Galaxies and solar systems may form around currents in space as in the plasma universe. This is a flux causing a looping around. The disks around proto-stars frequently have jets as do galaxies. This is a looping around causes a flux (jet). Faraday's and Ampere's laws at a huge scale.

- The red in equals the green out. Ampere's law.

- The green in equals the red out. Faraday's law.

- The red in equals the green out. Ampere's law.

- The green in equals the red out. Faraday's law.

**The speed of light:**
is the speed that the green B magnetic field or
the red E electric field, loops around and augers to the right. The index of refraction, of the medium, reduces the velocity. The quarter wavelength pulse of flux, through the quarter circle of area, produces a quarter wavelength looping around the circumference, a quarter wavelength advance of the electromagnetic wave, in wavelength/(4*c) seconds.

These waveforms are not the right shape. They do not go to zero at a change in direction. They are fun to make out of colored wires, see Appendix 5. The red and green are correctly, 90 degrees out of phase. They demonstate the torque around a perpendicular axis. A torque around two perpendicular axises produces a torque perpendicular to both in a gyroscope. Here the axises of the torque is moving with the waves.

The flux of E or B through an area makes a 90 degree turn and then B or E rotates around the circumference. In a centrifugal pump, the liquid enters the eye of the pump, the center of the impeller, makes a 90 degree turn and is slung outward by the motor along a path that ends with rotation along the circumference.

This question was answered. By adjusting the phase of parallel beams of light, rotating the polarization, the beams may be made to attract or repell each other. This is demonstrated in this Nature article or this Discover article.

** Do we pretty much know everything? **We have no deep knowledge of the underlying reality. Our ignorance is more profound than just the missing link between quantum mechanics and relativity. Perhaps both are flawed and the pieces that each contributes to the puzzle of reality need to be rearranged by cherry-picking the best pieces of each. Science is a puzzle. When you close your eyes or walk in the dark to another room, you still know where you are because of your internal world model. Consciousness is seeing oneself mirror-like in ones internal world model. Our knowledge of reality is as riddled with voids as is swiss cheese. Our consciousness papers over these voids so our world model is perceived as smooth and uncomplicated for quick actions necessary for survival. We evolved to quickly see the face of a predator or prey in the shadows. We also see faces in the clouds. Some see the face of God. Apparently, we only see the shiny bits not the voids. We assemble these bits to quickly paint a shallow picture of reality and proceed to live our lives by rules-of-thumb based on these perceptions.

What are forces? We see the puppets move but we don't see the strings. How are forces propagated? What is their velocity of propagation? What is inertia? These are big unanswered questions which are close to home. Do you see the absurdity of trying to answer deep question about reality, like these, with sentences which include words like "virtual"? Do you see virtual photons in the clouds? Are you seduced by these shiny bits? Do our perceptions and behaviors seem so-ape-like?

The red

The green **B** magnetic field has units of **Weber's/m ^{2} = Teslas = kg/(A*s^{2}) = kg*m/(s^{2}) *1/(A*m) ,**

**Poincaré stress and energy density:** “Poincaré 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*s^{3})

**E ^{2} = B^{2}*c^{2}**, squared.

kg*m/s

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.

**Converting Ampere's law to Faraday's law/(c*u0):**

**d(E*pi*r ^{2})/dt *e0 = 2*pi*r*B/u0 = amps.** Start with Ampere's law. c*u0 = 376.73_ohms.

**Figure 3: First on the left, Faraday's law/(c*u0):**

**d(B*pi*r**^{2})/dt /(c*u0) = 2*pi*r*E/(c*u0) = amps.

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. B, E and the area of their loops may be constant but there is looping. A change in direction is also a change over time in the flux, a dB/dt or dE/dt.

**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.

**Third, Ampere's law:**

**e0*d(E*pi*r**Maxwell's changing red poloidal displacement current times the area of the tube equals the toroidal green current times the circumference of the tube.^{2})/dt = 2*pi*r*B/u0 = amps.

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, the former red toroidal is now red poroidal and the former green poroidal is now green toroidal. This perpendicular transformation 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 ring.

