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Journal of Electrostatics 107 (2020) 103477
1
Put Strong Limits on All Proposed Theories so far Assessing Electrostatic Propulsion: Does a
Charged High-Voltage Capacitor Produce Thrust?
M. Tajmar
1
and T. Schreiber
2
Institute of Aerospace Engineering, Technische Universität Dresden, 01307 Dresden, Germany
Abstract
Several claims appeared in the literature that a charged high-voltage capacitor produces thrust. This
dates back to the so-called Biefeld-Brown effect that was later explained as a Corona-wind effect.
However, part of the claim was that the capacitor still moves even if no ionization takes place and a
dielectric is used. Recently, theories appeared supporting such an electrostatic propulsion-scheme.
Here we describe an experimental-setup allowing to measure weight changes/forces of capacitors up
to 10kV, eliminating important side-effects from high-voltages down to +/-0.3mg. No force was
detected for a variety of configurations ruling out most theories by many orders of magnitude.
Keywords: Biefeld-Brown effect, Anomalous forces
1. Introduction
Does a charged high-voltage capacitor produce thrust? This question was first raised nearly 100 years
ago in a patent [1] and follow-up paper [2] by T.T. Brown, which later became known as the Biefeld-
Brown effect. In this early work, a parallel plate or spherical high voltage capacitor with a dielectric
between the electrodes was observed to move towards its positive electrode while charged up to very
high voltages (up to 300 kV). The capacitor was placed on a torsion pendulum connected with thin
wires in order to observe the movement. It was claimed that the force depended on the applied voltage
and the mass of the dielectric. The applied current was only necessary to overcome the overall
leakages in order to maintain the applied voltage. This was further illustrated by showing that the
capacitor was put inside an insulating oil tank in order to limit any discharge effect or leakage. It was
claimed that this observation is a new electro-gravitational effect.
Brown later worked on larger models without oil insulation and observed high thrusts in ambient air
with or without dielectric isolation, observing that the effect increased, if the shape of the electrodes
were asymmetrical (e.g. flat cathode and wire anode) [3,4]. This became mainstream science known
as electrohydrodynamics (EHD), corona/ion wind propulsion or plasma actuators [5,6], an active field
of research up to the present day investigating alternative propulsion means for heavier-then-air
model-airplane propulsion [7] or micro-drones [8]. The explanation is rather simple: A corona
discharge drags ambient air molecules generating thrust. This seems to put the claim of a new electro-
gravitational effect at rest [6,9] – at least for configurations with discharges in air.
Still, a few publications appeared with claims that there is a force in addition to the usual corona wind
effect which is only electrostatic in nature [10–14], crucially linking it to the dielectric material between
the electrodes similar to Brown’s original observation. A recent paper also reports of an anomalous
force, if there is a discharge through the dielectric [15]. However, like Brown’s work, these claims lack
a proper setup to definitely rule out conventional explanations. In addition, theoretical models
appeared predicting such an electrostatic effect [12,13,16–19]. If true, this could lead among many
other things to a novel space propulsion scheme which would be of high interest [20].
1
Institute Director and Head of Space Systems Chair, EMail: martin.tajmar@tu-dresden.de
2
Now at Fraunhofer FEP
Journal of Electrostatics 107 (2020) 103477
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Previously, we assessed claimed weight anomalies with permanently polarized dielectric materials
(electrets) finding a null-result within our resolution [21]. However, capacitors are better suited to
obtain drift-free measurements because the dielectric polarization can be turned on and off in a
controlled manner. In this paper, we want to review predictions for anomalous forces due to
electrostatic polarization of dielectrics and present an experimental setup that is well suited to
investigate such polarization-thrust claims, taking not only ion winds but also other high-voltage
induced side-effects into account. Finally, we will present a set of measurements targeting to evaluate
each of the claims to answer the question if a high voltage capacitor indeed generates an anomalous
force. This included standard parallel-plate capacitors that have symmetric or asymmetric electrodes,
a capacitor with an asymmetrical dielectric as well as a capacitor that allows a leakage current through
its dielectric (see Fig. 1).
