The electron and proton have mass, charge, angular momentum and magnetic moment which can be tied together with the dynamic structure of a ring. They are tiny machines which have energy in orbit like Bohr's planetary atoms, helical electromagnetic waves and the Cosmos.
Ring electron: Drawn with the awesome and free k3dsurf. This is a hollow torus made out of a flux tube. The tube is very much smaller than the ring so the pretty drawing on the left is not to scale. The line drawing of the ellipse on the right is much closer to scale. The radius of the ring is rring and the radius of the tube is rtube. The ratio of rring/rtube = pi/alpha = 430.511. This ratio is like a one inch diameter garden hose with a length of 225 feet making a ring with a diameter of 72 feet. When you can see all of the ring it looks like a line drawing of an ellipse not a hollow torus. The ring proton also has this same ring/tube ratio but it is much smaller. A ring proton at this scale would be a dot smaller than a forth the width of the line. A charge may travel around the ring like water in a hose or be confined to a cross sectional ring or surface or both. Does charge have volume or does it only have surface? In the ring electron, there is a flux of charge, a current, flowing around a very skinny circular flux tube at the speed of light. Since this current must flow without loss, the electron is a superconductor.
Ratio of electrostatic to gravitational forces
FCE = ce2/(4*pi*e0*r2), this is the electrostatic repulsive force between two electrons with a charge of ce at a separation of r = 1 meter but rc = ce2/(4*pi*e0*me*c2) where rc is the classical radius of the electron or me*c2*rc = ce2/(4*pi*e0). FCE = me*c2*rc/r2, substituted me*c2*rc = ce2/(4*pi*e0) where the mass of the electron is me and c is the speed of light.
FGE = G*me2/r2, this is the gravitational force between two electrons at a separation of r = 1 meter. G is the gravitational constant.
FCE/FGE = c2*rc/(G*me) = 4.16E42, this is the huge ratio of electrostatic repulsive forces to gravitational attractive forces between two electrons.
FCE = FGE? We can write, the electrostatic repulsion of the charge of the electrons equals the gravitational attraction of the electrons, and see what happens. me*c2*rc/r2 = G*me2/r2. c2*rc = G*me, this is the blackhole formula with radius = rc and mass = me. r = G*me/c2 = 6.76E-58_m, the radius using the mass of the electron and the black hole formula which is based on gravity holding energy in orbit. This radius is far too small for the electron to have angular momentum or spin but this radius times the ratio of the electrostatic to gravitational forces equals rc. This is the classical radius of the electron. G*me/c2 * c2*rc/(G*me) = rc The ring electron can be described as having energy in orbit like a black hole but based on electromagnetic not gravitational forces holding the energy equivalent of mass in orbit. For an alternate approach see Don J. Stevens here or here.
Electrons
Electrons have a charge and a magnetic field. Moving charge is a current which produces a magnetic field so we may say the charge orbits in the electron producing its magnetic field. Does the charge loop because of the magnetic field or does the looping charge cause a magnetic field? We do know a charge and magnetic moment co-exist in the electron. The electron has an angular momentum and magnetic moment which require the energy equivalent of mass to orbit at a certain radius, which we use, so it is unlikely to be a point particle. The geometry of a ring electron can accommodate the electrodynamics necessary, for charge moving at the
speed of light, to be restrained by its magnetic field. Bergman's and Wesley's 1990 ring electron paper, ring protons and dual ring electron-proton neutrons are at this site worth exploring.
Planck's law
energy = hp*frequency, Planck's constant is hp = 6.6260755E-34_kg*m2/s. me*c2 = hp*frequency = 8.1871044E-14_kg*m2/s2, the energy of the electron. me*c2 = hp*c/wavelength, substituted for frequency. wavelength = hp*c/(me*c2) = hp/(me*c) = Compton's wavelength, isolated wavelength. r = wavelength/(2*pi) = hp/(2*pi*me*c) = rc/alpha, since hp = 2*pi*me*c*rc/alpha. me*c2 = hp *c/(2*pi*rc/alpha), this is hp*frequency. me*c2 = hp*c/(2*pi*rring) = hp *1.23559E20_1/s, frequency = c/(2*pi*rring). Planck's law implies the radius of the electron is rring = rc/alpha.