E and B are sine and cosine waves because they are ninety degrees out of phase. B is the cosine since it has a sign change in its derivative. Lenz's law comes from the sign change in the derivative. d(cos)/dt = -sin or d(-cos)/dt = sin. Faraday's law is applied twice per wavelength so there is no net sign change per wavelength since, -1*-1 = 1. This sign change does not occur in Ampere's law, noting d(sin)/dt = cos or d(-sin)/dt = -cos, does not have a sign change.

Our derivation of Faraday's law starts with the idea that the rate of change of B is 4*pi*B times the frequency of the wave.

When we divide the voltage on both sides of Faraday's law by the resistance of a loop or coil of wire then we get Ohm's law: volts/resistance = amps.

**Integrals of Faraday's law:
E*ds = -d( _{B})/dt,** integral form of Faraday's law.
Hyperphysics or Wiki

Our derivation of Ampere's law is very similar to Faraday's law. The rate of change of E is 4*pi*E times the frequency of the wave.

Toroidal green B times the circumference of the loop equals one over c squared times the rate of change of the poloidal electrical flux of red E times the area of the loop. Ampere's law.

**Integrals of Ampere's law:
B*ds = 1/c ^{2}*d(_{E})/dt**

**dV = R*dI,** R is a resistor and a traditional electrical element.

**dq = C*dV,** C is a capacitor and a traditional electrical element.

**d _{B} = L*dI,** L is a inductor and a traditional electrical element.

We have R, C, and L defined by unique groupings of dV, dq, dI and d

**Ampere's law = Faraday's law/(c*u0),** amps = amps.

**B*c = E,** in electromagnetic waves.

**2*pi*r*B/u0 = 2*pi*r*E/(c*u0),** multiply both sides by 2*pi*r/(c*u0). This is,
Ampere's law = Faraday's law/(c*u0).

**2*pi*r*B/u0 = 2*pi*r*B*c/(c*u0),** E = B*c in electromagnetic waves.

**2*pi*r*B/u0 = 2*pi*r*B/u0,** They are equal. The amps from both laws must be equal for one law to transform into the other.

The energy is located along the rotating circular rings of circumference of the flux tubes. E and B rotate in opposite directions. Where the E and B flux tubes touch there is a rolling contact and transfer of energy and circumference as the flux tubes change size. This is a three dimensional view
of an action which occurs over time on the two dimensional surface of the expanding spherical wavefront. The action and flux tubes are created by expanding and shrinking ring pairs on the wavefront.
We have an alternating electric field flux tube which spirals along an alternating magnetic field flux tube and an alternating magnetic field flux tube which spirals along an alternating electric field flux tube. They are braided. A line between the centers of the E and B flux tubes traces out the icon of life, a double helix. Life preceeded by light. Nature also shows us this shape in a stream of water or the chop on a lake. There is a circular circulation in a cross section of a
wave of water or a wave of light. Here the waves only appear bean like or volume like when seen over time, but they exist only as swirling rings of energy on an expanding spherical wave front, only
in the here and now, rain drops making rings on still water.

- Red in green out, red exerts a torque around green, +E → +B, d(sine)/dt → cosine.
**Row 1 on figure 2E**.

**e0*d(E*pi*r**Ampere's law. Maxwell's red changing poloidal displacement current times the area of the loop equals the green toroidal current times the circumference of the loop.^{2})/dt = 2*pi*r*B/u0 = amps, - Green in -pink out, green exerts a torque around -pink, +B → -E, d(cosine)/dt → -sine.
**Row 2 on figure 2E**.

**(d(B*pi*r**Faraday's law/(c*u0). The changing green poloidal current times the area of the loop equals the toroidal pink current times the circumference of the loop.^{2})/dt) /(c*u0) = 2*pi*r*-E /(c*u0) = amps, - -Pink in -cyan out, -pink exerts a torque around -cyan, -E → -B, d(-sine)/dt → -cosine.
**Row 3 on figure 2E**.