2. Theoretical Predictions
Here we want to shortly review the models that have appeared recently, predicting an electrostatic
effect causing the self-acceleration of a dielectric when polarized. Although one would immediately
dismiss any such claims on the basis of energy and momentum conservation, self-acceleration is a
known consequence of an inertial dipole that has even been observed in the laboratory [22]. Inertial
dipoles may be created in an environment that generates a negative effective mass, which allows self-
acceleration without violating conservation rules [23]. Most of the models presented here do not
involve negative inertial effects, however, it would seem plausible that such a connection must exist if
any of the experimental claims turns out to be true.
The first model predicting an electrostatic self-acceleration effect has been proposed by Ivanov [16].
He argues that static electric or magnetic fields induce so-called Weyl-Majumdar-Papapetrou solutions
for the metric of spacetime that create effects many orders of magnitude larger than usually expected.
An electrostatic field is predicted to generate a gravitational field which accelerates the dielectric. The
generated force for a simple parallel-plate capacitor (see Fig. 1a) is given by
(1)
where G is Newton’s gravitational constant, and the vacuum and relative electric permittivity, m
the mass of the dielectric, d it’s thickness and V the applied voltage. An analogous relationship is also
predicted for magnetic fields. Musha proposed a similar equation with the addition that it is multiplied
with the atomic number Z [12]. His model includes an electro-gravitational coupling that indeed
assumes a gravitational dipole around the center of the atom that generates the self-acceleration
force. Also Zhu [17] arrived at a same relationship (without dielectric) based on the gravitational
redshift/blueshift and the law of conservation of energy. This remarkably simple Equ. (1) leads to
forces in the order of up to 10 µN (or an equivalent of 1 mg of mass change if put on a balance) for
standard high-voltage capacitors. This force is small enough that it may not have been clearly identified
yet.
Another model was proposed by Porcelli and dos Santos Filho [13,14], which is empirically based on
the Clausius-Mossotti relationship for the polarizability of dielectric materials as well as the similarity
to dielectrophoretic forces. It is given by
(2)
Journal of Electrostatics 107 (2020) 103477
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where E is the applied electric field and A is the area of the plate for a symmetrical parallel-plate
capacitor. For asymmetrical capacitors, this equation is modified to
(3)
where A1 is the area of the larger electrode and A2 the area of the smaller one. These equations are
expected to provide much larger forces up to several 1000s of µN (or equivalent several 100s of mg)
for typical high voltage capacitors, which should be detected rather easily.
The next model was recently proposed by Minotti [19], who derived his relationship as a consequence
of a scalar-tensor theory of gravitation proposed by Mbelek and Lachièze-Rey [18]. It is based on a
Kaluza-Klein-type 5D theory with an additional stabilizing scalar field of electromagnetic origin that is
minimally coupling to gravity. Following Minotti’s notation, the coupling constant is empirically found
by fitting temporal changes of the Earth’s magnetic field to the large error bar when comparing
different measurements of the gravitational constant. He proposed a force equation for a spherical
capacitor, which is only half-filled with a dielectric as shown in Fig. 1b, that is given by
(4)
where is the density of the dielectric material and a and b are the inner and outer radius of the
spherical capacitor respectively. However, Minotti forgot to include the relative permittivity of the
dielectric in his derivation (which leads to multiply Equ. (4) with
). Moreover, also here we can
simply use the case of a parallel-plate capacitor to arrive at a much simpler equation given by
(5)
With a coupling constant of
, the predicted forces are right between Ivanov’s
and Porcelli and dos Santos Filho’s values with hundreds of µN (or equivalent tens of mg). Note that
Minotti re-evaluated Mbelek and Lachièze-Rey’s original theory and arrived at a 4 orders of magnitude
lower coupling constant than originally proposed [24]. It should also be noted that Mbelek claims to
have evidence for his original coupling constant by a recently published experiment [25]. The values
derived with Minotti’s latest constant should therefore be considered as a lower minimum value and
that even much higher forces could be observable.