Electron magnetic moment
current *area, the current flowing around a loop times the area enclosed by the loop is the magnetic moment. The electron must have a shape. Current*area suggests the electron is a disk. We seek current as a ring and magnetic field as something like a disk. charge *frequency *area, substituted for current. charge *velocity/circumference *area, substituted for frequency. charge *velocity/(2*pi*r) *pi*r2, collected terms. .5*charge*velocity*radius = .5*q*v*radius = magnetic moment. .5*ce*c*rring = me*c2/(2*B) = magnetic moment where rring is the radius of the ring electron. .5*ce*c*rring = hp/(4*pi) *ce/me, equate with hp/(4*pi) *ce/me, the magnetic moment of the electron. .5*me*c*rring = hp/(4*pi), collected terms. The ce terms cancel and me is transposed. This is the same equation we see in the angular momentum. The incongruity between the magnetic moment and the angular momentum has been resolved in a simplistic even humorus way. Is this a too easy result? Are these simplistic solutions hiding a more complex underlying reality? The incongruity between two things being resolved in an odd way is one definition of a joke. We see a similar almost too simple pattern in the appendix, with e0*u0 = 1/c2 and z0 = 1/(e0*c) = c*u0_ohms. rring = hp /(2*pi*me*c) = rc/alpha, isolated rring where hp = 2*pi *me *c *rc/alpha. .5*q*v*rring = .5*ce*c*rc/alpha = mm = magnetic moment The magnetic moment implies that the radius of the electron is rring = rc/alpha.
The huge magnetic field of the electron from the electron magnetic moment is BrE = me*c2/(ce*c*rring) where the magnetic field increases as rringdecreases or BrE = me*c2/(ce*c*rc/alpha) = 4.41399827402E9_kg/(A*s2), 4 billion Tesla? A magnetic field this big would disrupt orbits in the atom were it not concealed in a loop.
Proton magnetic moment
.5 *charge *velocity *radius = magnetic moment. .5 *ce *c *rRP = hp/(4*pi) *ce/mp, equate with hp/(4*pi) *ce/mp, the magnetic moment of the proton. Spin is constant in both the electron and proton at hp/(4*pi). The magnetic moment is spin times the charge divided by the mass,
spin *ce/mp, hp/(4*pi) *ce/mp. The magnetic moment decreases with increasing mass of the proton. .5*mp *c *rRP = hp/(4*pi), collected terms.
rRP = hp /(2*pi*mp*c), isolated the radius of the ring proton. rRP = 2*pi*me*c*rc /(2*pi*mp*c*alpha), substituted for hp = 2*pi*me*c*rc/alpha. rRP = rRE * me/mp = rc/alpha *me/mp = 2.10309114269E-16_m, the radius of a ring proton is mp/me, 1836.15267145 times smaller than the ring electron.
The radius of the tube of the ring proton is 4.88510138648E-19_m.
Proton magnetic field
B = mp*c2/(ce*c*rp), the huge magnetic field of the proton from the proton magnetic moment. BrP = BrE *(mp/me)2 = mp*c2/(ce*c *rc/alpha *me/mp) = 1.48816037584E16_kg/(A*s2), a magnetic field this big would disrupt orbits in the atom were it not concealed in a loop.
Bohr magneton or electron magnetic moment
mm = .5*charge*velocity*radius. .5 *ce *v *rring = .5 *ce *c *rc/alpha = 9.27E-24_A*m2.
The accepted value of the magnetic moment, mm = 9.284770E-24_A*m2, is about (1+1/862) or (1+alpha/(2*pi)) times bigger than the Bohr magneton. Where do all those decimal places come from? We use a lot of decimal places only as a means of finding errors. We paint with a broad brush omitting small corrections. Small corrections imply perfect knowledge. We will see that alpha/pi is the ratio of the radii of the ring electron.
