The Experiment to Negate Maxwell Theory

Scientific Paper
Title	The Experiment to Negate Maxwell Theory
Read in full	Link to paper
Author(s)	Qing Zeng
Keywords	mutual generation field, electric field generates magnetic field, magnetic field generates electric field, ether displacement current
Published	2010
No. of pages	11

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Abstract

Maxwell brought forward the viewpoint that "time variable magnetic field generates electric field", according to Faraday's law. At the mean time, he also thought that conductive current was successive in the free space (ether space), so the time variable electric field in the capacity (ether displacement current) generated magnetic field the same as conductive current. Therefore, it was derived the mutual generation theory [1, 2] that "magnetic field generates electric field and electric field generates magnetic field. But since more than one hundred years, nobody performed the direct experiment of mutual generation field theory. This article introduces the experimental method to verify the theory, and directly verify whether the displacement current in the vaccum really generates magnetic field. This article analyzes through "experiment", and derives: displacement current of vaccum (ether) does not generate magnetic field, the physical essence of electromagnetic induction is Lorentz force, and not the displacement current, which means that it needs to reconsider whether Maxwell Curl Field Theory is correct.

Overview

Zeng Qingping, a professor at the Air Force Radar Academy in Wuhan, attacks what he calls Maxwell's "mutual generation field" theory — the doctrine that a time-varying magnetic field generates an electric field and a time-varying electric field generates a magnetic field, each sustaining the other. Against this he sets what he calls independent radiation: a time-varying current radiates a magnetic field by itself, a time-varying charge radiates an electric field by itself, and, in the phrase he attributes to Lorentz and to Hertz, "the motion of charges is the root to generate all electromagnetic fields" — "one field does not generate another field."

The paper's distinctive move is that it is framed as a call for experiment rather than as a derivation. Zeng argues that in more than a century nobody has directly tested whether vacuum displacement current produces a magnetic field, and he proposes three benchtop arrangements to settle it. He is candid that he cannot afford to do them himself — he estimates three million yuan for the full set and describes himself as "just a poor professor" — and asks physicists in wealthier countries to carry them out. He also states in advance what he expects the answer to be. His larger target is Einstein: since the 1905 paper opens by invoking the magnet-and-conductor asymmetry within Maxwell's electrodynamics, Zeng holds that undermining Maxwell's curl equations "shakes the argument of relativity principle".

The argument

Objections to the derivation of displacement current

Zeng lists five complaints against Maxwell's route to ∂D/∂t. The Earth's polar magnetic field moves with the Earth and yet induces no electric field in free space. Maxwell used Stokes's theorem to convert Ampère's circuital law into the curl relation ∇×H = J, which Zeng says holds only inside a conductor. Maxwell applied Green's theorem to a capacitor circuit and deformed the Ampèrian surface to pass between the plates, whereas the theorem requires the integrand to have continuous first partial derivatives on the surface and its boundary. Continuity of current, ∇·J = −∂ρ/∂t, was extended from the wire to all of free space, but Kirchhoff's law applies only inside conductors. And if the displacement current really equalled the conduction current, I_D = I_C, then "the capacity will be equivalent to short circuit", contradicting the fact that charge accumulates on the plates.

General Lorentz magnetic force

Zeng's replacement mechanism for induction is a generalisation of the Lorentz force. Case one is textbook: a conductor moving at V_q through a static field feels F = qV_q×B, the electrons drift, and a current flows. Case two holds the conductor still and moves the magnet at V_B; here ∂H/∂t is nonzero and Maxwell would invoke an induced electric field. Zeng instead substitutes V_q = −V_B to obtain

F = q(−V_B) × B

and remarks that the minus sign "is not added randomly": relative to still space the magnet's motion is opposite to the conductor's. Combining the two he writes the General Lorentz magnetic force F = q(v_e ∨ −V_B) × B, where ∨ denotes "or". He repeats the construction for a coil crossing curved ("trumpet-flower") field lines, deriving the induced current I = snev and, via the differential form of Ohm's law, the electromotive force dU = Idl/σs. His conclusion is a claim about priority of cause: the Lorentz force is "the physical essence" of induction, while Lenz's and Faraday's laws "only describe the physical phenomenon". Faraday, Lenz and Lorentz located induction on the conductor; Maxwell located it in free space, and that is the point at issue.

The three proposed experiments

Figures 5 and 6 are a comparison. Move a magnet near a real conducting loop: the induced current i_C creates a back field B_L′ opposing the magnet's, so a gaussmeter reads a weakened field. Now repeat with only a fictitious loop in free space: on Maxwell's account an eddy displacement current i_D should arise and produce its own opposing B_M′, weakening the reading similarly. Zeng predicts B_M′ will simply not be there.