The last claim we investigated is based on a discharge through a thin dielectric sheet [15]. The authors
say that their effect can by predicted by a modified inertia model based on Unruh radiation forming a
so-called Rindler horizon which is affecting the electron’s mass [26]. However, no actual force model
is shown that allows calculating thrust based on their experimental conditions. We digitized their plot
of measured force versus discharge power for various dielectric thicknesses and performed an
exponential fit (similar to the authors observation). We arrive at the following empirical relationship:
(6)
Journal of Electrostatics 107 (2020) 103477
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where P is the discharge power in mW, d the dielectric thickness in µm and F the force in µN. This
matches their observed forces well (R²=0.9996) leading to a deviation of only a few percent at the
thickness we will use for our test.
3. Experimental Setup
Most published measurements were done with commercial analytical balances; therefore, we chose
to follow a similar approach. The reliable measurement of small weight changes of a high voltage
capacitor on a balance causes many side-effects which can cause false readings. During our
experiments, the most important factors were:
1. Corona wind effects: Most papers do not disclose which high voltage cable was used to connect
the capacitor to the high voltage power supply, which was always next to the balance. If a thin
cable was used, probably not even isolated to reduce cable stiffness for high resolution weight
readings, air will get ionized around the wire causing a corona discharge. This will produce the well-
known EHD force that masks any anomalous effect. The origin of corona winds must not be limited
to the cable but also to the connection between the cable and the capacitor, which needs to be
protected properly. Sharp edges (e.g. due to soldering the end of the cable to the capacitor) create
much higher field strengths which can cause ionization even if (too thin) isolation tape is used.
2. High voltage induced mechanical stress: Wires under high voltage bend due to electrostatic forces.
This happens not only between different wires (e.g. the connection to the positive and negative
polarity) but also along a single wire itself. This can immediately cause false balance readings if the
cable is coming from an outside fixed power supply to the capacitor on the balance. But there is
even a more sophisticated error which we observed in our measurements: A slight bending of a
wire under high voltage causes a shift of the center of mass, which in turn can again lead to a
recorded weight change which may falsely be identified as a new effect.
3. Buoyancy: If a power supply is used on the balance, heat is generated depending on the generated
voltage. This can cause buoyancy and again false balance readings. Just imagine a box of
10x10x10 cm³. A change of 1°C in that volume causes a buoyancy force equivalent to 4 mg of mass.
Therefore, temperature stability is very important for reliable sub-mg readings.
4. Electromagnetic interactions with the environment: The experiment is surrounded by
electromagnetic fields which may influence the measurement such as the Earth’s magnetic field
or not properly shielded power supplies. An onboard power supply may e.g. create a magnetic
field if not properly shielded.
In addition, air movement and seismic noise must be taken into account to obtain high resolution. And
most important: The experiment must include some sort of null measurement where a zero reading
on the balance should occur even if the full high voltage is applied. If that is the case, typically most of
the important side-effects should be covered.
After many iterations, we arrived at the following setup as illustrated in Fig. 2:
The experiment was done inside a custom-built Faraday cage with a front door that can be closed
airtight. This large box sits on top of a massive granite table which is isolated to the ground with rubber
isolation pads. The overall setup therefore provides a good seismic isolation as well as protection from
air flow in addition to basic EMI shielding.
We used a Sartorius MSE1203S-100-DE analytical balance which has a maximum weight capacity of
1200 g with a custom enhanced resolution to 0.1 mg (standard is 1 mg). This was necessary as usual
0.1 mg balances have a too low maximum weight capability for all of our experiments. This balance
Journal of Electrostatics 107 (2020) 103477
5
sits on top of a stable aluminum profile construction. It features a hook which allows to connect our
experiment from the bottom to a single point. This was essential to reduce side-effects from changes
due to center of mass shifts e.g. from bending cables or rotating the capacitors.