Electron angular momentum or spin
mass current * area, the mass flowing around a loop times the area enclosed by the loop is the angular momentum or spin. This implies that the electron is a disk as noted above mass *frequency *area, substituted for mass current. mass *velocity/circumference *area, substituted for frequency. me *c/(2*pi*r) *pi*r2, collected terms. .5 *me *c *rring = hp/(4*pi), equate with hp/(4*pi) the spin of the electron. This is the same equation we found in the magnetic moment. rring = hp /(2*pi*me*c) = rc/alpha = rc*137.036 = 3.86E-13_m, isolated rring.
The angular momentum implies that the radius of the electron is rring = rc/alpha.
Electron spin
Spin is constant at hp/(4*pi). We can write hp = 2*pi*me*c*rring. If the relativistic mass of me increases as the radius of rring decreases then the spin at hp/(4*pi) stays constant. The magnetic moment however hp/(4*pi) *ce/me decreases with increasing mass.
Planck's law, the spin and the magnet moment of the electron imply that the radius of the electron is rring = rc/alpha and that the circumference is, Compton's wavelength = 2*pi*rc/alpha = hp/(me*c). If me increases while rring decreases then the angular momentum may stay constant. If the mass me and therefore the rest energy increases then the radius of
the electron rring must decrease. The electron ring must show a very small radius at high energy in a particle accelerator. The electron tube is pi/alpha = 430.511 times smaller. The radii are ever smaller at higher energy. This is not evidence that the electron is a point particle. A point particle
must incorporate infinite magnetic pinch pressure, force/area, to restrain the infinite electrostatic pressure of repulsion, energy/volume, due to the charge of the electron being confined to the infinitely small volume of
a point. This makes a point particle electron infinitely improbable. While we abhor infinities, the gigantic ring currents and magnetic fields we calculate also strain credibility however, so much energy in such a small volume has to come from somewhere.
The g-factor
This is a quote from Wiki, "The spin of a charged particle is associated with a magnetic dipole moment with a g-factor differing from 1. This is incompatible with classical physics, assuming that the charge and mass of the particle are distributed evenly in spheres of equal radius." Of course, from the name of this paper, one might astutely infer we are not taking the electron as a sphere.
The electron is not a sphere
Is the electron a disk or a ring or what? Angular momentum = I *w, where I is the moment of inertia and w is the angular velocity. hp/(4*pi) = I *w, substitute for the angular momentum of the electron,
where w = v/r = c/r and the velocity is v = c in the electron. hp/(4*pi) = I *c/r, substitute for w. r = I * 4*pi*c/hp, isolate r. r = m*r2 * 4*pi*c/hp, substitute for the moment of inertia of a ring: I = m*r2. r = hp/(4*pi*me*c), isolate r. This is the radius for a ring with the correct angular momentum.
r = I * 4*pi*c/hp, from above. r = 1/2*m*r2 * 4*pi*c/hp, substitute for the moment of inertia of a disk: I = 1/2*m*r2. r = hp/(2*pi*me*c) = rc/alpha = 3.86E-13_m, isolate r. This is the radius for a disk with the correct angular momentum.
I speculate, the ambiguity in the shape of the electron, in its moment of inertia, might be resolved in favor of the disk shaped electron. We have toroidal currents along the circumference of the ring of the electron and poloidal magnetic flux through the area of the ring of the electron. Both of which have energy and therefore mass.
It would be hard to say the mass is only confined to the ring. The mass might be said to be confined to something like a disk which includes the ring.
q*E = q*c*B
The charge of the electron is q = ce, the electric field is E or force per charge. B is the magnetic field or force per charge per velocity. q*E is a radial force like centrifugal force. q*c*B is a center seeking force like gravity. E = c*B when canceling q in an electromagnetic wave. force = q*v*B = A*s*m/s*B = amp*second*meters/second*B = amp*meter*B = A*m*B. This q*v*B force is what keeps charge in orbit in the electromagnetic wave, cyclotron, tokamak and ring electron and what causes the spiral of charged particles in the magnetic field of a bubble chamber as the particles loose velocity. q*v*B acts like a central force to keep the charge and its energy equivalent of mass in orbit. We are comfortable with the not-so-obvious central force of gravity holding the planets in orbit. This central force is more obscure. There is no central object to provide a central force. There is only q*v*B. The direction of the moving charge is changed by B.How does this work? We know how it acts sometimes. We seek a metaphor to describe this peculiar force.
