Primer: Alexander V. Frolov, "free power from the potential field"

Folder: Researchers/Frollov-Alexander (the folder name has a double "l"; the author is Alexander V. Frolov, Faraday Laboratories, St Petersburg). Built from: arbiter.md (final verdicts, including its "QE revision" section and that section's "Round 2" subsection), qe.md, the deep reads in deep/FreeEnergy-db73c1.md (PDF pp.10-16 with Figs 8-12 viewed; and, in Round 2, PDF pp.1-5 with Figs 1-3 viewed), physicist.md, mathematician.md, contrarian.md, and my own reading of the two source PDFs. Worked example re-derived and checked in example.py.

Source tags: [read] = from Frolov's documents; [web] = from an Internet source (URL given; these were collected by the reviewers and arbiter, not re-fetched for this primer); [memory] = recalled, with confidence.

Source note. The folder holds only two documents, both by Frolov: a 3-page 1994 note, "The Single-Wire Electric Power Transmission" (New Energy News, Dec 1994), and an 18-page 2003 magazine article (New Energy Technologies #2, pp. 11-28, file FreeEnergy.pdf). Both were read as text; the second half of the 2003 article (PDF pp.10-16) was later deep-read after quality engineering (QE) found it had been skipped, and a second round deep-read PDF pp.1-5 (the closed-loop argument, Figs 1-3, a 1995 coil experiment). Figures 1-3 and 8-12 were viewed as page images; Figs 4-7 (PDF pp.6-9) and the 1994 note's figure were not, and PDF pp.6-9 rest on digest and text reading only. Page numbers: 2003 citations in this primer are the magazine's own page numbers (11-28); magazine page = PDF page + 10, so "mag. p.21" is PDF p.11. Nothing about other people's devices (T. T. Brown, Floyd Sweet, John Searle, Avramenko, Strebkov, Kozyrev) is in the folder in primary form. Everything about those devices is Frolov's second-hand report plus a few web summaries, and this primer says so where it matters.

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1. The idea in one paragraph

Frolov starts from a true fact: an electric field can push charges and do work on them, and a charged object sitting in a field costs nothing to keep there. He then argues that if you could stop the field from taking that work back, for example by switching it off, screening it or flipping its polarity at the right moment, the field would become a free fuel. His concrete example is "single-wire" power transmission. A high-voltage, high-frequency source is connected by one wire (no return wire) to a pair of diodes, called an "Avramenko plug", and a load. The current in the single wire is what engineers call "wattless": it sloshes back and forth and on average carries no power. Frolov believes the diodes turn this wattless current into real power in the load without the source paying for it. To explain where the energy comes from, he proposes that energy conservation must be "generalized" to include processes running backwards in time, with the vacuum (the "aether") as an unlimited reservoir. He also describes a few bench experiments of his own: a vacuum tube whose battery is switched off while the electrons are still in flight, so that the battery is "not discharging"; a 1995 transformer with a flat spiral secondary coil where, he says, a lamp on the secondary drew no input power from the primary; a ferrite-core alternator whose core he says cools itself, a rotor he says is accelerated by its own back-EMF (the voltage a generator coil induces against its driver), and an arc in a transformer secondary that he says made the battery input fall to zero and reverse. Each is told in a few sentences with no numbers except one current (about 300 mA). He also argues that in electrolysis the field, not the battery, moves the ions, so the battery need not pay. And he lists dozens of other inventors' devices, with second-hand power figures, as supporting examples. The physics he starts from is real. Where it fails is the energy bookkeeping: whoever switches, screens or rectifies the field pays for the work, and his own measurement shows the load getting 3% of what the source consumed.