The experiment was done inside a lightweight box with a base of 150x150 mm and a height of 100 mm
which consisted of thin aluminum profiles on the edges for mechanical stability. The base plate was
0.5 mm thick and made from mu-metal and the sides are covered with 100 µm mu-metal foil. This cage
therefore shields both electric and lower-frequency magnetic fields due to the high magnetic
permeability of mu-metal. The connection to the hook is done with a three plastic cord suspension,
which can be adjusted in length using screws. A small tubular spirit level enables to properly orient the
box.
The inside of the box consisted of two parts: an on-board high voltage power supply and a rotation rig
which allows to mount capacitors and change their orientation without opening and influencing the
experiment. We used an EMCO CB101 power supply which can generate up to 10 kV at 100 µA and
includes a voltage and current monitor signal. This compact and lightweight power supply was
wrapped inside a box made of thermal isolation foam in order to limit heat conduction from the power
supply to the ambient air which can cause buoyancy effects (see Fig. 2c). The temperature of the power
supply was monitored with a TI LM35 sensor. The rotation rig next to the power supply was made from
3D printed PLA parts. It features a small 28BYJ-48 stepper motor and a Megatron MAD12AH absolute
position encoder (see Fig. 2d) as well as a mounting structure for the capacitors. All electric
connections are going through a 16-pin Galinstan liquid-metal feedthrough as shown in Fig. 2e. This
allows to power and control all components inside the box with only low-voltage signals without any
mechanical influence. That is a huge advantage compared to all other experiments published so far
[11–14]. One of the pin-connectors is used to externally ground the experiment box. All pins go through
a Sub-D pin connector through the outer box and are connected to a power supply, a LabJack T7 data
acquisition board and a unipolar stepper motor driver (Weedtech WTSMD-M).
A LabView software is executing the measurements. It runs pre-defined profiles with an off- and on-
period and different voltage settings. Several identical profiles can be signal-averaged in order to
improve the signal-to-noise ratio and get statistical significance. Moreover, the software can
automatically eliminate drifts by using a linear fit along the off-periods.
The balance was calibrated with a voice-coil (BEI Kimco LA05-05-000A), which was mounted in the
middle of the bottom of the experiment box as shown in Fig. 3a. This allows verifying if the liquid-metal
feedthroughs have any influence on the measurement down to our digital resolution of 0.1 mg. The
voice-coil itself was calibrated on a dedicated setup which verified its calibration constant of 0.758
µN/µA. A precise current, commanded with a Keithley 2450 SourceMeter, through the coil generated
a force, which we used to check the balance response. Fig. 3b shows the excellent linearity of the
balance between 0.1-10 mg (it was actually tested until 100 mg without any change). It was difficult to
mount the voice-coil such that both the magnet and the experiment box were perfectly aligned due to
the hanging mounting of the experiment box. Nevertheless, we measured a weight change on the
balance corresponding to 92% of the commanded force. Fig. 3c shows a representative measurement
of a commanded force of 10 µN and the balance response (equivalent to 1 mg). We see that the
balance only takes a few seconds to record that low change in weight. Our profile settings later on are
always much larger than that to ensure that there is enough time to record a weight change. We
conclude that our setup can reliably measure forces/weight changes with a precision down to the 0.1
mg resolution limit.
The complete setup then was verified by performing a null-measurement: Instead of a capacitor, a
high voltage resistor (EMCO V1G) was used instead. Because no dielectric polarization takes place
Journal of Electrostatics 107 (2020) 103477
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(ignoring capacity effects from the on-board high voltage power supply which is cover by this
measurement), no weight-change should be recorded if voltage is applied to the resistor only. The
measurement is shown in Fig. 4 with the weight changes for several voltage settings ranging from 2-
10 kV on the top and the normalized voltage signal that corresponds to the profile settings on the
bottom. All measurements are signal-averaged from 20 individual profiles and the voltage on/off-
period was set to 60 seconds each with a sampling rate of 1 Hz. We can see that most profiles are
within the +/- 0.1 mg range, which is the digital resolution/precision of our balance. Only the 10 kV
signal raises to a peak of 0.3 mg at the end of the profile, however the average along the profile is also
at the 0.1 mg resolution level. Taking a 3 approach, we can say that up to 10 kV, all signals averaged
along the on-period below 0.3 mg are noise. Our accuracy is therefore +/- 0.3 mg.