Poincare stress and energy density
"Poincare stress" has to be present to prevent the electric charge of an electron from flying apart due to the Coulomb repulsion". See Paul Marmet.
q*E = q*c*B: The electrostatic force of repulsion of the charge equals the magnetic pinch force of attraction of the charge when the charge moves at the speed of light. E = c*B, cancelled q, units are volts per meter, force per charge or kg*m/(A*s3) E2 = B2*c2, squared. E2 = B2 *1/(u0*e0), substituted c2 = 1/(u0*e0) E2*e0 = B2/u0 = 1.55E25_kg/(m*s2), The energy density or pressure of the E and B fields are equal. force/area = energy/volume = kg/(m*s2) = pressure = Pascals
kg*m/s2 /m2 = kg*m2/s2 /m3 = kg/(m*s2)
This is the magnetic pinch pressure equals the electrostatic pressure of repulsion. This magnetic pinch pressure restrains the charge to the thin ring of the electron like a hose restrains
water.
Electron energy
force *radius = energy, in an orbiting system. q*v*B *rring = me*c2, energy of the orbiting electron where v is velocity c and rring is radius.
Cyclotron formula
q*c*B = me*c2/rring, the cyclotron formula with centrifugal force = mass*v2/rring,
where the q*c*B force holds the mass energy of the electron charge in orbit.
Electronmagnetic field
B = me*c/(ce*rring) = me*c*alpha/(ce*rc), isolated B with q = ce. B = me*c2/(mm*2) = 4.414E9_kg/(A*s2), Four billion Teslas. This is the huge magnetic field calculated from the mass and the magnetic moment. A magnetic field this big would disrupt orbits of atoms were the magnetic field not contained within a loop. See the Beaty video. This is the B at rring which holds the charge in orbit. This same value of B is next used at rtube. It is used with the current and Ampere's law to define the radius of the tube. The huge magnetic field of the electron is derived from the well measured mm = electron magnetic moment. mm = .5*charge*velocity*radius = magnetic moment mm = .5*ce*c*rring = .5*ce*c*rc/alpha = ce*hp/(4*pi*me). 2*mm*B = 2 * .5*ce*c*rring * me*c/(ce*rring) = me*c2 2*mm*B = me*c2, the magnetic potential energy is the rest mass energy. 2*mm*B = hp *frequency, this is the electron spin resonance formula. The amount of rotational work is the torque times the angle to rotate the electron from alignment with the magnetic field to alignment plus 180 degrees which is a spin flip. me*c2/hp = 1.23559E20_1/s, the frequency of the ring electron. me*c2*alpha2/hp = 6.57968E15_1/s, the frequency of the Bohr atom.
Toroidal electron current
amps = current = charge *frequency = charge * velocity/circumference amps = ce *c/(2*pi*rring) = ce *c *me*c/hp = ce *me*c2/hp = ce2*c2/(4*pi*mm) = 19.8_A
Ampere’s law
The poloidal magnetic field around the tube of the electron is associated with the toroidal current along the ring of the electron. 2*pi*rtube*B/u0 = amps, The loop around rtube times B/u0 equals the toroidal current. rtube = amps/B *u0/(2*pi), radius of the tube rtube = ce*c/(2*pi*rring) *ce*rring/(me*c) *u0/(2*pi) = ce2/(2*pi*me) *u0/(2*pi) =
rtube = ce2/(4*pi*e0*me*c2 *pi) = rc/pi = 8.97E-16_m
rring = hp/(2*pi*me*c) = rc/alpha = 3.86E-13_m
rtube = alpha/pi *rring = alpha/pi *rc/alpha = rc/pi = rring /430.511
The ratio rring/rtube = pi/alpha = 430.511 stays constant with increasing rest energy so that the relative proportions of the electron stay the same with decreasing size of the electron at higher electron masses.
