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Discussion of precise voltage measurement

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Bohnenberger electrometer

DD
Dr. David Kirkby
Tue, Mar 6, 2018 9:40 AM

Sorry this is not precision voltage measurement, but it is not unrelated.

As a radio club project, we are building a simple electroscope, with no
active components. The gold leave variety would work, but two bits of
alluminum foil do too.

My plan was to go one better, and build a Bohnenberger electrometer. Does
anyone here have experience of building a Bohnenberger electrometer, or
know much about them? They are similar to the gold-leaf electroscope, but
have one leaf sitting in an electric field. So the leaf moves one way or
the other, depending on the polarity of the charge. Or some other
electrometer, that does not use any active components - no ICs or
transistors.

I believe the original design was built with some sort of battery, but my
intention was to use a capacitor and charge it up. I'm not sure of what
sort of electric field / energy / stored charge is required though. I have
two obvious options for a voltage source based on what I can find at home.

  1. 2 nF 15 kV capacitor which I can charge to about 4.2 kV easily (Q = 5.4
    uC)
  2. 2200 uF 400 V electrolytic capacitor which I can charge to 400 V (Q=0.8
    C)

Clearly capacitor 2 stores a lot more charge, but for any given spacing of
plates, capacitor 1 creates am electric field 10 times higher than
capacitor 2.

Obviously if gold leaf or aluminum foil moves, that takes energy. Will that
come from the charge one puts on the top of the electroscope, or will some
come from the capacitor, so discharging the capacitor? If the latter,
capacitor 1 might discharge quite quickly due to its small capacitance,
whereas 2200 uF of capacitor 2 would not.

I do not wish the unit to be mains operated. I don't mind charging the
capacitor from the mains, but I want it to be standalone, independent of
any supply voltage.

Dave

Sorry this is not precision voltage measurement, but it is not unrelated. As a radio club project, we are building a simple electroscope, with no active components. The gold leave variety would work, but two bits of alluminum foil do too. My plan was to go one better, and build a Bohnenberger electrometer. Does anyone here have experience of building a Bohnenberger electrometer, or know much about them? They are similar to the gold-leaf electroscope, but have one leaf sitting in an electric field. So the leaf moves one way or the other, depending on the polarity of the charge. Or some other electrometer, that does not use any active components - no ICs or transistors. I believe the original design was built with some sort of battery, but my intention was to use a capacitor and charge it up. I'm not sure of what sort of electric field / energy / stored charge is required though. I have two obvious options for a voltage source based on what I can find at home. 1) 2 nF 15 kV capacitor which I can charge to about 4.2 kV easily (Q = 5.4 uC) 2) 2200 uF 400 V electrolytic capacitor which I can charge to 400 V (Q=0.8 C) Clearly capacitor 2 stores a lot more charge, but for any given spacing of plates, capacitor 1 creates am electric field 10 times higher than capacitor 2. Obviously if gold leaf or aluminum foil moves, that takes energy. Will that come from the charge one puts on the top of the electroscope, or will some come from the capacitor, so discharging the capacitor? If the latter, capacitor 1 might discharge quite quickly due to its small capacitance, whereas 2200 uF of capacitor 2 would not. I do not wish the unit to be mains operated. I don't mind charging the capacitor from the mains, but I want it to be standalone, independent of any supply voltage. Dave
BC
Brooke Clarke
Tue, Mar 6, 2018 8:17 PM

Hi Dave:

Here's a free on line book "Magnetism and Electricity", 1877
https://books.google.com/books?id=y45PAAAAYAAJ&pg=PA169#v=onepage&q&f=false
Chapter 6 Electroscopes and Electrometers starts on book page 74 (pdf pg 81)
but . .
Chapter 11 Voltaic, Dynamical or Current Electricity is where paragraph 214 Bohnenberger's Electroscope appears on book
pg 169 (pdf 176).
This is the chapter for the Voltaic Pile so that's probably why since it's a way to testing polarity.

--
Have Fun,

Brooke Clarke
http://www.PRC68.com
http://www.end2partygovernment.com/2012Issues.html

-------- Original Message --------

Bohnenberger electrometer

Hi Dave: Here's a free on line book "Magnetism and Electricity", 1877 https://books.google.com/books?id=y45PAAAAYAAJ&pg=PA169#v=onepage&q&f=false Chapter 6 Electroscopes and Electrometers starts on book page 74 (pdf pg 81) but . . Chapter 11 Voltaic, Dynamical or Current Electricity is where paragraph 214 Bohnenberger's Electroscope appears on book pg 169 (pdf 176). This is the chapter for the Voltaic Pile so that's probably why since it's a way to testing polarity. -- Have Fun, Brooke Clarke http://www.PRC68.com http://www.end2partygovernment.com/2012Issues.html -------- Original Message -------- > Bohnenberger electrometer
EB
ed breya
Tue, Mar 6, 2018 10:34 PM

For static bias, look up "electret" for ideas on some other possible
options.