4. Capacitor Measurements
A summary of all tests performed with a description of the test items and a comparison to the
theoretical predictions is given in Table 1.
4.1 Symmetric Plate-Plate Capacitor with Ceramic Dielectric
In our first test, we used commercially available high voltage capacitors with a high permittivity ceramic
dielectric (Murata DHRB34A102MF1B). Two of them were mounted in a parallel configuration on the
rotation rig with their expected force showing in the same direction (+/- aligned). Next, we made
profile measurements up to 10 kV with the capacitor assembly pointing at different directions as
shown in Fig. 5, using an average of 10 profiles for each direction. A real force would have been easily
identified: At 0° a weight change would be recorded, at 180° the same value would have appeared
with a different sign, and at 90° and 270° no weight change would be visible. As shown in our
measurements, no such behavior is visible. All data is below our previously defined +/-0.3 mg
resolution.
From the theoretical models, only Ivanov’s Equ. (1) predicts weight changes above our threshold with
mIvanov=2.4 mg, which is around one order of magnitude above our noise.
4.2 Symmetric Plate-Plate Capacitor with Teflon Dielectric
Next, we tested a self-assembled symmetric capacitor using Teflon as dielectric. According to the
theoretical models, this large difference in electric permittivity compared to the commercial ceramic
capacitor (r,Teflon=2.1 versus r,Ceramic=4500) should results in significant differences. The assembly of
the Teflon capacitor is shown in Fig. 6a-b. Copper plates with a thickness of 1 mm and a diameter of
40 mm were used as the electrodes and a Teflon plate with a thickness of 1.5 mm and a diameter of
50 mm was used as the dielectric. After attaching the connection wires with a silver-filled adhesive,
the whole capacitor was covered with Scotchweld 2216 B/A adhesive, which is an excellent isolator. In
addition, a urethane spray with an isolation of 80 kV/mm was applied several times as a second
isolation layer.
The same procedure as with the ceramic capacitor was executed with one single Teflon capacitor,
averaging 10 profiles for a voltage of 10 kV at different orientations as shown in Fig. 7. Also here, all
signals were below our resolution threshold of 0.3 mg. Porcelli’s and Minotti’s Equs. (2) and (5) for
symmetric capacitors predicted much higher forces, which should have resulted in mPorcelli=118.8 mg
for the case of Porcelli and mMinotti=11.8 mg for the case of Minotti. Porcelli’s model can be safely
ruled out with nearly three orders of magnitude above our noise. It should be noted that Porcelli and
dos Santos Filho used polystyrene (C8H8) for their symmetric capacitor, which has a similar relative
permittivity (r,C8H8=2.4-2.7) compared to Teflon (r,Teflon=2.1). However, they did not use this number
for their analysis but an even lower value of r=1.086 based on hydrogen atoms weakly bounded in the
Journal of Electrostatics 107 (2020) 103477
7
styrene monomer. This doubles the prediction of the force and rules out their model even more.
Similarly, also Minotti’s prediction is two orders of magnitude above our noise which should have been
easily detectable.
4.3 Asymmetric Plate-Plate Capacitor with Teflon Dielectric
We now tried to investigate asymmetrically shaped capacitors, which according to Brown’s claim [3,4]
and Filho and Porcelli’s measurements and models [14] should produce even larger forces. The
capacitor was made similar to our Teflon capacitor before, but here we replaced one copper electrode
with a high-voltage cable having a conductor wire in the middle with 0.8 mm diameter that was
mounted directly through a hole in the middle of a second Teflon dielectric plate, which served as a
good alignment and could be easily mounted on top of the first dielectric plate (see Fig. 6c). The whole
assembly was then isolated with Scotchweld and urethane spray as before. No current was recorded
when charged up to high voltage indicating that the dielectric was not damaged from electric
breakdowns that can occur from sharper edges like our thin conductor electrode.