Bergman and Wesley in their version of the ring electron used charge/area = surface charge density. I see current through the tube which implies charge/volume = charge density. The ring electron model may illuminate some of these questions but we are very far from understanding nature.
righthandrule
Right hand rule modified 20111224
When you grab a ring with your right hand, the thumb points in the toroidal direction along the ring while the fingers curl through the area of the ring in the perpendicular poloidal direction around the tube. Poloidal flux, which occurs through an area, and perpendicular toroidal looping around, which occurs along a circumference, are always associated. A flux or current has magnitude and direction. It has a rate of change d/dt, if its direction changes, even if its magnitude, area or circumference do not change.
The flux of red E and green B, seen below, are as real as a mudslide. If they are real, what are they? We know their units. The mathematical interaction of units tells us something about the consistancy of our world model but one might mistake superficial knowledge of units for the deep knowledge of reality.
Ampere's and Faraday's laws
The red E electric field has units of volts/meter, kg*m/(A*s3) = kg*m/(s2) *1/(A*s), E = force/q, force per charge or force per (amp*second). force = q*E. q = A*s is charge.
The green B magnetic field has units of Weber's/m2 = Teslas = kg/(A*s2) = kg*m/(s2) *1/(A*m) , B = force/(charge*velocity), charge*velocity = amps*seconds*meters/second = amps*meters.
force = B*q*v = B*A*s*m/s = B*A*m. v is velocity. This B*q*v force is what keeps charge in orbit in the electromagnetic wave, cyclotron, tokamak and ring electron. B*q*v = kg*v2/r, where kg*v2/r = centrifugal force. r is the orbital radius. B*q*v acts like a central force to keep the charge and its energy equivalent of mass in orbit.
First on the left, Faraday's law/(c*u0): The red ring is the moving electron charge which is a toroidal electron current in amps. The green arrow is the magnetic flux. d(B*pi*r2)/dt /(c*u0) = 2*pi*r*E/(c*u0) = amps, Faraday's law/(c*u0).
The poloidal green flux of B/(c*u0) times the area of the ring equals the toroidal red E/(c*u0) times the circumference of the ring. Red exerts a torque around green. Second: The poloidal green flux which was shown as a green arrow is now shown as a green poloidal looping around the red torroidal current.
The green flux is still out of the ring like the north pole of a magnet. We will use the cyclotron formula to calculate the poloidal green flux of B. Third, Ampere's law: e0*d(E*pi*r2)/dt = 2*pi*r*B/u0 = amps. Maxwell's changing red poloidal displacement current times the area of the tube equals the toroidal green current times the circumference of the tube.
Green exerts a torque around red. This is a cross section through the second figure. It shows a single green loop of the poloidal flux around the tube and a piece of the red ring is now shown as a red arrow. In this cross section, showing the tube of the electron, the former red toroidal is now red poloidal and the former green poloidal is now green toroidal. This perpendicular transformation, in going to a cross section, changes our viewpoint from Faraday to Ampere. Forth: The poloidal red flux which was shown as a red arrow is now shown as a red poloidal looping around a green torroidal current.
The red flux is still out of the cross section of the tube. The red flux is the toroidal electron current along the ring of the electron.
Another view of ring electrons
Click images to enlarge! They are something like a wave guide. First on the left: A green helix on a red torus. The red electron current is surrounded by a green magnetic helix. As the distance between the green loops becomes infinitesmal, the green helix becomes a green tube, the green totally encloses the red like a hose encloses water. Second: A red helix on the green helix. The red torus is omitted for clarity. The green magnetic helix is surrounded by a red helical current layer. The red loops separation become infinitesmal in a different way than the green loops separation become infinitesmal. Third: The red helix of a red helix becomes a pink torroidal current. The green helix is omitted for clarity. As the distance between the red loops becomes infinitesmal, the field between the neighbor loops cancel where they are in opposite directions. The loops at the center of the tube, the pink current inside the green layer, reinforce each other where these loops are pointing in the same direction. The loops on the outside of the tube, outside of the green layer, reinforce each other, where they are pointing in the same direction. The residual field is the original electron current which is here shown as pink in the center of the tube, a green magnetic layer which is not shown and a current on the outside of the torus flowing in a direction opposite to the current in the center of the torus. Forth: A red helix on on a green helix on a pink torus of current. This is the view when all three layers are stacked up. The red electron current, in the center of the torus, is here shown as pink for clarity.