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2. What you need to know first

2.1 Conservative fields, line integrals and Stokes' theorem. A force is conservative if the work it does moving an object from A to B depends only on A and B, not on the path. Then the work around any closed loop is zero. For an electrostatic field E (the electric field, in volts per metre, V/m) this follows from curl E = 0. Stokes' theorem turns the loop integral of E into a surface integral of curl E, which is zero. Gravity near the Earth (force mg down) is conservative too. Read: Griffiths, Introduction to Electrodynamics (4th ed.), Chapter 1 (vector calculus, Stokes) and Chapter 2 (electrostatics) [memory, high].

2.2 Capacitor energy. A capacitor of capacitance C (farads, F) charged to voltage V (volts) holds charge Q = CV (coulombs, C) and stores energy E = ½CV² (joules, J). The energy sits in the electric field between the plates, and it was put there by whatever charged the capacitor. Read: Griffiths Ch. 2 (section on capacitors and electrostatic energy) [memory, high].

2.3 Displacement current. Charge cannot flow through the gap of a capacitor. Yet an alternating current (AC) "flows through" a capacitor in the sense that charge piles up on one plate while it leaves the other. Maxwell added the term ε₀ ∂E/∂t (ε₀ = 8.85 × 10⁻¹² F/m, the permittivity of free space; ∂/∂t = rate of change in time) to Ampère's law and called it displacement current. With it, total current (conduction plus displacement) always flows in closed loops. This matters here. A "single wire" connected to anything is part of a closed loop for AC, closed through the stray capacitance between the far end and the surroundings (the ground, the room, the transformer). Read: Griffiths Ch. 7 (Maxwell's equations) [memory, high].

2.4 AC power, reactive ("wattless") current and power factor. The instantaneous power delivered by a source is p(t) = v(t)·i(t). The real, or average, power is the time average of that product. If v = V₀ sin ωt and the current is i = I₀ sin(ωt + φ), then the average power is ½V₀I₀ cos φ. Here ω = 2πf is the angular frequency, f is the frequency in hertz, and φ is the phase shift between current and voltage. For a pure capacitor, φ = 90°, so cos φ = 0. The current is real (you can measure it) but on average carries no power. Energy goes into the capacitor for a quarter cycle and comes back the next quarter. Power engineers call this reactive or, in older language, wattless current. Current that is in phase with voltage is active or wattful. Two consequences: multiplying a meter's volts by its amps does not give power unless you know φ, and a non-linear element such as a diode changes the waveform, so the current is no longer purely reactive. Read: Horowitz and Hill, The Art of Electronics (3rd ed.), Chapter 1 [memory, high].

2.5 Diodes and rectifiers. A diode lets current flow one way only. A diode plus a capacitor turns AC into a stack of DC charge (a rectifier). Two diodes and capacitors can form a voltage doubler, a "charge pump" that pushes a little charge onto a storage capacitor every cycle. Read: Horowitz and Hill, Chapter 1 [memory, high].

2.6 Resonance and Q. A driven circuit with inductance L (henries, H), capacitance C and resistance R (ohms, Ω) resonates at f₀ = 1/(2π√(LC)). At resonance the voltage across C is Q times the drive voltage, where Q = (1/R)√(L/C) is the quality factor. That is a gain in amplitude. It is not a gain in power: the average power taken from the source equals the power dissipated in R. Read: Taylor, Classical Mechanics, Chapter 5 (driven damped oscillators, the mechanical twin) [memory, high].

2.7 The two laws of thermodynamics and "perpetual motion". The first law says energy is conserved. A perpetual motion machine of the first kind makes energy from nothing. The second law (Kelvin-Planck form) says no cycle can turn heat from a single reservoir entirely into work. Breaking that would be a second-kind machine, for example a magnet that cools itself while producing electricity. Frolov uses this same classification [read, 2003]. Read: Schroeder, An Introduction to Thermal Physics, Chapters 1 and 4 [memory, high].