Fig. 8 shows the measurement done at 0° and 90° with 20 averaged profiles. No change is visible within
our 0.3 mg threshold. The Filho and Porcelli model predicted an astonishing mPorcelli=29.7 kg (the
whole experiment would have lifted off), which is again ruled out with even higher margin by this
measurement.
4.4 Asymmetric Spherical Capacitor – Half-Filled with Bee-Wax
Next, we tried to replicate the setup that was suggested in Minotti’s paper [19] with a spherical
capacitor that was half-filled with bee wax as a dielectric (see Fig. 1b). Our assembly is illustrated in
Fig. 9. It consists of two hollow spheres that could be disassembled into two halves. First, the bottom
half of the larger sphere with an inner diameter of 56 mm was filled with bee wax with the full second
sphere in the middle with an outer diameter of 30 mm. Then a 7 mm diameter hole was drilled through
the second half of the larger sphere and a high-voltage cable was connected from the outside towards
the inner sphere fixed again with silver-filled epoxy. Then the outer sphere was put together and sealed
with Kapton tape in the middle and a second electric connection to the outer surface was done. The
total weight of the finished spherical capacitor was 315 g.
The spherical capacitor was put into the experiment box with the high voltage cable pointing upwards
and the bee wax at the bottom half as illustrated in Fig. 1b. The measurement at 10 kV with 20
averaged profiles is shown in Fig. 10. Again, all data points are without our 0.3 mg resolution. According
to Minotti, a mMinotti=24.4 mg was predicted according to Equ. (4) (and a smaller mMinotti=7.5 mg if
one corrects for the missing
). This is nearly two orders of magnitude above our noise level.
4.5 Capacitor with Leakage Current
This was the most difficult experiment because the setup was poorly described and hard to replicate
(discharge always at 5 kV, cutting of electrode or using sandpaper on the cathode surface to facilitate
field emission) [15]. We decided to use 90 µm thick aluminum foil for the electrodes with a diameter
of 40 mm. The surface of one electrode was perforated several times with a needle for better electron
emission as shown in Fig. 11. A 90 µm thick polyethylene (PE) foil was used as a dielectric, which was
close to the ones used by Bhatt and Becker (13-80 µm thicknesses). After connection wires were again
fixed to the electrodes with silver-filled epoxy, the whole capacitor was isolated with Scotchweld
epoxy. This gave both electrical isolation and mechanical strength and thus allowed the capacitor to
retain its flat and plane shape.
For the experiments, a 100 MOhm resistor was put in series in order to limit the current and to protect
the high voltage power supply. We first tried to determine the voltage to emit a current of 10 µA,
Journal of Electrostatics 107 (2020) 103477
8
which was the maximum current observed in the Bhatt and Becker experiments [15]. Initially, the
voltage went up to 4 kV until the discharge was triggered. However, later tests showed a reduced
discharge voltage down to 2.1 kV, indicating that the first discharge probably increased the leakage of
the dielectric through conduction paths. In order to not further damage the dielectric, we decided to
reduce the on/off-period to 30 s each and to an average of 5 profiles only. The results are shown in
Fig. 12 with the weight change on the top and the emitted current on the bottom, for anode
orientations pointing upwards, downwards and vertical (which should give a zero result). Also here,
we still do not measure signals above our noise threshold of 0.3 mg.
Using the extrapolation formula in Equ. (6), we estimate the predicted weight change as
mBhatt=6.8 mg, which is an order of magnitude above our noise level. However, there are some
differences in our setup and capacitor which may influence this result: The discharge voltage was lower
with 2.1 kV instead of 5 kV, the dielectric foil was bigger than the largest one’s used by Bhatt and
Becker (90 µm versus 80 µm) and the distance of the capacitor to the experimental box may be
different to the one of Bhatt and Becker which could influence the force as they observed force
blocking by bringing conductive materials close to their capacitor. Still, our null result is important for
comparison with a clean setup although it may not completely rule out the claim due to the exact
replica uncertainties.