Helical loops cancel when oppositely directed and add when commonly directed:
These helical current loops wrap around the green magnetic field which wraps around the torus.
The red side of the loops and the blue side of the loops go in different directions, so they have a tendency to cancel when they are close together. Where the loops point in a common direction they have a tendency to add like the blue line at the top, which touches the torus, and the red line at the bottom, which is a little farther out from the torus.
Appendix
Volume and density: 2*pi*rring *2*pi*rtube = 1.367E-26_m2, ring electron torus surface area. Ce /(2*pi*rring *2*pi*rtube) = 11.716E6_A*s/m2, surface charge density. 2*pi*rring *pi*rtube2 = 2*pi*rc/alpha *pi*rc2/pi2 = 2*rc3/alpha = 6.1328E-42_m3, ring electron torus volume. Ce *alpha/(2*rc3) = 2.61246E22_A*s/m3, charge volume density. me *alpha/(2*rc3) = 1.4853E11_kg/m3. Ring electron density. Nuclear density is much larger at 10E21_kg/m3.
me*c2 *alpha/(2*rc3) = 1.3349E28_kg/(m*s2). Ring electron energy density using only the volume of the ring. This is 861.0224 times the energy density of B2/u0 or E2*e0. me*c2 *alpha/(2*rc3) / {B2/u0} = 861.0224 me*c2 *alpha/(2*rc3) / {(me*c*alpha/(ce*rc))2/u0} =
me*c2 *alpha/(2*rc3) / {me2*c2*alpha2/(ce2*rc2*u0)} =
1/(2*rc) / {me*alpha/(ce2*u0)} =
ce2*u0/(2*rc* me*alpha) = 861.0224 = 2*pi/alpha
ce2/(2*rc* me*c2*e0*alpha) = 861.0224 = 2*pi/alpha or rc = ce2/(4*pi*e0 *me*c2), This is true.
Constants: me = 9.109E-31_kg, mass of the electron ce = 1.602E-19_A*s, charge of the electron e0 = 1E7/(4*pi*c2)_A2*s2/(kg*m), permittivity of free space. u0 = 4*pi/1E7_kg*m/(A2*s2), permeability of free space e0*u0 = 1/c2 z0 = 1/(e0*c) = c*u0 = 376.73_kg*m2/(A2*s3) = ohms, impedance of space 4*pi/u0 = e0*4*pi*c2 = ce2/(me*rc) = 1E7_A2*s2/(kg*m)
rc = ce2/(4*pi*e0*me*c2) = 2.82E-15_m, the classical radius of the electron. me*c2 = ce2/(4*pi *e0 *rc), The rest energy me*c2 equals the energy associated with the charge of the electron of ce and a radius of rc. If the rest energy increases then rc decreases.
alpha = fine structure constant = .007297 or 1/137.036
hp = Planck's constant = 2*pi*me*c*rc/alpha = 6.626E-34 _kg*m2/s
frequency*wavelength = c
me*c2 = hp*frequency
me*c2 = hp*c/wavelength
wavelength = hp/(me*c) = Compton's wavelength = 2.426E-12_m, the circumference of the ring electron. hp*alpha = 2*pi*me*c*rc = ce2 /(2*c*e0)
Any symbolic definition of hp uses alpha and any symbolic definition of alpha uses hp. This gives us at least two definitions each of both hp and alpha. Combinations of the above three terms are
seen. Electron spin comes from the first and second while rc comes from the first and second or the second and third.
me*c2*rc = ce2/(4*pi*e0) = 2.307E-28_kg*m3/s2, for comparison with, 1.41E-28_m3/(kg*s3) = c3/Mc = G/age, Mc is the mass of the cosmos about 1.91E53_kg. G about 6.67 E-11_m3/(kg*s2) is the gravitational constant. Age is the age of the cosmos about 15 billion years = 4.74E17_s.
