Forces due to moving charge
23 March 2013

Electron and proton currents and magnetic fields
On the left, parallel electron currents attract.
In the middle, parallel electron and proton currents repel.
On the right, oppositly directed parallel electron and proton currents attract.
  • B = force/(velocity*charge) = magnetic field strength or
  • force = charge*velocity*B = q*v*B. We know a formula not the origin of the force.
  • E = force/charge = electric field strength or
  • force = charge*E = q*E
  • The green magnetic field created by the parallel red electron currents attract each other as shown by the little blue rectangle magnets.
  • The relative velocity of the electrons may be zero if they travel at the same velocity in the same direction in separate parallel wires.
  • The magnetic fields are created by the velocity of the charges relative to a usually unspecified background which Newton called absolute space and Mach called the background stars. Inertia, the pointing of a gyroscope or the figure of the Earth which is shaped by its spin as it rotates not in 24 hours with respect to the sun but in 23 hours 56 minutes 4 seconds are also with respect to this background. This is the sidereal rate of rotation.

When electron and proton currents attract
On the left, oppositly directed parallel electron and proton currents attract.
On the right, the orbiting dipole of the electron and proton, in an atom, are also parallel currents which attract each other.
  • The Coulomb forces are the attractive forces which holds the electron and proton together in orbit. The Coulomb forces are balanced by the outward directed centrifugal forces so that the orbits endure. See the Bohr Atom as a binary system.
  • The Coulomb forces are 59 thousand times stronger than the magnetic forces.
  • The red electron and blue proton currents are traveling in opposite directions on opposite sides of the barycenter. The proton has an opposite charge to the electron, so its magnetic field is reversed. As far as its magnetic field is concerned, the proton current can be considered to be an electron current moving in the opposite direction.
  • The moving electron and proton charges produce magnetic fields which attract each other across the barycenter.
  • The electron and proton also have an inherent magnetic moment independant of the forces due to moving charge.
  • The inherent magnetic moment may have their north pole spin up or spin down. This aids or opposes the magnetic field created by the movement of charge. The currents and magnetic fields calculated from the magnetic moment are gigantic. We are forced to consider a magnetic moment without an external magnetic field. See the Beaty video.

Constants used with orbiting electron and proton binary systems
me and mp are the mass of the electron and proton.
vE and vP are the velocity in orbit of the electron and proton.
rE and rP are the distance to the barycenter of the electron and proton. The barycenter is the center of the atom and the center of gravity of the atom.
cd = rE+rP is the center distance sum between the electron and proton.
cd = rc/(alpha2*k) The classical radius of the electron is rc. The fine structure constant is alpha.
k = mp/(me+mp) = 1 - me/mp = 0.999455 and 1/k = 1 + me/mp = 1.00054461703.
me*vE = mp*vP or mp/me = vE/vP = 1836.1526
me*rE = mp*rP or mp/me = rE/rP = 1836.1526
vE = c*alpha*k and rE = cd*k = rc/alpha2
vE/rE = vP/rP = c*alpha3*k/rc.
Electron and proton angular momentum or spin
mass current * area, the mass flowing around a loop, times the frequency, times the area enclosed by the loop is the angular momentum or spin.
mass *frequency *area, substituted for mass current.
mass *velocity/circumference *area, substituted for frequency.
mass *velocity/(2*pi*r) *pi*r2 = .5*mass*velocity*radius, collected terms.
For the orbiting electron, .5*me*vE*rE = .5*me* c*alpha*k* rc/alpha2 =
.5*me*c*k* rc/alpha = 5.26999317E-35_kg*m2/s

For the orbiting proton, .5*mp*vP*rP = .5 *mp *vE*me/mp *rE*me/mp =
.5*me*vE*rE*me/mp = .5* me *c*alpha*k*me/mp *rc/alpha2*me/mp =
.5 *me*c*k *rc/alpha *me/mp = 2.870128E-38_kg*m2/s
, me/mp of the electron angular momentum.
Electron and proton magnetic moment
The magnetic moment mm = .5*charge*velocity*radius.
The ring electron mm = .5 *ce *v *rring = .5 *ce *c *rc/alpha = 9.2740154E-24_A*m2.
The orbiting electron mm = .5 *ce *vE *rE = .5 *ce *c*alpha*k *rc/alpha2 =
.5 *ce *c*k *rc/alpha = 9.26896737E-24_A*m2.

The orbiting proton magnetic moment = .5 *ce *vP *rP = .5 *ce *vE*me/mp *rE*me/mp =
.5 *ce *c*alpha*k*me/mp *rc/alpha2*me/mp =
.5 *ce *c*k *rc/alpha*(me/mp)2 = 2.749247E-30_A*m2.

Electron and proton ring currents are equal in the binary atom
amps = i = current = charge *frequency, these are ring currents.
amps = i = charge *velocity/circumference = q *v/(2*pi*r) or q*v/i = 2*pi*r
iE = q*vE/(2*pi*rE) = ce *c*alpha3*k/(2*pi*rc) = 1.05360735557E-3_A

vP = vE*me/mp and rP = rE *me/mp = rc/alpha2 *me/mp
vP/rP = vE*me/(mp) *mp/(rE*me) = vE/rE
iP = q*vP/(2*pi*rP) = q*vE/(2*pi*rE), so iE = iP.