2.8 Electrolysis energy. In electrolysis a source of electromotive force (EMF) V (volts) drives charge q (coulombs) through a cell, and the source does work W = Vq, no matter what physically moves the ions. One mole of electrons carries F = 96,485 C (the Faraday constant). Splitting water into one mole of hydrogen (H₂) moves 2 moles of electrons. The Gibbs free energy change ΔG (J/mol) is the minimum electrical work a reaction needs at constant temperature and pressure; the enthalpy change ΔH is the total energy, including heat. They differ by TΔS (absolute temperature times entropy change), which a cell can take from its surroundings as heat. For water at 25 °C, ΔG ≈ 237 kJ/mol and ΔH ≈ 286 kJ/mol [memory, high], so the minimum cell voltage is ΔG/(2F) ≈ 1.23 V [web: https://en.wikipedia.org/wiki/Electrolysis_of_water]. Read: Atkins, Physical Chemistry, the chapters on equilibrium electrochemistry [memory, medium on chapter titles; no numbers given].

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3. The textbook view

Work around a loop in a static field. For a charge q (coulombs) in a static field E:

W = ∮ q E · dl = q ∬ (∇ × E) · dA = 0, because ∇ × E = 0 for statics.

Here ∮ means "integral around a closed path", dl is a small step along the path, dA is a small piece of any surface bounded by the path, and ∇ × is the curl. This holds for every closed path. It is not a matter of a "positive half" cancelling a "negative half" by luck.

Time-varying fields. If the field changes in time, Faraday's law gives ∇ × E = −∂B/∂t (B = magnetic field, tesla). Separately, a field can be switched or moved between the outward and return legs. In either case the loop integral need not be zero, and a charge can gain net energy per cycle. Every particle accelerator and electric motor does this. The energy then comes from whatever drives the change. Poynting's theorem is the exact bookkeeping:

−dU/dt = ∮ S · dA + ∫ J · E dV

U is the field energy in a volume, S = E × B/μ₀ is the Poynting vector (power flow per unit area, W/m²), μ₀ = 4π × 10⁻⁷ H/m is the permeability of free space, J is current density (A/m²), and J·E is the power delivered to charges per unit volume. In words: energy given to charges comes out of the field's stored energy or flows in through the boundary from a source. Read: Griffiths Ch. 8 [memory, high].

Power in a circuit. Real power delivered = time average of v·i. In any network of passive components (resistors, capacitors, inductors, diodes), the total real power out equals the real power in minus losses. Tellegen's theorem states this in general for lumped circuits [memory, high].

Single-wire and "single-terminal" operation. Tesla demonstrated lamps and small motors running on a single conductor at high frequency and voltage in his London lectures of February 1892 [web: https://teslauniverse.com/nikola-tesla/articles/mr-tesla-london-institution-electical-engineers-and-royal-institution]. The return path is the capacitance of the far end to the surroundings. Russian engineers at VIESH (the All-Russian Institute for Electrification of Agriculture: Strebkov, Avramenko, Nekrasov and others) have built resonant single-wire systems, reported by the authors at up to 20 kW, with efficiencies below 100% [web: https://viesh.ru/pre/development-of-resonance-methods-of-electric-power-transmission/ and https://link.springer.com/article/10.1007/s43236-022-00383-4, search summaries]. The "Avramenko plug" is described in those sources as a diode-capacitor block that gives pulsed DC to a load from a single-wire line. In other words, the effect itself is real engineering.

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4. Where Frolov departs

The exact point of departure is the first row. Note that Frolov never writes the closed-loop theorem as an equation: the only formula-like items in his argument are the bookkeeping lines "A + B = 0" and "A + B + C + ... = 0" [read, 2003 mag. pp.11-12, 14]. He states the theorem in words, concedes it, and then answers the question "what is the source of the power?" with aether density and a reversed-time process instead of an energy account. Frolov correctly sees that a time-varying field can do net work per cycle. He then treats the act of varying it as free. Everything else follows from that one omission. The electrolysis row is the same mistake in chemistry: the field that moves the ions is the source's field, so "the field does the work" and "the source pays" are the same statement.