I would recommend against your option 2 capacitor - that's a dangerous
amount of energy to store in something that may be fooled around with
experimentally. Also, even though it's a lot of C, being electrolytic,
the charge will eventually leak off anyway - probably faster than any
charge loss from using the machine.

The option 2 (2 nF at 4.2 kV) seems more appropriate for this use,
because of the much higher sensitivity attainable. It's charge will leak
off too, but since it's likely a plastic or oil capacitor, the retention
time will hopefully be OK overall.

I wouldn't want to take a jolt from either one. In the ultimate design,
be sure to use some sort of series current limiting resistance to
isolate the capacitor from the outside world. The R can be quite high
(megohms, and of course suitable for the maximum voltage) since not much
current is needed for operation, so the contact/fault hazard would be
reduced from dangerous to a tingle. It would be good to also have a safe
discharging method - another R - that can be switched or jammed in, to
quickly clear the charge for safe keeping when not in use, or during
design.

In the old days, optical methods were used for "gain," as in a mirror
galvanometer, for instance. Putting some simple magnification and
illumination (sun light if electricity is a no-no) in the system can
increase the visibility of any deflection.

Lastly, regarding capacitors, a good option if available, is to use the
nice HV oil caps that can be salvaged from older-era (before they went
to switching supplies) microwave ovens. These are typically rated around
1 uF, 2 kV AC. Two in series would do for up to 4-5 kV service. Since
you don't want bleeder/balancing Rs in this application, it would be
best to use identical caps, or slightly more complicated charging
circuitry. They can bought new, but may be pretty spendy, depending on
the project budget. I have dozens of them - saved from every microwave
oven I've junked out over the years.

At 1 uF, these would have much better retention time, with hazard energy
between the original options.

Ed

For static bias, look up "electret" for ideas on some other possible options. I would recommend against your option 2 capacitor - that's a dangerous amount of energy to store in something that may be fooled around with experimentally. Also, even though it's a lot of C, being electrolytic, the charge will eventually leak off anyway - probably faster than any charge loss from using the machine. The option 2 (2 nF at 4.2 kV) seems more appropriate for this use, because of the much higher sensitivity attainable. It's charge will leak off too, but since it's likely a plastic or oil capacitor, the retention time will hopefully be OK overall. I wouldn't want to take a jolt from either one. In the ultimate design, be sure to use some sort of series current limiting resistance to isolate the capacitor from the outside world. The R can be quite high (megohms, and of course suitable for the maximum voltage) since not much current is needed for operation, so the contact/fault hazard would be reduced from dangerous to a tingle. It would be good to also have a safe discharging method - another R - that can be switched or jammed in, to quickly clear the charge for safe keeping when not in use, or during design. In the old days, optical methods were used for "gain," as in a mirror galvanometer, for instance. Putting some simple magnification and illumination (sun light if electricity is a no-no) in the system can increase the visibility of any deflection. Lastly, regarding capacitors, a good option if available, is to use the nice HV oil caps that can be salvaged from older-era (before they went to switching supplies) microwave ovens. These are typically rated around 1 uF, 2 kV AC. Two in series would do for up to 4-5 kV service. Since you don't want bleeder/balancing Rs in this application, it would be best to use identical caps, or slightly more complicated charging circuitry. They can bought new, but may be pretty spendy, depending on the project budget. I have dozens of them - saved from every microwave oven I've junked out over the years. At 1 uF, these would have much better retention time, with hazard energy between the original options. Ed
EB
ed breya
Tue, Mar 6, 2018 11:45 PM

Oops - forgot to mention a detail about microwave oven caps. Sometimes
they have built-in bleeder resistors, which would of course spoil this
kind of application.  Ed

Oops - forgot to mention a detail about microwave oven caps. Sometimes they have built-in bleeder resistors, which would of course spoil this kind of application.  Ed
EB
ed breya
Wed, Mar 7, 2018 12:11 AM

I looked at that link that Brooke put up about Bohnenberger's
Electroscope. I don't know what your specific arrangement needs to be,
but it appears you need a plus and a minus HV wrt ground in the most
general form. If so, then this would mean having to split the voltage of
a single cap, or have two caps, one for each polarity.  Then I'd
recommend using good old microwave oven caps. You could charge them both
to say 2 kV from one HV source, then switch them around so they're
stacked and grounded at the midpoint.

