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This is the twinned paper of the increased mass paper, “ Gravity is acting at superluminous infinite speed, thus collapsing special theory of relativity of Einstein, an explanation for almost everything (according to the authors’ rigorous mathematical proof and overwhelming experimental evidence)" [1] . In the present paper, we describe the repeated spark or repeat current in terms of the hidden, Non-Relativistic Longitudinal Cardinal Ampere Force which is not found yet infallible for every case. The impressive finding is the fact that these repeated sparks as we shall see, have no back-emf, but forward-emf and forward-Ampere-motive-force. The only consumption is the resistive load with the very high currents needed. This means its total energy consumption is less than the released energy-output work plus heat, plus the energy recharging the batteries. All these are in excess of the consumed input energy. This means the Repeated sparking is “over-unity” efficiency and that, using super-conductive materials, we shall have constructed the first “perpetual mobile” plus producing extra electrical energy. Several previous journals that we did not mention here their names did not dare to publish our disliked papers of very important and revolutionary results but were not able to counter argue our arguments. They preferred the silence and have not answered us at all for many years now. Even some of them were involved previously with the repeated sparking which is the same topic of our present paper.

The repeated sparking is not a practical and common for the need of use of very high currents. However, it is a very interesting theoretically for having partially non-closed circuits due to the finite speed of the spark. For this reason, the usual Lorentz force law is inappropriate. The correct for this particular case, Ampere force law may be used only instead.

The Ampere force was hidden and was very little known and almost unknown in the literature for 180 years, since 1826, and until the Authors published [

The correct Lorentz force is only when it coincides with the closed integral of the Ampere force for absolutely closed electric current circuits, when the later force is integrated along the closed circuit which acts as the source of the “magnetic” field and then only coincides with the Lorentz force. In every other case, the correct Ampere force integral is not the same as the Lorentz force and this Lorentz force is incorrect, violating [

The Ampere force alone makes the Ampere Electrodynamics, much simpler than Maxwell’s Electromagnetism with the unsolvable Maxwell’s equations. The Ampere Electrodynamics determines directly all the motive forces and Electromagnetic waves [

We performed a rigorous explanation of the “Repeated sparking” by the longitudinal non-relativistic Ampere force. The Ampere force also obeys correctly the action-reaction principle of Newtonian Mechanics that today is valid in everyday life. Never, and nowhere it has been falsified. On the contrary, the Lorentz force does not obey Newtonian mechanics, violating momentum, angular momentum principles of conservation, never observed true in practice [

Here, we shall discuss the main dominant and fundamental principle of operation of the so-called repeated sparking, based on the longitudinal, non-relativistic, Ampere contact force:

d 2 F 12 = k r 12 I 1 I 2 r 12 3 { 2 d s 2 ⋅ d s 1 − 3 r 12 2 d s 2 ⋅ r 12 d s 1 ⋅ r 12 } (1),

where ds_{1} is the infinitesimal length which contacts the current I_{1} and produces the infinitesimal force dF_{12} on the infinitesimal section ds_{2}, curing the current I_{2}

or

d 2 F 12 = ( μ 0 / 4 π ) d q 1 d q 2 ( r 12 / r 12 3 ) { 2 V 1 ⋅ V 2 − ( 3 / r 12 2 ) V 2 ⋅ r 12 V 1 ⋅ r 12 } (2)

taking into account I d s = ( d q / d t ) d s = d q d s / d t = d q v , and ds/dt is the drift velocity V of electrons [

Finally the Ampere force parametrized by the motive parameters of the drift velocities V_{1}, V_{2} of the two charges dq_{1}, dq_{2} involved.

For F_{12} = λr_{12}, F_{21} = λr_{21}, λ > 0, we have a repulsion, F_{12} and r_{12}, F_{21} and r_{21} have the same direction. That means, the endpoints of a non-closed current straight line section of a spark, or the straight parts of a lightning repel each other generating energy for both the spark and the lighting. The latter case charges the Geo-electric field [

With similar dq and opposite Vs, λ < 0, we have an attraction._{ }

For an isolated current like lightning falling from the sky, the endpoints of lightning repel and the lighting becomes self-propelled, gaining energy. Thus, lightning charges up, not discharges, the Geo-electric field by offering energy to it and thus maintaining it, according to meteorology ( [

90% of lightning brings negative charges to the negative ground [

Similar small charges on a cloud are pushed by the wind, causing a non-closed section current of moving charges. The currents might be in different directions, depending on the direction of the wind. Thus, lighting is self-created, self-propelled and self-energy producer and powered, breaking in many different directions, no evidence of particular potential difference direction. It does not follow a particular direction. It is self-propelled and is breaking in many different directions, even reversing direction by 90 or even 180, 360 degrees. Often the lightning extinguishes, terminating to nowhere. Many times, lightning trajectories cross one another without following any conservative field, such as the electrical field, for which classical theory proves its lines of field can not cross each other. For confirmation, see the pictures of lighting farther below: Lightning is not the first phenomenon of energy production. Energy production appears in many phenomena as sparks, lightning, similar to mass production [

direction of the pulses, identical light bulbs for realistic energy direct comparison, confirming the abstract, so to speak, oscilloscope images, in Athens Greece and welcomed to stay for as long they wish, eventually until they will be convinced, preferable physicists, knowing electronics or just electronic engineers! Contact us to make arrangements, our email is indicated under the title of the present.

From

Due to the fact an isolated spark, because of the finite speed of propagation electric current repels its ends and behaves like a compressed spring when it is released, point B with respect to the ground, surpasses the potential of point A with respect of the ground (

For, the first time, the proper analysis of the repeated sparking is made. The basis was the only appropriate and infallible cardinal [

Pappas, P., Pappas, T. and Pappas, E. (2018) Repeated Sparks Produce Free Energy: A Rigorous Mathematical Explanation of the Authors, by the Hidden Ampere Force Law. Journal of Applied Mathematics and Physics, 6, 155-160. https://doi.org/10.4236/jamp.2018.61015