Electron and proton magnetic fields due to moving charge
u0*i/b = 2*pi*r or i/b = 2*pi*r*e0*c2
bE = iE/(2*pi*rE*e0*c2) = ce*vE/(4*pi*e0*pi*c2*rE2) = 3.98205511152_kg/(A*s2), almost four Tesla.
bP = bE *mp/me = 7311.66113078_kg/(A*s2), but bP = bE* mp/me or 1836.1526 times bigger than bE. These huge magnetic fields exert forces on their neighbor atoms.

Electron and proton equal and opposite attractive or repulsive magnetic forces
force = charge*velocity*magnetic field = q*v*B where also q*v*B = u0*i2
fE = ce*vE*bE =
fP = ce*vP*bP = ce* vE*me/mp* bE*mp/me = ce*vE*bE so fP = fE =
ce2*vE2/(4*pi*e0*pi*c2*rE2) = ce2/(4*pi*e0*rE2) *vE2/(pi*c2) =
Coulomb force *vE2/(pi*c2) = me*c2*rc *vE2/(pi*c2*rE2) = me*rc *vE2/(pi*rE2) =
me*rc/pi *vE2/rE2 = me*rc/pi *c2*alpha6 *k2/rc2 =
me*c2 *alpha6 *mp2/(pi*rc*(me+mp)2) = 1.39497829995E-12_kg*m/s2

Electron and proton magnetic energy
The electron energy based on magnetic force =
fE*.5*rE = 3.069095694694E-23_kg*m2/s2 = 0.00023037131_eV.
The proton energy based on magnetic force =
fP*.5*rP = 2.010157981E-26_kg*m2/s2 = 0.0000001254641_eV.
The electron plus the proton magnetic energy is 0.00023049678_eV
Electron and proton kinetic energy
The orbiting electron kinetic energy =
kE = .5*me*vE2 = .5 *me* (c*alpha*k)2 = 2.17750E-18_kg*m2/s2 = 13.59089_eV
The orbiting proton kinetic energy =
kP = .5*mp*vP2 = .5 *mp* (c*alpha*k*me/mp)2 = 1.18590E-21_kg*m2/s2 = 0.00740183_eV
kP = kE * me/mp.
The electron plus the proton kinetic energy = 13.598292_eV. This is the ionization energy. The energy added to pull the electron and proton apart.

A horizontal flip - causes a change in direction, kinetic energy and a rotational movement of the electron and proton to the opposite sides of their orbits if the flip occurs with the electron and proton in a horizontal line. If the electron and proton are in a verticle line then the flip is like the set below.

A verticle flip - causes a change in direction and kinetic energy while the electron and proton rotate in place with the electron and proton on a horizontal line. If the kinetic energy goes through zero and reverses direction we expect to see a 27. 2_eV flip transistion energy not the 0.00004_eV which is measured. We are forced to seek a Euler equation like precession. This requires the atom to have an inherent energy in its three dimensional rotational motion as you would expect of dipoles which always rotate around their center of mass - even at absolute zero. So we have rotations and torques around the x,y and z axes of the center of mass of the dipoles. Is this the zero-point energy? How is this related to superconductivity?

The forces due to moving charge work in parallel with the Coulomb forces between the electron and proton. Since the centrifugal and Coulomb forces are,
ce2/(4*pi*e0*cd2) = Coulomb force = 8.22974928053E-8_kg*m/s2, while the forces due to Bohr orbiting charge are,
ce2/(4*pi*e0*rE2) *vE2/(pi*c2) = electron Coulomb force *vE2/(pi*c2) = 1.39497829995E-12_kg*m/s2, which is 58995.536 times smaller so the,
Total force = Coulomb force *(1 +/- vE2/(pi*c2)) = 1 + .000016195043 or 1 - .000016195043 times the centrifugal or Coulomb forces depending on the direction of the spin of the proton and electron.
The electron and proton have very large circulating ring currents, magnetic fields and forces which are defined by their spin and magnetic moment. These forces are so large that we must look for a mechanism that allows a magnetic moment without a huge magnetic field. See the Beaty video.
The 3 to 2 Balmer hydrogen alpha transition - See the Balmer series spectral lines
3 2 656.2852_nm = 1.88918239631_eV, n=3, base=2, hydrogen alpha, electron spin up?
3 2 656.2720_nm = 1.8892203946_eV, n=3, base=2, hydrogen alpha, electron spin down?
The measured difference in the wavelength 0.0132_nm or 0.000038_eV is attributed to the interaction between the electron spin S and the orbital angular momentum L.
This is called Hydrogen Fine Structure = .000045_eV according to Hyperphysics.
Hyperfine splitting = 0.0000059_eV, E = h*frequency, at 1420.4_Mhz in the 21.1_cm band of radio telescopes. E = h*frequency = h*c/wavelength = 9.411676_kg*m2/s2 = 5.8743E-6_eV. This transistion has a half-life of 10E6_years.
The Lamb shift = 0.000004372_eV, E = h*frequency, at 1057_Mhz = h*1057E6_1/s = 7.00376_kg*m2/s2 = 4.3714E-6_eV
Atomic frequencies
frequency = amps/charge = iE/ce = 6.57609704E15_1/s. This is the frequency of atomic hydrogen that must pervade reality. If Ray Kurzweil and Moore's law are right then this frequency should be accessible in thirteen years if a terahertz is accessible now. What will beams of this frequency do to atoms? Will it disrupt atoms? There may be other uses for this frequency. See electric gravity.