Ed

I looked at that link that Brooke put up about Bohnenberger's Electroscope. I don't know what your specific arrangement needs to be, but it appears you need a plus and a minus HV wrt ground in the most general form. If so, then this would mean having to split the voltage of a single cap, or have two caps, one for each polarity.  Then I'd recommend using good old microwave oven caps. You could charge them both to say 2 kV from one HV source, then switch them around so they're stacked and grounded at the midpoint. Ed
A
Andre
Wed, Mar 7, 2018 6:29 AM

Please be VERY VERY careful. To be honest its far safer to use CCFL drivers and rectify them with camera diodes in series and the absolute minimum capacitance for the job, shunted with a high value resistor.
I have a few inverters , 10M resistor packs and diode strips here if anyone has a use on the understanding they are only to be used at your own risk, and for the intended purpose.

Microwave capacitors can be deadly (you could DIE!) under the wrong circumstances, fibrillation can occur even with quite small shocks down to <8J if you get hit badly or have an undetected problem. I don't want to scare people but it is a serious risk.
Had to scale back one of my projects because I had a near miss with a setup very much like the one described  in earlier posts and despite dual failsafes still got a belt large enough to require medical treatment.
(hint: the experiment is on Youtube, saying no more)
Very fortunately my systems weren't seriously affected but I probably did some damage.

Still have a 380J 215uF/2.5KV capacitor here and that one is staying shunted and under lock and key until I have the appropriate safety knowledge and experience. Dielectric memory is a bth!

-A


From: volt-nuts volt-nuts-bounces@febo.com on behalf of ed breya eb@telight.com
Sent: 07 March 2018 00:11
To: volt-nuts@febo.com
Subject: Re: [volt-nuts] Bohnenberger electrometer

I looked at that link that Brooke put up about Bohnenberger's
Electroscope. I don't know what your specific arrangement needs to be,
but it appears you need a plus and a minus HV wrt ground in the most
general form. If so, then this would mean having to split the voltage of
a single cap, or have two caps, one for each polarity.  Then I'd
recommend using good old microwave oven caps. You could charge them both
to say 2 kV from one HV source, then switch them around so they're
stacked and grounded at the midpoint.

Ed


volt-nuts mailing list -- volt-nuts@febo.com
To unsubscribe, go to https://www.febo.com/cgi-bin/mailman/listinfo/volt-nuts
and follow the instructions there.

Please be VERY VERY careful. To be honest its far safer to use CCFL drivers and rectify them with camera diodes in series and the absolute minimum capacitance for the job, shunted with a high value resistor. I have a few inverters , 10M resistor packs and diode strips here if anyone has a use on the understanding they are only to be used at your own risk, and for the intended purpose. Microwave capacitors can be deadly (you could DIE!) under the wrong circumstances, fibrillation can occur even with quite small shocks down to <8J if you get hit badly or have an undetected problem. I don't want to scare people but it is a serious risk. Had to scale back one of my projects because I had a near miss with a setup very much like the one described in earlier posts and despite dual failsafes still got a belt large enough to require medical treatment. (hint: the experiment is on Youtube, saying no more) Very fortunately my systems weren't seriously affected but I probably did some damage. Still have a 380J 215uF/2.5KV capacitor here and that one is staying shunted and under lock and key until I have the appropriate safety knowledge and experience. Dielectric memory is a b*t*h! -A ________________________________________ From: volt-nuts <volt-nuts-bounces@febo.com> on behalf of ed breya <eb@telight.com> Sent: 07 March 2018 00:11 To: volt-nuts@febo.com Subject: Re: [volt-nuts] Bohnenberger electrometer I looked at that link that Brooke put up about Bohnenberger's Electroscope. I don't know what your specific arrangement needs to be, but it appears you need a plus and a minus HV wrt ground in the most general form. If so, then this would mean having to split the voltage of a single cap, or have two caps, one for each polarity. Then I'd recommend using good old microwave oven caps. You could charge them both to say 2 kV from one HV source, then switch them around so they're stacked and grounded at the midpoint. Ed _______________________________________________ volt-nuts mailing list -- volt-nuts@febo.com To unsubscribe, go to https://www.febo.com/cgi-bin/mailman/listinfo/volt-nuts and follow the instructions there.
DD
Dr. David Kirkby
Wed, Mar 7, 2018 10:34 AM

On 7 March 2018 at 06:29, Andre Andre@lanoe.net wrote:

Please be VERY VERY careful. To be honest its far safer to use CCFL
drivers and rectify them with camera diodes in series and the absolute
minimum capacitance for the job, shunted with a high value resistor.