**e0*d(-E*pi*r**Ampere's law. Maxwell's changing pink poloidal displacement current times the area of the loop equals the toroidal cyan current times the circumference of the loop.^{2})/dt = 2*pi*r*-B/u0 = amps, - -Cyan in red out, -cyan exerts a torque around red, -B → +E, d(-cosine)/dt → sine.
**Row 4 on figure 2E**.

**(d(-B*pi*r**Faraday's law/(c*u0). The changing poloidal cyan current times the area of the loop equals the toroidal red current times the circumference of the loop.^{2})/dt) /(c*u0) = 2*pi*r*E /(c*u0) = amps,

The energy is located along the rotating circular rings of circumference of the flux tubes. E and B rotate in opposite directions. Where the E an B rings touch there is a rolling contact and transfer of energy and circumference as the rings change size. This is an action which occurs over time on the two dimensional surface of the expanding spherical wavefront. The action and flux tubes are created by expanding and shrinking ring pairs on the wavefront. We have an alternating electric field ring which spirals along an alternating magnetic field ring and an alternating magnetic field ring which spirals along an alternating electric field ring. They are braided. A line between the centers of the E and B rings or the flux tubes traces out the icon of life, a double helix. Life preceeded by light.

We saw on figure 2D top and side views showing sine and cosine waves. This is a movie array showing 24 cross sections through those flux tubes per wavelength. Here we have end views of
cross sections of figure 2D. The cross sections through the flux tubes are loops or rings. The sequence is +red→+green→-pink→-cyan→+red.
The expanding spherical shell of any electromagnetic wavefront would hawidth="443" height="194" ave
polka-dots of this pattern. These rings are the only substance an electromagnetic wave has. They only exist on a wavefront.

We only see the sine and cosine waves or flux tubes of figure 2D through the persistance of vision of an oscilloscope. The circles in the animation are vaguely reminiscent of accreation disks, like those found in binary star systems, where one star streams material onto the other star. **Here we expect a current to stream from one ring to the other at their point of rolling contact.**

**On the left**, a capacitor ring is shown in two stages as it shrinks.- A string of charges making a ring has a uniform charge per unit length. The charge
**Q**along the rings per unit length is uniform but the circumference and area is changing. The ring looses charge as it shrinks. A shrinking or expanding ring with a charge per unit length would show**dQ/dt**which is amps. - A charge has an electric field
**E**. The electric field along the ring is uniform but the length and area is changing so it shows**dE/dt**. This is Ampere's law. **On the right**, a magnetic ring is shown in two stages as it shrinks.- A string of magnetic beads making a ring has a uniform magnetic charge per unit length. The magnetic field
**B**along the ring per unit length is uniform but the circumference and area is changing so it shows**dB/dt**. This is Faraday's law.

The central axis of the wave is at the right angle of the triangle. The energy is proportional to the radius or circumference of the rings. The electric field E flux ring +red or -pink moves up or down along the y axis and rotates counter-clockwise. The magnetic field B flux ring +green or -cyan moves left or right along the x axis and rotates clockwise. The verticle or horizontal straight line motions of the rings in and out of the right angle on figure 2E are sine or cosine flux tube waves when seen over time from the perpendicular point of view of figure 2D.

**Hypothenuse and wavelength: **The rings rotate in opposite directions. The ring to ring transfers occur along the line between their centers, the hypotenuse. The hypotenuse rotates tracing out a double helix over time. When the hypotenuse of the triangle is **h = wavelength/(8*pi)** the sum of the circumference of the ring pairs is **2*pi*h = wavelength/4.** The charge content of the rings rotates at the
speed of light as the rings transfer energy to their partner. This is a string or ribbon of charge with a length of **2*pi*h = wavelength/4** in a ring orbit, making four ring to ring transfers per wavelength while traveling a distance of one wavelength at the speed of light. The hypotenuse in this figure is about **7_mm** so this could be a life size cross sectional diagram of a **7_mm*8*pi = 176_mm wavelength, 1.7_Ghz**
electromagnetic wave.

**Ring radius:
h ^{2}= x^{2} + y^{2},** Pythagorean theorem. h is the hypotenuse of the right triangle in figure 2E and the distance between the rings and the maximum radius of the flux tubes of figure 2D.