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5. Worked example: where does the spark energy come from?

This uses Frolov's own 1994 experiment [read, 1994 p. 2]. A 30 V, 10 kHz generator draws 3 W from DC (30 V × 0.1 A) and feeds a step-up transformer to 2-5 kV. One high-voltage wire goes to two diodes (the Avramenko plug). The load is a 10 nF capacitor whose legs are bent into a 0.5-1 mm spark gap. It sparks 1-10 times per second, and he uses V = 2 kV and 5 sparks/s. Fig. 1 of the article [read: page image p. 2] shows one end of the secondary connected to a loop of two diodes with the load on the far side of the loop, and nothing else connected.

Step 1: check his arithmetic. - Energy per spark: E = ½CV² = ½ × (10 × 10⁻⁹ F) × (2000 V)² = 0.5 × 10⁻⁸ × 4 × 10⁶ = 0.020 J. - Power: P = E × f_spark = 0.020 J × 5 s⁻¹ = 0.10 W. - Efficiency: 0.10 W / 3 W = 3.3%. His arithmetic is right, and his own numbers show the load getting a small fraction of the input.

Step 2: how much current must reach the load? Charge per spark Q = CV = 10⁻⁸ × 2000 = 2 × 10⁻⁵ C. At 5 sparks/s the mean current is I = 2 × 10⁻⁵ × 5 = 1.0 × 10⁻⁴ A = 0.1 mA.

Step 3: can ordinary stray capacitance carry that? Model the conventional circuit. The wire end sits at source voltage v(t) = V₀ sin ωt. Diode D1 feeds node P and diode D2 drains node N. The 10 nF load C_L sits between P and N. P and N each have a small stray capacitance C_s to the surroundings, and that is the return path. Because C_L ≫ C_s, P and N swing up and down together, by 2V₀ − u each half-cycle, where u is the load voltage. Each swing pushes charge C_s(2V₀ − u) through C_L, always in the same direction because of the diodes. Averaged over many cycles:

du/dt = 2f C_s (2V₀ − u) / C_L, with solution u(t) = 2V₀ (1 − e^(−2f C_s t / C_L)).

Set u = V_s (the spark voltage) at t = t_sp and solve:

C_s = C_L ln[2V₀ / (2V₀ − V_s)] / (2 f t_sp).

Put in C_L = 10 nF, f = 10 kHz, an assumed peak V₀ = 3 kV (he says 2-5 kV), V_s = 2 kV and t_sp = 0.2 s (5 sparks/s):

ln(6000/4000) = ln 1.5 = 0.405; C_s = 10⁻⁸ × 0.405 / (2 × 10⁴ × 0.2) = 1.0 × 10⁻¹² F ≈ 1 pF.

The reviewers' cruder estimate, I = 2πf C_sV, gives 0.8 pF. The two agree in order of magnitude. A wire end, a diode pair and a capacitor body near a bench or a hand have stray capacitance of a few pF [memory, high], so ordinary displacement current through stray capacitance is enough to explain the sparks. No new physics is needed. (This shows the conventional explanation is sufficient. It does not prove it is the only one. That needs the control measurement in Step 5.)

Step 4: who pays? (energy ledger, from example.py). Simulate the same circuit with ideal diodes for one second and add up the work done by the source, ∫ v i dt. - Without the diodes (wire straight to the stray capacitance): source work over 1 s ≈ 10⁻¹⁹ J, effectively zero. The current is purely reactive, "wattless" exactly as Frolov says. - With the diodes: 4 sparks of 0.020 J in the first second (the fifth is due at t = 1.0 s, with 0.020 J already stored), and the source does 0.100 J of work, a mean of 0.100 W. Source work = spark energy + stored energy, to within 5 × 10⁻⁸ J.