Conclusion
We described a novel experimental setup that allows to measure weight changes of capacitors up to
10 kV using an analytical balance that eliminates all important side-effects triggered by working at high
voltages down to an accuracy of +/-0.3 mg with a precision of +/-0.1 mg. It features a thermally isolated
on-board high voltage power supply inside a mu-metal/Faraday cage powered by liquid-metal fed low-
voltage only-connection lines and a rotation rig, which allows to test capacitors at different
orientations without re-opening the experimental setup. This significantly improves the reliability of
such measurements contrary to previously reported results [10–14] and allows for testing theoretical
predictions claiming forces for electrically polarized dielectrics with high accuracy [12,13,16–19].
In general, all measurements showed no force or weight change within our resolution including
symmetric and asymmetric capacitors as well as capacitors with leakage currents. This allows to rule
out the models proposed by Porcelli and Filho [13,14] by close to three orders of magnitude and the
model by Minotti [19] by two orders of magnitude. As Minotti’s model is a consequence of the scalar-
tensor theory of gravitation proposed by Mbelek and Lachièze-Rey [18], it may put strong limits on
that theory as well.
The model by Ivanov and others [12,16,17] is ruled out by one order of magnitude, however this is
quite close to our resolution. Considering that some assumptions were used to derive the models,
further tests should be done at even higher resolution. Similarly, the force claim from Bhatt and Becker
[15] on leakage current capacitors is ruled out by an order of magnitude, but also here, the actual
experimental configuration leaves enough uncertainty that this should be re-checked with a higher
resolution. Nevertheless, important constraints can be made on these two claims based on our
measurements.
Can we answer the question if a charged high-voltage capacitor produces thrust? So far, our answer
must be: No – within our measurement accuracy. Some of the presented models (Ivanov [16], Bhatt
[15]) are worth to be pursued with better setups in the future. Our balance also allows testing for mass
changes and not only forces, which may arise from polarized dielectrics. Some theories point into such
a possibility, however without a clear prediction of the magnitude yet [27,28].
Journal of Electrostatics 107 (2020) 103477
9
Acknowledgement
We gratefully acknowledge the support by the German National Space Agency DLR (Deutsches
Zentrum fuer Luft- und Raumfahrttechnik) by funding from the Federal Ministry of Economic Affairs
and Energy (BMWi) by approval from German Parliament (50RS1704).
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[17] Y. Zhu, Gravitational-magnetic-electric Field Interaction Results in Physics Gravitational-
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Journal of Electrostatics 107 (2020) 103477
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Type
Configuration
Theory [13–16,19]
Experiment (3)
Symmetric Capacitor (V=10 kV)
2xCeramic dielectric (Murata DHRB34A102MF1B):
2x1000 pF, m=2x5.8 g, , r=7.5 mm, d=7 mm
mIvanov=2.4 mg
mPorcelli=0.4 mg
mMinotti=8.6×10-6 mg
m<0.3 mg (all)
Teflon dielectric:
m=4.1 g, , r=20 mm, d=1.5 mm
mIvanov=0.1 mg
mPorcelli=118.8 mg
mMinotti=11.8 mg
Asymmetric Capacitor (V=10 kV)
Teflon Dielectric:
, r1=20 mm, r2=0.04 mm, d=1.5 mm
mPorcelli=29.7 kg
Spherical Capacitor with half-filled Wax dielectric:
, g/cm³, a=15 mm, b=28 mm
mMinotti=24.4 mg
mMinotti=7.5 mg (with
correction)
Capacitor with Leakage Current
Anode: 90 µm Al foil, r=20 mm
Cathode: 90 µm Al foil, r=20 mm, perforated
Dielectric: 90 µm PE foil
Discharge: 2100 V, 10 µA, P=21 mW
mBhatt7 mg (Extrapolation)
Table 1 Summary of Measurements and Comparison to Theoretical Models (m=F/g0 using Equs. (1-6)), Bold Theory Values are much Larger than
Experimental Limit
Journal of Electrostatics 107 (2020) 103477
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Fig.
