[The S-Motor] Mechanical and AC Power Generator. No Batteries or Capacitors.

[kmarinas86]

https://disqus.com/home/discussion/peswiki/directorysyairs_replication_of_no_back_emf_generator/#comment-1714110485

No batteries.
No capacitors.

Just Mechanical and AC Power.

Estimated cost to build a (nice, sizable) prototype: $250-350 (see spreadsheet)

Prototype build to commence this year (2015).

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One major key is understanding that while the emf [in volts] induced into a closed loop by a magnetic field is not uniform along its path [i.e. the distribution of V/m as derived from v x B], the current is.
For illustration:
* Take a letter-sized piece of paper and cut out a 2" or 5 cm thick strip (depending on your preference).
* With this strip of paper, draw four arrows, one across within each margin, as close as to the edge of the paper as possible in the same rotating direction (i.e. clockwise or counter-clockwise).
* For clarity, add additional chevrons (or "arrowarms") on the long arrows so you will see the direction of each arrow even when you cannot see the arrowheads.
* Do the same on the other side of the paper but in the opposite rotating direction.
* Now make two creases in the paper in a proportion of pi/2:1:pi/2 dividing the long side (11" in the U.S.) (so approximately 4 1/6", 2 2/3", 4 1/6").
* Curl the pi/2 portions so they now form an S shape, with both pi/2 pieces having the curvature of a semi-circle, while the center piece of proportion remains flat.
* Now cut out a rectangle within the strip, leaving a 0.5" margin containing the arrows you drew.
After completing the above steps, you have created paper model of an "S-coil".
Consider the following:
* Now compare short edges (2" or 5 cm) and the flat segment in the middle piece (2 2/3" in the U.S.).
* You will notice that the arrows on the short edges and arrows in the middle piece run in opposite rotating directions in the plane which intersects both [the "central plane"].
* If you rotated a bar magnet inside the center of the "S-coil" so that the movement of the field lines would run perpendicular to the short edges but parallel to the curved pieces, you will realize that:
** Most of the EMF will be induced on the short (2" or 5 cm) edges.
** The rest of the EMF will be induced on the flat (2 2/3") middle piece.
** No EMF will be induced on the curved (4 1/6") portions.
** Most of the current in the "central plane" runs in the direction of the flat (2 2/3") middle piece (because 2 2/3" > 2").
* If you imagine the magnetic field from current flowing with the arrows, you will notice that:
** The magnetic field from the curved pieces will intersect the "central plane" at an oblique angle, reducing the effective field strength through that plane.
** The magnetic field from the non-curved segments will intersect the "central plane" perpendicularly, thus substantially contributing to the effective field strength through that plane.
Consider the moment when the magnet rotates through the "central plane":
* If the magnetic force were solely due to the (qv x B) force on the wire, it is easy to see that rotating the bar magnet would induce an emf in the short (2" or 5 cm) segments, generating a current which slows down the bar magnet.
* However, there is also a magnetic force on the bar magnet from the current in the flat middle piece, even though minimal EMF is induced into it by the bar magnet; this is possible to due the unequal distribution between the induced field on each wire element and the resultant current running through each wire element.
* The direction the magnet will turn is ultimately determined by effective "amp turns" acting on the magnet, and here the current in the flat middle pieces wins because the magnetic field from the curved pi/2 segments is largely oblique (and as well as cancelling) at the "central plane", while the current from the short (2" or 5 cm) edges clearly produces less magnetic flux through the central plane due to having less "amp x meters".
http://en.wikipedia.org/wiki/H...
"[T]he Lagrangian of a non-relativistic classical particle in an electromagnetic field is (in SI Units):"
(https://a.disquscdn.com/get?url=http%3A%2F%2Fupload.wikimedia.org%2Fmath%2F8%2F5%2F0%2F8502f581770b120147a669354563a344.png&key=JFmxiKo-bOaZ9aT_xaWmeg&w=800&h=43) The 1st term on the RHS [1/2 m |v|^2] is the kinetic energy. [m = "mass"; v = "velocity"]
The 2nd term on the RHS [+ e v·A] is the magnetic potential energy. [e = "charge"; v="velocity"; A="magnetic vector potential"]
The 3rd term on the RHS [- eΦ] is the electric potential energy. [e = "charge"; Φ="electric potential"]
Now consider what happens in the coil:
* Along the wire are differential path elements (s') along ("along" = "directed with") the wire.
* dA/dt = -1 * E_induced,q [Where: dA/dt is the total derivative of the magnetic vector potential with respect to time (perspective of a moving charge), and the E_induced,q is the induced electric field from the rotating magnet (in q's frame of reference)]