So the diodes do turn wattless current into wattful current, which is Frolov's phrase. But in doing so they change the phase of the current, and the source then delivers exactly the real power that appears in the sparks. Nothing is free. The 3 W the generator draws is mostly the generator's and transformer's own losses, and the 0.1 W load is a small extra on top.

Step 5: the measurement that would settle it. Measure the generator's true input power (DC volts × amps, or the average of v·i on an oscilloscope) in three cases: load connected, load disconnected, and diodes shorted. Conventional physics predicts that input rises by about 0.1 W (plus diode and spark-gap losses) when the load is connected. If it does not rise, or falls, that would be a real anomaly. Frolov reports no such control [read].

Run it yourself: .venv/bin/python review/Frollov-Alexander/example.py (takes about 10 s).

A second, shorter check: resonance (Claim 3). Take L = 1 mH, C = 1 nF and R = 10 Ω. Then f₀ = 1/(2π√(10⁻¹²)) = 159 kHz and Q = (1/10)√(10⁻³/10⁻⁹) = 100. A 10 V peak drive gives 1000 V peak across C, a 100× voltage gain. The input power is V²/(2R) = 100/20 = 5 W, and that is exactly the power burned in R. Voltage went up a hundredfold. Power did not go up at all. [physicist.md, re-checked]

A third check: electrolysis (who pays when "the field moves the ions"?). Also in example.py. One mole of H₂ needs 2 moles of electrons, q = 2 × 96,485 = 192,970 C. - At the minimum voltage 1.23 V the source does W = 1.229 V × 192,970 C ≈ 237 kJ. That is ΔG. - Burning that hydrogen gives back ΔH ≈ 286 kJ. The extra 49 kJ (TΔS) is heat the cell drew from the room while running between 1.23 V and the "thermoneutral" 1.48 V. It is not energy from the field. So "the gases burn hotter than the electricity put in" can be true and still give no surplus once that ambient heat is counted. - Goriatchev's claimed 0.2 V pulses [read, 2003 mag. p.24, second-hand]: at a mean of 0.2 V the source supplies 38.6 kJ per mole of H₂, 16% of the 237 kJ minimum. Steady water splitting at that average voltage is impossible, so the "1500%" must compare quantities defined differently (for example peak versus average, or gas heat against part of the input). The arbiter rates "no primary power required" Refuted by calculation and Goriatchev's figure Never properly tested.

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6. Evidence table

A self-contradiction worth noticing: Frolov sets aside "electrokinetic apparatus" as mere ionization flow, yet the Brown patent figure he reproduces (Fig. 4) is titled "Electrokinetic apparatus by T.T. Brown" [read, 2003 mag. pp.15-16]. The arbiter's Round 2 changed no verdict for Claims 1-7; it added Claim 8 (the 1995 coil) and extended Claim 1a to Fig. 2. No item moved to Tested, not supported, because no test record exists for any of them.

On "suppression": the arbiter found no case where a Frolov claim was dismissed without testing. His own claims were never put in testable form (no input with and without load, no waveforms, no calorimetry), so there was nothing for critics to test or reanalyse [arbiter.md]. The article does allege suppression of other people's work, and the arbiter rates each as unsourced beyond the document: - Filimonenko: extra power from heavy-water electrolysis (1957); support from Kurchatov, Korolev and Zhukov in 1960 and a "secret resolution"; then suppression "by people of nuclear power plant team"; a 1994 Moscow City Council commission urged renewal [read, 2003 mag. p.25]. His sources are an unnamed declassified document and two Russian journals, none quoted; Frolov himself calls the military-interest explanation "an assumption". No independent source was found or checked, and whether the effect was ever tested under control is unknown. - Johnson's patent: filed 6 Dec 1973, granted 24 Apr 1979 [read, mag. p.21]. That the delay was because "it is 'perpetuum mobile'" is Frolov's inference. - Russian institutes blocking new ideas, plagiarism, "two worlds" of hidden knowledge: assertions with no named case [read, mag. pp.25-26].