The problem with 2.2 nF is it is difficult to know what voltage is on the
capacitor at any time, since with a 10 M ohm multimeter, the time constant
is 22 ms. I have a high voltage probe around somewhere, which probably has
a 100 M ohm input impedance, but that would still only give a time constant
of 220 ms, which is too short to measure easily.

I have 47 uF @ 650 V (or it might have been 550 V) capacitor on order, but
I might go to something a bit lower capacitance if the charge storage is
not required.

I would like to know where the energy comes from to move the leaf. I wonder
if any is taken from the capacitor. In the gold leaf electrometer, with no
internal supply, it is clear the energy much come from the charge on the
plates. But when there's an electric field, that might not be the case. I
was thinking of sticking a 50 uA FSD meter inside, to see if any current is
take from the capacitor, but I don't know if 50 uA would be sufficiently
sensitive to deflect.

Clearly having an electrometer here would be useful for these sorts of
experiments, but I don't have one. I see a reference on here recently to
the Keithley 642 being one of the best, but whilst the basic meters are not
that expensive, the test head and cable are much rarer, so attract a much
higher price.

In any case, there's not a single half-decent electrometer on eBay in the
UK at the minute, and I need it before Monday.

I have a few inverters , 10M resistor packs and diode strips here if
anyone has a use on the understanding they are only to be used at your own
risk, and for the intended purpose.

Microwave capacitors can be deadly (you could DIE!) under the wrong
circumstances, fibrillation can occur even with quite small shocks down to
<8J if you get hit badly or have an undetected problem. I don't want to
scare people but it is a serious risk.

It's fairly obvious to me, based on a few quick experiements last night,
that kV is not needed for this. Whilst I'm not doubting one could make an
electrometer (electroscope???) of greater sensitivity using a higher
electric field, this is good enough for a demonstration, and to learn a
bit. For quantitative measurements, I will look for a Keithley
electrometer, at a later date.

-A

Dave

On 7 March 2018 at 06:29, Andre <Andre@lanoe.net> wrote: > Please be VERY VERY careful. To be honest its far safer to use CCFL > drivers and rectify them with camera diodes in series and the absolute > minimum capacitance for the job, shunted with a high value resistor. > The problem with 2.2 nF is it is difficult to know what voltage is on the capacitor at any time, since with a 10 M ohm multimeter, the time constant is 22 ms. I have a high voltage probe around somewhere, which probably has a 100 M ohm input impedance, but that would still only give a time constant of 220 ms, which is too short to measure easily. I have 47 uF @ 650 V (or it might have been 550 V) capacitor on order, but I might go to something a bit lower capacitance if the charge storage is not required. I would like to know where the energy comes from to move the leaf. I wonder if any is taken from the capacitor. In the gold leaf electrometer, with no internal supply, it is clear the energy much come from the charge on the plates. But when there's an electric field, that might not be the case. I was thinking of sticking a 50 uA FSD meter inside, to see if any current is take from the capacitor, but I don't know if 50 uA would be sufficiently sensitive to deflect. Clearly having an electrometer here would be useful for these sorts of experiments, but I don't have one. I see a reference on here recently to the Keithley 642 being one of the best, but whilst the basic meters are not that expensive, the test head and cable are much rarer, so attract a much higher price. In any case, there's not a single half-decent electrometer on eBay in the UK at the minute, and I need it before Monday. > I have a few inverters , 10M resistor packs and diode strips here if > anyone has a use on the understanding they are only to be used at your own > risk, and for the intended purpose. > > Microwave capacitors can be deadly (you could DIE!) under the wrong > circumstances, fibrillation can occur even with quite small shocks down to > <8J if you get hit badly or have an undetected problem. I don't want to > scare people but it is a serious risk. > It's fairly obvious to me, based on a few quick experiements last night, that kV is not needed for this. Whilst I'm not doubting one could make an electrometer (electroscope???) of greater sensitivity using a higher electric field, this is good enough for a demonstration, and to learn a bit. For quantitative measurements, I will look for a Keithley electrometer, at a later date. > -A > Dave
A
Andre
Thu, Mar 8, 2018 7:19 AM

Hi, re. capacitors it might be worth mentioning that the normal equation assumes charge and discharge through a constant current.
Don't forget that the equation includes a non linear term so you'll need to take that into account (Q=CV2 iirc) where Q is Coulombs, C is capacitance.
If this is done using something like an LM317T in CC mode or even a string of them (my idea) with anti-overload circuitry added externally then this
may well work.
Any series resistance will cause problems so you'd need quite a lot of regulators but there are ways to use JFETs selected by hand if you really wanted to
make a test setup.