**Ring mass, energy and charge are shared between the rings:** The end views of figure 2E are useful. We have rings, masses, fluxes and currents which flow in the x and y directions. A
verticle current is a current_{y}. A horizontal current is a current_{x}.

**m _{t} = h_{p}*c/wavelength / c^{2} = h_{p}/(wavelength*c).** m

**q _{w} = q_{x} + q_{y},** q

**Rate of change of the circumference of the rings, d(2*pi*r*frequency)/dt:** The rate of change of the length of the circumference, d(2*pi*r)/dt, has units of velocity, meters/second.

**d(2*pi*r)/dt = d(2*pi*h*sin ^{2})/dt = 2*pi*wavelength/(8*pi)*d(sin^{2})/dt**

**Current in the rings, dq/dt: **

Current is the rate of change of the (amps*seconds) charge.

**q _{w} = Ce/(2*alpha)^{.5}= (h_{p}/(c*u0))^{.5} = amps*seconds.** q

dq/dt = q

This is in the form,

**E in the rings, dE/dt:**

Anything that has a charge has an electric field. The electric field may point charge to charge, or be generated in a loop like Faraday's law. We will see a loop as a bipolar unit, like a long bar magnet, length of spherical magnets or magnetic beads, whose oppositely charged ends have looped around and stuck together thereby loosing its bipolar character. The charge of the wave is quite small and is spread over the length of the rings. The static electric field due to this small charge is also very small. *A shrinking or expanding ring with a charge per unit length would have a dE/dt. *The dynamic rate of change of the electric field, which is a product of multiplication of the small charge by the rate of change of the circumference times the frequency, can be very large.

We postulate a further bipolar electric field for the flux units where opposite polarity may hold the flux units into rings. This constitutes a tensile strength associated with the electrical flux, an electrical pinch force. When the units in the rings from figure 4 are held together by this bipolar electric field the electric field is confined within the ring but the perpendicular bipolar magnetic field is exposed.

**E _{total}/(total length of loops) = E_{total}*4/wavelength,** This is the E charge per unit length. E

This is in the form,

**B in the rings, dB/dt:**

*A string of magnetic beads has a magnetic charge per unit length. A shrinking or expanding ring with a magnetic charge per unit length would show a dB/dt. *

**Magnetic pinch force:**

A ring of bipolar magnetic beads shows tensile strength. *Is this the magnetic pinch force? *We postulate a static bipolar magnetic field for the flux units where opposite polarity may hold the flux units into rings in this same way. When the units in the rings from figures 4 are held together by this bipolar magnetic field the magnetic field is confined within the ring but the perpendicular bipolar electric field is exposed.

**B _{total}/(total length of loops) = B_{total}*4/wavelength,** This is the B charge per unit length. B

This is in the form,

**New currents:** *The rate of change of the charge on each ring
as the rings change size constitutes a current which flows from ring to ring across the plane of the wavefront.* The extremes of the waves, on figure 2G, are the maximum currents flowing ring to ring which are,

**dq/dt = q _{w}*frequency = amps.**

**Is energy stored in the area or the circumference of the flux tubes?** At the cosmic scale, objects are
mostly volume and little surface. At the smallest scale, objects are mostly surface and little volume. Volume/surface of a sphere = radius/3. For the cosmos, radius/3 = 4.73E25_m. For red light,
wavelength/3 = 211E-9_m. At the smallest scale, objects are mostly circumference and little area. Area/circumference of a circle = radius/2. For red light, wavelength/2 = 316E-9_m. The
circumference is 3 million times bigger than the area. We would expect circumference to be much more important. The circumference of the ring pair does carry the charge. We previously noticed that when Ampere's law was written to show Maxwell's displacement current, "The toroidal amps in the loops equals the poloidal flux of amps through the area of the loop." Both area and circumference are important.

**Rate of change of the area of the rings, d(pi*r ^{2})/dt:**

The hypotenuse in this figure is about **37_mm** so this could be a life size cross sectional diagram of a **37_mm*8*pi = 930_mm wavelength, 322_Mhz** electromagnetic wave. This detailed
mechanistic view of electromagnetic waves makes falsifiable predictions. Standing waves of figure 2D have a fixed spacing of E and B fields. The E fields may be measured and located and the B
fields inferred. Properly spaced B fields of a certain strength would apply a predictable polarizing torsion.

