gravity and the cogravitational field (which I
called gravimagnetism) in Oleg D. Jefimenko's *Causality, Electromagnetic
Induction, and Gravitation* (ISBN 0-917406-12-5). Jefimenko also produces
the complete quantitative results you are looking for.
Regards,
Horace Heffner