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7. What a learner should take away

Solid. - His spark arithmetic (½CV² × f) is correct. - Single-wire power transfer is real, with the return path through capacitance. It goes back to Tesla, and Russian groups have built it at kilowatt scale. - A time-varying field can do net work on charges every cycle. - Resonance gives large voltage gain. - A non-uniform field pulls on a neutral dielectric (force proportional to the gradient of E², called dielectrophoresis) [memory, high]. - Brown-type asymmetric capacitors do produce a force in air.

Wrong, and why the mistake is instructive. Frolov's central error is a very common one: he counts the work the field does on the charge and leaves out the work done on the field by the switch, the screen or the diode. The worked example shows this precisely. Without the diodes, the current really is wattless, and the source does zero net work. The moment the diodes make the current do work in the load, they shift the current's phase, and the source starts delivering exactly that much real power. "Wattless" and "free" are not the same thing. A current that does no work costs nothing, and a current that does work is paid for. The resonance error has the same structure: amplitude is not power. So does the electrolysis argument: "the field moves the ions" is true, but that field belongs to the battery, which pays Vq. The pulsed tube of Fig. 2 is the same error in time instead of space: switching the battery off before the electrons land does not mean the battery spent nothing, because it already paid to accelerate them. The 1995 coil claim is the same error for transformers: a load on the secondary always reflects into the primary, so "free from input power" would need a measurement of primary power with and without the lamp, and none is given. And a rotor that speeds up is not an energy gain unless you have shown the kinetic energy plus all output exceeds every input. The four-dimensional "reversed-time" balance is what you get when the ordinary ledger refuses to balance in your favour and you add an unmeasurable column to make it.

Genuinely open (small, cheap and never done for his setups). - Does the generator's input power rise, stay flat or fall when his load is connected? This includes his arc-loading test, where he says input fell at about 300 mA, measured on the DC side [read, 2003]. Conventional physics predicts it rises. A bench measurement with an oscilloscope would settle it. - Is Avramenko's "60 mA at 50 V = 3 W" lamp figure a real-power measurement or a product of meter readings on a distorted waveform? (P ≤ V I, with equality only when current and voltage are in phase.) - What exactly produces the Brown force in air? Simple ballistic ion wind was estimated as too small, and ionic drift is the likelier candidate. - Is Frolov's figure of 100 kW for single-wire lines real? 20 kW is reported by the system's authors. - Does the ferrite core really cool? This is a cheap reader experiment: thermocouples on the ferrite core and on a non-ferrite dummy core, with the coil open and loaded, and the drive motor's input power logged. Local cooling is possible without any energy gain (losses and magnetic heating shift with the flux cycle); what would matter is net electrical output with the whole apparatus not warming. - Does the primary power of Frolov's 1995 flat-spiral-coil transformer change when the lamp is connected? This is a cheap reader experiment: a solenoid primary, a flat spiral secondary, and an oscilloscope logging primary v, i and their phase with and without the lamp. Conventional physics predicts the primary's real input rises by the lamp's power plus losses. - Does the arc test's battery current really fall to zero and reverse, as Frolov says he showed in 1996? Sample battery v(t) and i(t) fast enough to catch the pulses, average their product, and repeat at several gap lengths with the load on and off. A DC meter's average can miss pulsed current, and stored energy in the transformer or battery sag can mimic a fall.

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8. Check yourself

1. A 1 μC charge is carried once around a closed loop in the static field of a charged sphere. How much net work does the field do? Now a conducting screen is slid in to shield the return leg. Where does the energy bookkeeping change?
2. A 2 kV peak, 10 kHz sinusoid drives a 1 pF capacitor to ground. What is the peak current, and what is the average power?
3. In the worked example, by what factor does the required stray capacitance change if the spark rate is doubled to 10/s, with everything else fixed?
4. Frolov reports 0.1 W in the load and 3 W at the generator. Name the single measurement that would show whether the 0.1 W is "free", and the result conventional physics predicts.
5. A series RLC circuit has Q = 50 and is driven at resonance with 5 V peak. What is the peak voltage across C, and why does this not make the efficiency greater than 100%?