The electric field flux tube, in cross section, rotates counter-clockwise. The magnetic field flux tube, in cross section, rotates clockwise. This suggest a simple root for their differences. Inertia can be understood as the acceleration dependent gravitational influence of the background cosmos. We might understand the differences between the E an B fields in terms of the fields and rotation of the background cosmos.

**Pinch and repulsion:**

A row of parallel magnets, with their bi-poles pointing in the same direction, repell each other. If the parallel magnets are each rotated ninety degrees, they are in series, their poles now attract each other. They form rows or rings of magnets with a tensile strength. Call this opposite pair magnetic pinch and magnetic repulsion.

A row of parallel bipolar charges, with their bi-poles pointing in the same direction, repell each other. If the parallel bipolar charges are each rotated ninety degrees, they are in series, their poles now attract each other. They form rows or rings of bipolar charges with a tensile strength. Call this opposite pair electrostatic pinch and electrostatic repulsion.

Units may have both bipolar magnetism and bipolar charge arranged in a cross or square which are assembled into rows or chains which assemble into rings. The units may rotate in ninety degree steps and make rows and rings as follows:

We have magnetic force holding the row together, which is concealed, except for the ends which are also concealed when this loops into a ring, while showing perpendicular charge plus up.

We have electrostatic force holding the row together, which is concealed, except for the ends which are also concealed when this loops into a ring,
while showing perpendicular magnetism plus up.

We have magnetic pinch holding the row together, which is concealed, except for the ends which are also concealed when this loops into a ring, while showing perpendicular charge plus down.

We have electrostatic force holding the row together, which is concealed, except for the ends which are also concealed when this loops into a ring, while showing perpendicular magnetism plus down.

We have magnetic force holding the row together, which is concealed, except for the ends which are also concealed when this loops into a ring, while showing perpendicular charge plus up.

*Can you see the flux tubes of figure 2D and 2E and the rings of figure 4 in terms of series and parallel bipolar charges?*

**Rings of magnetic beads or spherical magnets:** have a lot of tensile strength. They are hard to pull apart. This must be related to the magnetic pinch force. Rings hide the bipolar glue of the units which holds them together in rings. Their hidden flux is confined to the ring. Rings of very strong spherical magnets
have a very weak external magnetic field. 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.

The ribbons share a lot with the field pattern of iron filings on a glass over a bar magnet. The field lines are made from tiny magnets made of the magnetized iron filings which are held together by the tensile strength of the magnetic field. The field lines of iron filings are held apart by the repulsion between the lines of tiny magnets. Experiments with spherical magnets show similar behavior. The field pattern of grass seeds in an insulating liquid or bits of thread in oil, between oppositly charged rods, shows the same pattern as the bar magnet and iron filings. Halliday and Resnick or Tipler have great pictures. Also see the pictures of sources and sinks. How could the particles stick together without opposite charge on opposite ends? What geometry allows an electron to show only its negative charge? The rings of figure 5 are a good guess.

**Antenna analogy:** We equate the amp form of Ampere's law, on the left, with the amp form of Faraday's law.

**2*pi*r*B/u0 = 2*pi*r*E/resistance = amps**

**resistance = E*u0/B,** divided by 2*pi*r

**resistance = B*c*u0/B,** E = B*c in electromagnetic waves.

**resistance = c*u0 = 376.73 ohms,** cancelled B

In Faraday's law a current is produced in a loop or coil: when the electric field loops around, or when the magnetic field varies, or the area of the loop varies. Without wires in an electromagnetic wave we see
the impedance of free space, c*u0 = (u0/e0)^{.5} = 376.73 ohms. 300 ohm antenna lead wires are matched to this impedance so that the antenna may transfer maximum energy.