* ∂A/∂t = -1 * E_induced,lab [Where: ∂A/∂t is the partial derivative of the magnetic vector potential with respect to time (perspective of the lab's inertial frame), and the E_induced,lab is the induced electric field from the rotating magnet (in the lab's frame of reference)]
* The vector potential [A] of the magnet wraps around the axis of the magnet in the same direction that a moving positive charge would generating the same field.
* The vector potential [A] generates an electric field which opposes it, and since electrons are accelerated in the opposite direction of the electric field, the induced electron flow follows the change of the magnetic vector potential, which resists the change of the magnetic vector potential.
* Because the magnitude of the vector potential decreases as angle away from the magnetic moment [m] decreases, the derivative of the vector potential (= -1 * E_induced,lab) intersects with the induced electron current (v_induced·(- E_induced),lab > 0; v_induced·∂A/∂t > 0) converting magnetic energy (Δ(e v·A) < 0) at (magnetic) pressure into some other form of energy at the short (2" or 5 cm) edges and intersects against the induced electron current (v_induced·(- E_induced),lab > 0; v_induced·∂A/∂t > 0) converting some form of energy into magnetic energy (Δ(e v·A) > 0) at (magnetic) pressure at the flat (2 2/3") middle piece, where "intersects with" means the angle is between -90 and +90 degrees (a positive dot product) and "intersects against" means the angle is between +90 and +270 (a negative dot product) [Note: we are considering the electron current, not conventional current]
* Force is a rate change of momentum (with respect to time). The force times a charge-to-mass ratio gives [e * a] or a product of charge and acceleration. The integration of this value with respect to time (assuming constant charge e) is [e * v]. The dot product between [e * v] and A gives the magnetic potential energy. If a force (e ∇Φ) is transferred from one charge (q_1) to another (q_2) via the electric field (∇Φ), the magnetic potential energy can be made to increase depending on how the vector potential intersects each one. Note that in principle, this requires a minimum of 3 charges, where one charge represents the source of the external magnetic field (with its spatially-varying vector potential), and the two remaining charges are those two being considered in this scenario which are subject to different vector potentials. It follows that this energy (if a positive change) must either come from kinetic energy, electrical potential energy, or something else:
** If it comes from kinetic energy, then the current in the S-coil will have an anomalous resistance in the flat middle portion where the induced electron current is flowing against the change of the magnetic vector potential. The magnetic potential energy is derived at the expense of current, consuming the power that was induced. What's normal about this is that the motor will not produce an energetic anomaly. What's unusual about this is that you can end up with a situation where there is no sustained current flow in the closed path despite that you would expect an EMF, and/or you can end up with an unusually large capacitance in the coil.
** If it comes from electrical potential energy, then it could mean that the electrical potential energy of charged particles (whether like or opposite pairs) is being consumed even though no battery or capacitor was added to the circuit. What is unusual about this is the source of the electrical potential energy [q Φ].
** If it comes from anything else, well that is already unusual.
My [i.e. kmarinas86's] prediction is that the only kinetic energy consumed would be that corresponding to displacement of the magnetic fields of each charged particle against the magnetic field of the bar magnet, which occurs at the same velocity as the drift velocity of the charge, whereas an anomalous electrical potential energy (in the absence of "attached" batteries and capacitors) will be consumed as a result of the magnetic flux (in units of webers) that is induced at the short (2" or 5 cm) edges "skipping" distance as it is conveyed from one free conduction electron to the next. One can imagine the energy of current "hopping" from one free conduction electron to another just like energy in an "engineered" capacitor where energy hops from electrons on one plate to electrons on another plate. The premise is that displacement current does not produce the same magnetic field as an equivalent conduction current, and any observed magnetic field between the plates is due to conduction current leading to and through the plates as it is being charged or discharged, as opposed to a "displacement current" literally flowing from one plate to another. Look up "Bill Miller" "displacement current": https://www.google.com/search?q="bill+miller"+"displacement+current"
Conclusion: Save up money to build an "S-Motor" (Discovered by kmarinas86 [me] this past summer [either July or August 2014] with these details resolved as of November 26, 2014).

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