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9. Further reading

Mainstream. - D. J. Griffiths, Introduction to Electrodynamics, 4th ed.: Ch. 2 (electrostatics, energy), Ch. 7 (displacement current, Maxwell's equations), Ch. 8 (Poynting's theorem). - P. Horowitz and W. Hill, The Art of Electronics, 3rd ed.: Ch. 1 (AC circuits, reactive power, diodes, rectifiers, voltage doublers). - J. R. Taylor, Classical Mechanics: Ch. 5 (oscillations, resonance, Q). - D. V. Schroeder, An Introduction to Thermal Physics: Ch. 4 (heat engines, second law). - P. Atkins and J. de Paula, Physical Chemistry: equilibrium electrochemistry (cell voltage, Gibbs energy, Faraday constant) [memory, medium on edition and chapter]. - Electrolysis of water, minimum and thermoneutral voltages [web: https://en.wikipedia.org/wiki/Electrolysis_of_water]. - T. B. Bahder and C. Fazi, "Force on an asymmetric capacitor", ARL-TR-3005 (2003) [web: https://arxiv.org/vc/physics/papers/0211/0211001v1.pdf]. - Biefeld-Brown effect overview, including the vacuum tests [web: https://en.wikipedia.org/wiki/Biefeld%E2%80%93Brown_effect]. - VIESH resonant single-wire transmission (Strebkov group) [web: https://viesh.ru/pre/development-of-resonance-methods-of-electric-power-transmission/].

Frolov's own (in the folder). - A. V. Frolov, "The Single-Wire Electric Power Transmission", New Energy News, Dec 1994, pp. 13-15 (single wire power transmission.pdf). - A. V. Frolov, article on the potential field and aether-dynamics, New Energy Technologies #2, Mar-Apr 2003, pp. 11-28 (FreeEnergy.pdf).

Cited by Frolov, not in the folder. - N. E. Zaev, S. V. Avramenko and V. N. Lisin, "The Measuring of Conduction Current That is Stimulated by Polarization Current" (1991, in Russian) [read: cited in the 1994 note]. - T. E. Bearden, "Overunity Electrical Power Efficiency Using Energy Shuttling Between Two Circuits" (1994) [read: cited].

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Answers

1. Zero: the field of a charged sphere is static, so ∮ E·dl = 0 on any path. A conducting screen carries induced charge. Sliding it in and out of the field changes the stored electrostatic energy, and the work needed to move it equals the work "saved" on the return leg. Over a full cycle of the whole system (charge plus screen), the net work is zero. Frolov leaves the screen out of the ledger.
2. The capacitor's impedance is X_C = 1/(2πfC) = 1/(2π × 10⁴ × 10⁻¹²) ≈ 1.59 × 10⁷ Ω, so the peak current is 2000/1.59 × 10⁷ ≈ 1.26 × 10⁻⁴ A ≈ 0.13 mA. The average power is zero, because the current leads the voltage by 90° and cos 90° = 0. This is the "wattless" current.
3. C_s = C_L ln[2V₀/(2V₀ − V_s)] / (2f t_sp), so C_s ∝ 1/t_sp. Halving t_sp doubles C_s, to about 2 pF, still an ordinary stray value.
4. Measure the generator's true input power with the load connected and with it disconnected (and with the diodes shorted). Conventional physics predicts the input rises by at least the 0.1 W the load takes, plus diode and gap losses. "Free" would require no rise.
5. 50 × 5 V = 250 V peak. The source still supplies average power V²/(2R), and in steady state all of it is dissipated in R (or a load). The high voltage is stored energy sloshing between L and C, built up over about Q cycles from the source's own input. Output power cannot exceed input power.