Figure 7 is the direct test of displacement current. A parallel-plate capacitor of area s = 0.01 m² and gap d = 0.01 m sits inside a vacuum tube, driven at f = 30 kHz and v_m = 10 000 V, with the leads shielded. With C = ε₀s/d = 8.8542×10⁻¹² F the current is

i = C dv/dt = 10 000 × 2π × 3×10⁴ × 8.8542×10⁻¹²×0.01/0.01 ≈ 1.65×10⁻² sin(ωt) A

A pickup coil L is placed first at section a (the gap, where only displacement current flows) and then at section b (the wire, carrying conduction current). If a signal appears at b and none at a, Zeng holds that the displacement current generates no magnetic field. He notes the practical limits honestly: commercial gaussmeters reach about 0.1 gauss (he gives the conversion 1 gauss = 80 A/m) below 30 kHz, so the drive voltage would have to be raised roughly tenfold, at a cost he prices at 120 000 yuan for the supply alone; and stray fringing fields can polarise the glass envelope and set up molecular currents that mimic a signal.

Consequences claimed

Zeng argues that a gaussmeter measuring the field of a time-varying current already demonstrates independent radiation, since the instrument responds to B and not to E; that successful radio reception does not prove the curl theory, because a dipole antenna can be read as an inductance radiating B from its current and a capacitance radiating E from its charge; and that independent radiation matches the engineering inverse-square law whereas mutual generation does not. He closes by saying that a null result would be as valuable as a positive one, and that if the curl theory falls, "Einstein's relativity principle will be questioned".

Assessment

What is attractive here is the instinct: Zeng wants a direct measurement of the magnetic field of a vacuum displacement current rather than an inference from the success of the wave equation, and he specifies apparatus, numbers and a decision rule instead of stopping at a verbal objection. He also states his expected result in advance and concedes that a negative outcome would still be worth publishing. That is a better scientific posture than most papers of this kind adopt.

The arithmetic. Equation (6) is right. With C = ε₀s/d = 8.8542×10⁻¹² F, ω = 2π(3×10⁴) and v_m = 10⁴ V, ωCv_m = 1.67×10⁻² A; his printed 1.65×10⁻² A differs only by his rounding of π. The unit conversion 1 gauss = 80 A/m is also correct (10⁻⁴ T / μ₀ = 79.6 A/m).

But the proposed experiment cannot work as specified, and that is fatal to it. A plate area of 0.01 m² means a plate radius of about 5.6 cm. The magnetic field at the rim of the gap, for a uniform displacement current of 1.67×10⁻² A, is B = μ₀I/2πR = 5.9×10⁻⁸ T, i.e. 5.9×10⁻⁴ gauss. Zeng's own gaussmeter resolution is 0.1 gauss — a factor of 170 too coarse. His proposed remedy of raising the voltage tenfold, to 100 kV, still leaves the signal 17 times below the noise floor; detection would need something of order 2 MV. So the experiment as designed is guaranteed to return "no field at section a" whether or not the field is there, and the null result he predicts would carry no information at all. This is why the measurement, when it was actually made, was made with resonant and lock-in methods rather than a gaussmeter.

The measurement has been made, and it came out the other way. The magnetic field between capacitor plates carrying no conduction current has been detected directly and repeatedly — Carver and Rajhel's "literal" demonstration (Am. J. Phys. 1974) and Bartlett and Corle's measurement of the field of a displacement current (Phys. Rev. Lett. 1985) are the standard references — and its magnitude agrees with μ₀ε₀∂E/∂t. The premise that "nobody has performed the direct experiment" is not correct.

The Ampèrian-surface objection is exactly backwards. Zeng's third and fourth complaints are that Ampère's law becomes ill-defined when the surface is deformed to pass between the plates. That is true, and it is the reason the displacement term exists: without ∂D/∂t the circuital law is surface-dependent and therefore inconsistent, and adding it restores surface-independence and, equivalently, local charge conservation. A standard textbook derivation is presented here as a refutation of the result it establishes. The related objection that I_D = I_C would "short circuit" the capacitor rests on treating displacement current as a flow of charge across the gap. It is not; no charge crosses, and ε₀∂E/∂t is a rate of change of field, which is why the plates go on accumulating charge exactly as observed.

The mechanism has a direct counterexample. If the Lorentz force on moving electrons cutting moving field lines is "the physical essence" of induction, then induction should require relative motion. A transformer has none: primary, core, secondary and observer are all at rest, nothing cuts anything, and the secondary nonetheless develops the full Faraday EMF. Zeng's construction has no v to supply. The deeper problem is that "moving magnetic lines" is not a defined quantity — field lines are level sets, not objects with identity or velocity, so V_B cannot be measured and −V_B×B is not a force law. What the standard treatment does with the same two cases is exactly what Zeng wants — one mechanism for both — but by transforming the fields between frames, so that E′ = −v×B in the conductor's rest frame. Zeng's "general Lorentz magnetic force" reproduces that transformation for the special case of uniform B and slow motion; it is not an alternative to it.

Two smaller points. The claim that "radiation electric field intensity is inversely proportional to the distance square" is not the engineering fact he appeals to: in the far field the field falls as 1/r and the power density as 1/r², which is what the Friis equation used in radar link budgets encodes. And the final inference — that questioning the curl equations questions relativity — inverts the historical logic. Einstein's opening paragraph does not derive relativity from the mutual-generation picture; it observes that Maxwell's theory gives two different descriptions of one observed current, and proposes relativity to remove that asymmetry.

See also

• Qing Zeng
• Maxwell's Equations
• Displacement Current
• Lorentz Force
• James Clerk Maxwell
• Heinrich Hertz
• Michael Faraday
• Electromagnetism