Does the Velocity of Magnetic Field Effects Violate Maxwell's Equations?

[yogi]

We will imagine a core ring of magnetic material (hi mu) encompassing the earth. At one station, we wrap a couple of loops of wire to form the primary winding of a transformer - say in Los Angeles. At another part of the earth, say Paris, we wrap a few turns to form a secondary winding - our thought experiment assumes no leakage inductance and no stray capacitance. Now energize the primary winding with an AC sin wave and measure the phase of the secondary - we know the divergence of the magnetic field is zero - and consequently the lines are continuous - therefore the magnetic lines should not be of greater strength near the source - neither near the North or South pole of the primary winding - nor should the density of the field vary along the circumference of the ring at any given instant

If the secondary and primary voltages are in phase, the signal is coupled at greater than c. If the phase of the secondary lags the primary, then the magnetic field lines are not continuous and the divergence is not zero which conflicts with our assumption re closed loop character of magnetic flux lines.

 

[Farsight]

You can't ignore inductance, yogi. It's how the primary voltage creates the secondary. And it takes time.

 

[pallidin]

I think that yogi is under the erroneous impression that a magnetic field propagates "instantaneously" It does not. The maximum velocity of a magnetic field is the speed of light.

 

[yogi]

You can't ignore inductance, yogi. It's how the primary voltage creates the secondary. And it takes time.

I know, inductance opposes a change in current - that is not the issue - its the continuity of flux - put a small secondary winding near the primay if you will - then measure the phase of the signals in the two secondary windings - magnetics tells us that the lines are continuous - non divergent, so both secondary voltages should be in phase is stray capacitance and leakage inductance are ignored

 

[yogi]

I think that yogi is under the erroneous impression that a magnetic field propagates "instantaneously" It does not. The maximum velocity of a magnetic field is the speed of light.

That is the whole point of the thought experiment - we all agree that em waves and photons travel at c in any inertial system - but we do not have good experimetal evidence that gravity, electrostatic and magnetic force producing fields travel at c - waves travel at c - but charges in motion move as though they where influenced by the instaneous position of the charges rather than their retarded position. In GR there is a term that comes out of the equations that almost balances the retarded potential - but there is not a similar term for magntics - so there is reason to ponder experiments that might verify whether the magnetic field becomes divergent at high frequency

 

[pervect]

I would say that Maxwell's equations are well tested, and we know that the magnetic vector potential A, and the associated B field (the curl of the vector potential) will change at the speed of light and not supraluminally.

Unfortunately, while I know this to be true in general, I don't have a good handle on how this applies to Yogi's specific problem.