1
Different Capacitor Configurations with Dielectric Permittivity (r), Electric Field (E),
Force (F), High Voltage (HV) as well as Radius a, b
Journal of Electrostatics 107 (2020) 103477
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a) Schematic Sketch
b) Picture of Experiment in Enclosure Box c) Inside of Experiment Box
d) Rotation Stage with HV Ceramic Capacitor e) Liquid-Metal Connection Pins
Fig.
2
Balance Setup
Journal of Electrostatics 107 (2020) 103477
14
a) Voice-Coil below Experiment Box
b) Balance Linearity c) Balance Response at 10 µN (=1 mg)
Fig.
3
Balance Calibration
020 40 60 80 100
0
1
2
3
4
5
6
7
8
9
10
Delta Weight [mg]
Voice Coil Thrust [µN]
020 40 60 80 100 120 140 160
0
1
2
3
4
5
6
7
8
9
10
11
12
Force [µN]
Time [s]
Voice-Coil Command
Balance
Journal of Electrostatics 107 (2020) 103477
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Fig.
4
Setup Verification
020 40 60 80 100 120 140 160 180
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
1.2
Normalized Voltage [V]
Time [s]
-0.3
-0.2
-0.1
0.0
0.1
0.2
0.3
2 kV
4 kV
6 kV
8 kV
10 kV
Delta Weight [mg]
Journal of Electrostatics 107 (2020) 103477
16
Fig.
5
Weight Change of High Voltage Ceramic Capacitor
020 40 60 80 100 120 140 160 180
-2
0
2
4
6
8
10
12
Voltage [kV]
Time [s]
-0.3
-0.2
-0.1
0.0
0.1
0.2
0.3
0°
90°
180°
270°
Delta Weight [mg]
Journal of Electrostatics 107 (2020) 103477
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a) Building Capacitor b) Symmetric Capacitor c) Asymmetric Capacitor
Fig.
6
Teflon Capacitors
Journal of Electrostatics 107 (2020) 103477
18
Fig.
7
Weight Change of Symmetric Teflon Capacitor
020 40 60 80 100 120 140 160 180
0
2
4
6
8
10
Voltage [kV]
Time [s]
-0.3
-0.2
-0.1
0.0
0.1
0.2
0.3
0°
90°
180°
270°
Delta Weight [mg]
Journal of Electrostatics 107 (2020) 103477
19
Fig.
8
Weight Change of Asymmetric Teflon Capacitor
020 40 60 80 100 120 140 160 180
-2
0
2
4
6
8
10
12
Voltage [kV]
Time [s]
-0.3
-0.2
-0.1
0.0
0.1
0.2
0.3
0°
90°
Delta Weight [mg]
Journal of Electrostatics 107 (2020) 103477
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Fig.
9
Spherical Capacitor with Wax Dielectric in Bottom Half
Journal of Electrostatics 107 (2020) 103477
21
Fig.
10
Weight Change of Spherical Capacitor
020 40 60 80 100 120 140 160 180
-2
0
2
4
6
8
10
12
Voltage [kV]
Time [s]
-0.3
-0.2
-0.1
0.0
0.1
0.2
0.3
Delta Weight [mg]
Journal of Electrostatics 107 (2020) 103477
22
Fig.
11
Leakage Current Capacitor with Perforated Cathode
Journal of Electrostatics 107 (2020) 103477
23
Fig.
12
Weight Change of Leakage Capacitor at 2100 V
020 40 60 80
-2
0
2
4
6
8
10
12
14
Current [µA]
Time [s]
-0.3
-0.2
-0.1
0.0
0.1
0.2
0.3
Anode Up
Anode Down
Vertical
Delta Weight [mg]