**Does space have resistance?** Space is empty. If space had any resistance, electromagnetic waves would be damped quickly, dissipate their energy as I^{2}R heat, instead of traveling
for billions of light years. The impedance of space, is more properly described as shorthand for the ratio, V/I = Faraday's voltage divided by Ampere's current in electromagnetic
waves = 376.73 ohms. Electromagnetic waves have this V/I ratio so antennas should be most efficient when matched to this V/I ratio. This ratio is called impedance because it has units of V/I or ohms.

**Antenna theory** says accelerated charges radiate. Changes in direction are regarded as accelerations so something in a circular orbit is accelerated. Accelerated charges are changing amps which
are produced by d(B)/dt. The flux of B through the area or rate of change of the circumference of the loop radiates the -E seen in the loop. Arcing, which is the radiation or emission of currents, occurs at a lower potential from pointed objects,
those with a smaller radius of curvature. The radius of curvature of the flux or of the loop is the wavelength/(2*pi) which can be very small so the radiation or emissions can be almost
instantaneous. The transition is proportional to the wavelength. See appendix 1.

**Euler's equations and electromagnetic wave dynamics:**

Euler's equations are used to express three dimensional rotational motions; roll, pitch and yaw in aircraft or spacecraft and precession or nutation in gyroscopes and rotating bodies. We use them to understand the flux and looping around of Faraday's and Ampere's laws in electromagnetic waves and
light.

**Top view, top:** Red exerts a torque around the green axis, which is into the page, in the top view.

**Side view, bottom:** Green exerts a torque around the red axis, which is into the page, in the side view.
These waveforms are not the right shape. They do not go to zero at a change in direction. They are fun to make out of colored wires, see Appendix 5. The red and green are correctly, 90 degrees out of phase. They demonstate the torque around a perpendicular axis. A torque around two perpendicular axises produces a torque perpendicular to both axises in a gyroscope.
Here the axises of the torque is moving with the waves.* How does this work?* This is gyroscopic precession and movement in the direction of travel of the wave. This is a very odd gyroscope indeed.

**E** exerts a torque around the **b** axis. **B** exerts a torque around the **e** axis. **E+B** exerts a torque around the **a** axis. The transfer of torque as angular momentum or spin is along the **a** axis.

**T _{a} = I_{a}*dw_{a}/dt +(I_{b}-I_{e})*w_{e}*w_{b}**

T_{b} = I_{b}*dw_{b}/dt +(I_{e}-I_{a})*w_{a}*w_{e}

T_{e} = I_{e}*dw_{e}/dt +(I_{a}-I_{b})*w_{b}*w_{a}

dw/dt is the the angular acceleration, the rate of change of the angular velocity.

The moment of inertia I

**If we have waves traveling unimpeded:** **w _{a} = w_{b} = w_{e} = w,** since the angular velocity w is constant, the rate of change of the angular velocity, the
angular acceleration,

T

T

**T _{b} = (I_{e}-I_{a})*w_{a}*w_{e}**

T_{b} = (m_{t}*h^{2}*(sin^{6}+sin^{4}) - m_{t}*h^{2}*(cos^{6}+cos^{4}+sin^{6}+sin^{4}))*w^{2}

T_{b} = m_{t}*h^{2}*w^{2}*(-cos^{6}-cos^{4})

**T _{e} = (I_{a}-I_{b})*w_{b}*w_{a}**The sum of the torques is zero.

T_{e} = (m_{t}*h^{2}*(cos^{6}+cos^{4} + sin^{6}+sin^{4}) - m_{t}*h^{2}*(cos^{6}+cos^{4})*w^{2}

T_{e} = m_{t}*h^{2}*w^{2}*(sin^{6}+sin^{4})

T_{a} + T_{b} + T_{e} = m_{t}*h^{2}*w^{2}*((cos^{6}+cos^{4}-sin^{6}-sin^{4}) +(-cos^{6}-cos^{4}) +(sin^{6}+sin^{4})) = 0,

**If the waves are impeded:** or impeded while being detected the d(w)/dt terms are no longer zero.

**T _{a} = I_{a}*dw_{a}/dt + (I_{b}-I_{e})*w_{e}*w_{b}**

T_{a} = m_{t}*h^{2}*(cos^{6}+cos^{4} + sin^{6}+sin^{4})*dw_{a}/dt + m_{t}*h^{2}*(cos^{6}+cos^{4} - sin^{6}-sin^{4})*w_{e}*w_{b}

T_{a} = m_{t}*h^{2} *[(cos^{6}+cos^{4} + sin^{6}+sin^{4})*dw_{a}/dt + ((cos^{6}+cos^{4} - sin^{6}-sin^{4})*w_{e}*w_{b})] = mass torque or spin.

