From: heathjohn2@gmail.com   
      
   On Wednesday, February 15, 2017 at 3:44:37 AM UTC-5, Jos Bergervoet wrote:   
   > On 2/12/2017 5:27 PM, John Heath wrote:   
   >> On Thursday, December 29, 2016 at 11:21:45 AM UTC-5, Jos Bergervoet wrote:   
   >>> On 12/29/2016 8:59 AM, John Heath wrote:   
   >     ...   
   >   ...   
   >>>> Two wires from floor to ceiling 1 inch apart with current moving up in   
   >>>> both wires. The force is attractive.   
   >>>   
   >>> Exactly, that's magnetic force. And the electric force   
   >>> between the parallel moving charges (the electrons) is   
   >>> repulsive, so that's the opposite.   
   >>>   
   >>>> There are as many electrons as   
   >>>> there are protons in the copper wire. As current starts to flow up in   
   >>>> both wires the electrons see the other electron as non relativistic as   
   >>>> they are both moving up . However the electrons see the protons as   
   >>>> length contracted therefore there is and attractive Coulomb force   
   >>>> between the wires.   
   >>>   
   >>> You now have stationary particles in addition to the   
   >>> parallel moving charges. The electric force between the   
   >>> moving charges is still repulsive and my only claim   
   >>> was that that one is opposite to the magnetic force!   
   >>   
   >> I wish this exchange of ideas were closer to 900 MHz vs 2.4 GHz as I   
   >> could use some help in this area. I suspect you feel my pain.   
   >   
   > Actually I might be missing your exact point (why not consider   
   > 5.8GHz?)   
   >   
   > But we certainly can look at the two currents for these   
   > frequencies. There are basically two situations to look at:   
   >    1) We could consider currents without phase delay over the   
   > whole length of two long parallel wires. The analog of   
   > parallel or anti-parallel static currents would be   
   > in-phase alternating currents or 180 degrees out-of-phase   
   > currents, in both cases changing direction simultaneously   
   > everywhere along the length of the wires. (In practice this   
   > is not a behavior that is easy to create!)   
   >    2) We could have waves propagating over the wires, again   
   > with the currents either in-phase or 180 deg. out of phase,   
   > and with the waves moving in the same direction. (This is   
   > the more natural situation in a transmission line.)   
   >   
   >    In case 1) the fields of each wire can be expressed in   
   > Hankel functions of the radial distance to the wire, at   
   > small distances equal to the 1/r fields of the static case.   
   > So with increasing distance between the wires, the case with   
   > attractive force for DC currents (equal-direction currents)   
   > will turn into repulsive force and then back to attractive   
   > (and in between also alternating forces with the double   
   > frequency of the current!). There are no unbalanced charges   
   > in the wires so we have no radial E-fields, the only force is   
   > from the B-field.   
   >   
   >    In case 2) we basically have the two-wire transmission   
   > line. Opposite currents require the differential-mode   
   > solution for the signal, in-phase currents the common-mode   
   > solution. These are both approximately TEM solutions (the   
   > common-mode solution only very approximately) which means   
   > that: a) the fields are shaped more or less like static   
   > fields, and b) the forces from radial E-fields and from   
   > the B-fields now approximately cancel each other. The latter   
   > follows from the fact that d rho/dt = dI/dx, the continuity   
   > equation for the charge. This gives equal charges where   
   > there are equal currents (current and voltage are in phase   
   > in a transmission line) and as we saw above: that means   
   > opposite electric and magnetic forces! That they are also   
   > (approximately) equal in magnitude is easy to verify from   
   > the equations.   
   >   
   > So, at RF frequencies, with transmission line behavior of   
   > the currents, the force is substantially smaller than for   
   > a pure DC current (without voltage). Of course if you add   
   > a DC voltage as well (with the ratio to the current equal   
   > to the characteristic impedance of the transmission line)   
   > then you will have the same cancellation for DC as well.   
   >   
   > --   
   > Jos   
      
   There is a way to simplify. A magnet field caused by a moving charge   
   equals it velocity period. If one runs to catch up to the moving charge   
   the magnetic field disappears. The magnetic field depends on the   
   movement of the observer relative to the charge. This was the point   
   brought up in the introduction to special relativity that a magnetic   
   force and a Coulomb force do not have symmetry. Can a magnetic force be   
   considered real if its measurement depends of relative movement? One can   
   always measure a Coulomb force regardless of relative movement but a   
   magnetic field requires relative movement to a charge. This breaks the   
   symmetry between a Coulomb force and a magnetic force. One way to   
   restore symmetry is to consider a magnetic field just a Coulomb force   
   caused by relative movement of charges. Lorentz's contraction is a nice   
   way to visualize how this could happen.   
      
   Yes 5 GHz , less crowded.   
      
   --- SoupGate-Win32 v1.05   
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