Are these small and similar numbers a clue linking the force between electrons and the cosmological constants or is this merely numerology ?
On the left, currents traveling in the same direction in parallel wires attract each other.
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 electrons relative to a usually unspecified background which Mach called the background stars. They are not relative to the velocity of the electrons in the other wire.
On the right, the electron and proton in orbit in an atom are also parallel currents which attract each other.
The red electron current and the blue proton current are traveling in opposite directions on opposite sides of the barycenter
but the proton current can be considered to be an electron current moving in the opposite direction as far as its magnetic field is concerned.
The electron and proton currents produce magnetic fields which attract each other across the barycenter.
The Coulomb forces which are 59 thousand times stronger than the magnetic forces.
The Coulomb forces are the central force which holds the electron and proton in orbit. They are caused by the opposite charges between the electron and proton across the barycenter. See the Bohr Atom as a binary system.
The above magnetic fields are only due to the electron and proton charge moving in orbit with each other.
The electron and proton also have an inherent magnetic moment which is ignored since we are only looking at 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 a magnetic field or without a current which creates a magnetic field.
Electron and proton toroidal currents in the Bohr 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
where me is the mass of the electron and mp is the mass of the proton
and cd = rE+rP is the center distance sum between the electron rE and rP the proton
where k = mp/(me+mp) and cd = rc/(alpha2*k) where rc is the classical radius of the electron
and vE and vP are the electron and proton velocity in orbit
while vE = c*alpha*k and rE = cd*k = rc/alpha2
and vE/rE = vP/rP = c*alpha3*k/rc. iE = q*vE/(2*pi*rE) = ce *c*alpha3*k/(2*pi*rc) = 1.05360735557E-3_a
While 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)= 1.05360735556E-3_a so iE = iP.
Electron and proton poloidal magnetic fields
u0*i/b = 2*pi*r bE = u0*iE/(2*pi*rE) = ce*vE/(4*pi*e0*pi*c2*rE2) = 3.98205511152_kg/(a*s2), almost four Tesla. bP = bE *mp/me = u0*iP/(2*pi*rP) = 7311.66113078_kg/(a*s2), but bP is mp/me or 1836.1526 times bigger than bE.
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 = 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 fE*.5*rE = 3.069095694694E-23_kg*m2/s2 = 0.00023037131_eV = electron kinetic energy
fP = ce*vP*bP = ce* vE*me/mp* bE*mp/me = ce*vE*bE = 1.39497829992E-12_kg*m/s2. fP*.5*rP = 2.010157981E-26_kg*m2/s2 = 0.0000001254641_eV = proton kinetic energy
The electron plus the proton kinetic energy is 0.00023049678_eV
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 between these first two rows is attributed
to the spin of the proton being spin up and the spin of the electron being either spin up or spin down.
These are forces that work in parallel with the Coulomb forces between the electron and proton. Since the centrifugal and Coulomb forces are, ce2/(4*pi*e0*rE2) = 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) =
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. These seem to be of the correct magnitude.
We need to calculate these forces to determine the spectral lines around the 3 to 2 hydrogen alpha Bohr transitions where the electron spin up and spin down are said to cause the observed differences in wavelength. These forces are caused by the movement of charge in the magnetic field created by the movement of the charge, q*v*B = the charge *the velocity of the charge *the magnetic field of the charge created by the movement of the charge = u0 *current2. These forces are with respect to some usually unspecified background, as is inertia or the pointing of a gyroscope or the figure of the Earth as it rotates not in 24 hours with respect to the sun but in 23 hours 56 minutes 4.091 seconds with respect to the background stars, the sidereal rate of rotation.
The ring electron and ring 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 magnetic field.
Physicist are fond of saying that spin or angular momentum and magnetic moment have no classical analogy - like we just calculated. We can push the limits of classical behavior.