T_{b} = I_{b}*dw_{b}/dt + (I_{e}-I_{a})*w_{a}*w_{e}

T_{b} = m_{t}*h^{2}*(cos^{6}+cos^{4})*dw_{b}/dt + m_{t}*h^{2}*(-cos^{6}-cos^{4})*w_{a}*w_{e}

T_{b} = m_{t}*h^{2}*(cos^{6}+cos^{4}) *[dw_{b}/dt + (-1*w_{a}*w_{e})] = magnetic torque

**T _{e} = I_{e}*dw_{e}/dt + (I_{a}-I_{b})*w_{b}*w_{a}**

T_{e} = m_{t}*h^{2}*(sin^{6}+sin^{4})*dw_{e}/dt + m_{t}*h^{2}*(sin^{6}+sin^{4})*w_{b}*w_{a}

T_{e} = m_{t}*h^{2}*(sin^{6}+sin^{4}) *[dw_{e}/dt + (w_{b}*w_{a})] = electrical torque

**Appendix 1: Transition math:**

**frequency*wavelength = c**

**wavelength = 4*transition,** so

**frequency*transition = c/4,** At higher frequencies the transition is shorter.

**energy = h _{p}*frequency,** h

Energy or frequency changes result in tensile or compressive forces. The circumference and rate of change of the circumference, of the rings of figure 2E, changes. Electromagnetic waves can be viewed as a coiled spring. When the wavelength increases the distance between the coils increases. This is a tensile force on the medium. When the wavelength decreases the distance between the coils decreases. This is a compressive force on the medium. There can be huge forces, at high currents anywhere the wavelength or frequency varies. Exploding wires which look like fragmented spaghetti and compression damage in rail guns have been noted. See Graneau and Graneau in, "Newton versus Einstein" for these and other details of the ongoing conflict between theory and experiment.

**Appendix 2:**

**E = force/q**, force_{E} = q*E

**B = force/(q*v)**, force_{B} = q*v*B

force_{E} = force_{B}

**q*E = q*v*B:**J. J. Thomson determined the mass to charge ratio of
the electron using this equation. This is similar to the Lorentz force = q*E + q*v*B if the forces are equal. We only use it with the
velocity v equal to c, the charge moves at the speed of light and the two forces are equal.

The electrostatic force of repulsion by the charge equals the magnetic pinch force of attraction on the charge. We see it in the ring electron and the electromagnetic wave.

E

**Appendix 3: Derivation of the wave parameters:**

There are four variables with values that we seek; B, E, q and amps.