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 electrostatic or electrodynamic gravity.
Magnets
Magnets
modified 20111107
Iron filings and bar magnets
When you look at the pattern of iron filings on a glass or plastic over a short bar magnet you see lines of magnetized iron filings stuck together by magnetism. The iron filings have become lines of tiny series magnets, lines of tiny series dipoles, curving around to the opposite poles of the bar magnet. Energy is stored in each dipole. We have serial tensile forces. We have to add the binding energy of the dipoles to pull them apart. The lines of tiny series magnets repel each other which accounts for their spacing. The lines repel each other because their poles point in the same direction and like poles repel. The lines may stick together and clump when they are close to each other and their centers are offset. K&J has an interesting magnetic field calculator which shows a pattern similar to the above for thin disk magnets. Helmholtz coils are similar. See hyperphysics for a loop or ring current.
We might say that magnetic field lines originate at the top of a magnet and return at the bottom of a magnet as they do in the figure above. A much longer magnet would have its field lines stretched into a solenoid, loosing its circular symmetry, but the lines still leave the top and return to the bottom of the magnet. When this long magnet is bent and closed into a loop, its top and bottom and the source and destination of the lines merge so the lines disappear so the magnetic field in a ring is concealed. If the green magnet above is stretched into a long bar magnet and bent and closed into a loop then the external field of the magnet disappears. The huge ring currents in the electron and proton if seen would have huge magnetic fields which would disrupt the orbits of the electron and proton in the atom but since the ring current is closed into a loop the external fields disappears. The ring currents still cause the magnetic moment so we are left with the peculiar situation of a magnetic moment without an obvious source magnetic field. In the electron and proton where the charge q moves at the speed of light c we have, q*E = q*c*B, which can be written E = c*B, E2 = c2*B2, E2 = B2/(e0*u0),
E2*e0 = B2/u0, energy/volume Coulomb repulsion pressure = force/area magnetic pinch pressure. Is this something which suppresses the huge magnetic field of the electron which is due to its magnetic moment?
Rings of magnetic beads or spherical magnets
have a lot of tensile strength and are hard to pull apart. They are series magnetic dipoles. Rings hide the bipolar glue of their dipolar units which holds them together in rings. Their hidden flux is confined to the ring. See helical electromagnetic waves. Toroidal transformers are used in radio work because of their low noise or signal leakage. Rings of very strong spherical magnets have a very strong internal magnetic field and a very weak external magnetic field but they still maintain their strong tensile forces. See the Beaty video. Magnets have other interesting structural assembly properties. Interesting sources are K&J and neocube. Warning! Magnets can be addictive. One might be subject to spousal abuse for spending too much money on too many magnets.
In a similar way, the field lines from a charge dipole or polarized atom might leave from one end and return to the other end of the dipole so we might expect a series of charge dipoles to act like the series of magnetic dipoles and hide the majority of their lines in a ring with only minor leakage and still maintain their strong tensile forces.
Magnetic beads
Bipolar atoms stick together like magnetized iron filings or strings of magnetic beads. This is like the magnetic beads in the figure below. The ends of the rows of polarized atoms have a strong polarity and strong attractive and repulsive forces.
Neodymium magnets
are a fun way to experiment with bipolar ideas. The ends of rows of magnetic beads have a strong polarity. These rows of magnets stick together because they are offset, close together and their poles point in the same direction.
Like poles repell
These rows of magnets repell each other because like charges repell.
Opposite poles attract
These rows of magnets stick together because opposite poles attract.
Loops of magnets
Magnets stick together to make a helix out of a long string of magnets. Only the ends are exposed and show the polarity. The two loops of magnets on the right attract each other because opposite poles attract. Loops of electrostatic dipoles attract each other in just this way.
Magnets and dipoles
Both have poles. Poles have polarity. Oppositely charged poles are bipoles or dipoles.
The forces between their charged ends may be expressed, by us, with parallel and perpendicular components. They assemble in complex structures.
Magnets are accessible. Magnets are magnetic dipoles which are a model for charge dipoles which are a model for gravity.