**2*pi*r*E = volts = energy/q,** Faraday's law

**E*q = energy/2*pi*r,** force, energy/wavelength, q = charge

**E*q = h _{p}*c/(wavelength*2*pi*r),** force, energy = h

**2*pi*r*B = amps*u0,** Ampere's law, B = force/(amps*meters)

**B = amps*u0/2*pi*r or B = amps*u0/wavelength.** kg/(a*s^{2})

**B*q / B = h _{p}/(wavelength*2*pi*r) * 2*pi*r/(amps*u0)**

**q*amps = h _{p}/(wavelength*u0),**

**2*pi*r*B = force/amps,** Ampere's law

**2*pi*r*B = B*c*q/amps,** substituted for force

**q _{2} = amps*2*pi*r/c or q = amps*wavelength/c**

**q _{2} = q_{1},**

**(c*h _{p}/u0)^{.5} = 3.976E-10_A*m,** amps*wavelength is a constant.

**amps = (c*h _{p}/u0)^{.5}/(wavelength*2*pi*r)^{.5}** or

**q _{2} = amps * 2*pi*r/c,**

**(c/(u0*h _{p}))^{.5} = 6.000359E23_a*s/(kg*m),** curiously close to Avogadro's number

**amps = q _{w}*frequency**

**B = amps*u0/2*pi*r,** kg/(a*s^{2}). Ampere's law.

**B = (c*h _{p}/u0)^{.5}/(wavelength*2*pi*r)^{.5} *uo/(2*pi*r),** substituted for amps

**(c*h _{p}*u0)^{.5} = h_{p}/q_{w} = 4.996E-16_kg*m^{2}/(A*s^{2}),** energy/amps is constant.

**B = (c*h _{p}*u0)^{.5}/(wavelength*2*pi*r)^{.5}/(2*pi*r)** or

**B ^{2}*wavelength^{3}/u0 = c*h_{p}/wavelength,** energy. This is energy density times wavelength cube.

**E = c*B = c*(c*h _{p}*u0)^{.5}/wavelength^{2}.**

**E ^{2}*wavelength^{3}*e0 = c*h_{p}/wavelength,** energy. This is energy density times wavelength cube.

**Powers of 1/wavelength:**

** energy = h _{p}*c/wavelength,** one over wavelength

**Red light example:**

**wavelength = 633E-9_m,** for red light

**frequency = c/wavelength = 4.736E14_1/s**

**q _{w} = (h_{p}/(c*u0))^{.5} = 1.326E-18_A*s,** charge

**Electron gamma ray example:**

**me*c ^{2} = h_{p}*c/wavelength = 8.187E-14_kg*m^{2}/s^{2},** energy. me = mass of the electron

A and q

**Appendix 5:**

**Tipler's reciprocal results:**

"Physics for scientist and engineers", 4th. ed., p. 1000-1001; "Maxwell's modification of Ampere's law shows that a changing electric flux produces a magnetic field whose line integral around a
curve is proportional to the rate of change of the electric flux. We thus have the interesting reciprocal result that a changing magnetic field produces an electric field (Faraday's law) and a
changing electric field produces a magnetic field (generalized form of Ampere's law)."

**Fat text books can be articulate old friends:**

Tipler's; "Physics for scientist and engineers" or Halliday and Resnick's; "Physics for students of science and engineering", both offer the comprehensive coverage and detail useful in
understanding this field. They are not dumbed down. The internet is like Lake Okeechobee with its shallows miles wide and its occasional pockets of deep water. Is this as shallow as a mud flat or is this a pocket of deep
water? Rose Anne says this website is like the mathematician in "A Beautiful Mind" putting his letters in an unused mailbox for pickup by imagined readers.

**Storyland:** Before there was writing there were stories. Theories are little stories we use to think about and describe reality; scientific, political or otherwise. Apparently we prefer
our ideas served on the platter of a story. Something in us wants us to believe a story. Repetition makes the heart grow fonder. These are addictive memes. We are even seduced by a weak story. A
story is an audio, visual, sensory experience as required by neuromarketing. Brain scans would show stories activate pleasure centers while facts do not. There is a narcotic effect in the mantra or
in constant repetition of stories. The opiate of the masses is endorphine based. This makes us vulnerable to manipulation. Fancy theories, flag wavers, fundamentalist and fanatics all have their
stories. The best stories to believe are based on evidence from multiple sources. Some, which are widely accepted, have only hearsay (he said) evidence or anecdotal (more little stories) evidence.
Some, which are properly called dogma, are said to be accepted without evidence, as a requirement for membership in a group. Monkey see, monkey do. We are primates if you prefer the story of
evolution instead of the story of Noah's ark. Parotting a plethora of preposterous stories, taken unquestioned at face value, papers ones reality with a crazy quilt of pernicious perculating
absurdities. There are so many zombies addicted to stories, so many sacred cows, so many mad dogs ready to kill, if your story is different from theirs. Humor them. We seek clarity, (a clear simple
story - like the following).

My son gave me a LED flashlight which uses Faraday's law. A magnet moving bi-directionally in a tube, through a coil of wire, provides a reversing current. That current charges a energy storage capacitor through diodes that keep the reversing current flowing in one direction. The capacitor acts like a battery to light the LED.