From: volt-nuts volt-nuts-bounces@febo.com on behalf of Dr. David Kirkby drkirkby@kirkbymicrowave.co.uk
Sent: 07 March 2018 10:34
To: Discussion of precise voltage measurement
Subject: Re: [volt-nuts] Bohnenberger electrometer DANGER

On 7 March 2018 at 06:29, Andre Andre@lanoe.net wrote:

Please be VERY VERY careful. To be honest its far safer to use CCFL
drivers and rectify them with camera diodes in series and the absolute
minimum capacitance for the job, shunted with a high value resistor.

The problem with 2.2 nF is it is difficult to know what voltage is on the
capacitor at any time, since with a 10 M ohm multimeter, the time constant
is 22 ms. I have a high voltage probe around somewhere, which probably has
a 100 M ohm input impedance, but that would still only give a time constant
of 220 ms, which is too short to measure easily.

I have 47 uF @ 650 V (or it might have been 550 V) capacitor on order, but
I might go to something a bit lower capacitance if the charge storage is
not required.

I would like to know where the energy comes from to move the leaf. I wonder
if any is taken from the capacitor. In the gold leaf electrometer, with no
internal supply, it is clear the energy much come from the charge on the
plates. But when there's an electric field, that might not be the case. I
was thinking of sticking a 50 uA FSD meter inside, to see if any current is
take from the capacitor, but I don't know if 50 uA would be sufficiently
sensitive to deflect.

Clearly having an electrometer here would be useful for these sorts of

Hi, re. capacitors it might be worth mentioning that the normal equation assumes charge and discharge through a constant current. Don't forget that the equation includes a non linear term so you'll need to take that into account (Q=CV2 iirc) where Q is Coulombs, C is capacitance. If this is done using something like an LM317T in CC mode or even a string of them (my idea) with anti-overload circuitry added externally then this may well work. Any series resistance will cause problems so you'd need quite a lot of regulators but there are ways to use JFETs selected by hand if you really wanted to make a test setup. ________________________________________ From: volt-nuts <volt-nuts-bounces@febo.com> on behalf of Dr. David Kirkby <drkirkby@kirkbymicrowave.co.uk> Sent: 07 March 2018 10:34 To: Discussion of precise voltage measurement Subject: Re: [volt-nuts] Bohnenberger electrometer DANGER On 7 March 2018 at 06:29, Andre <Andre@lanoe.net> wrote: > Please be VERY VERY careful. To be honest its far safer to use CCFL > drivers and rectify them with camera diodes in series and the absolute > minimum capacitance for the job, shunted with a high value resistor. > The problem with 2.2 nF is it is difficult to know what voltage is on the capacitor at any time, since with a 10 M ohm multimeter, the time constant is 22 ms. I have a high voltage probe around somewhere, which probably has a 100 M ohm input impedance, but that would still only give a time constant of 220 ms, which is too short to measure easily. I have 47 uF @ 650 V (or it might have been 550 V) capacitor on order, but I might go to something a bit lower capacitance if the charge storage is not required. I would like to know where the energy comes from to move the leaf. I wonder if any is taken from the capacitor. In the gold leaf electrometer, with no internal supply, it is clear the energy much come from the charge on the plates. But when there's an electric field, that might not be the case. I was thinking of sticking a 50 uA FSD meter inside, to see if any current is take from the capacitor, but I don't know if 50 uA would be sufficiently sensitive to deflect. Clearly having an electrometer here would be useful for these sorts of
DD
Dr. David Kirkby
Thu, Mar 8, 2018 7:46 PM

On 8 March 2018 at 07:19, Andre Andre@lanoe.net wrote:

Hi, re. capacitors it might be worth mentioning that the normal equation
assumes charge and discharge through a constant current.

What 'normal equation' do you mean?

Don't forget that the equation includes a non linear term so you'll need
to take that into account (Q=CV2 iirc) where Q is Coulombs, C is
capacitance.

I am puzzled by CV2.  The energy (joules) stored in a capacitor is 1/2 C
V^2, where C is the capacitance and V the voltage. I don't know if that's
what you mean.

If this is done using something like an LM317T in CC mode or even a string
of them (my idea) with anti-overload circuitry added externally then this
may well work.
Any series resistance will cause problems so you'd need quite a lot of
regulators but there are ways to use JFETs selected by hand if you really
wanted to
make a test setup.

I am totally lost here!

If anyone has an explanation of whether any of the energy to move the leaf
comes from the battery/capacitor, or does it all come from the charge
applied to the unit, I would like to know.  If no energy (apart from
leakage) comes from the device applying the electric field, a small
capacitor is suitable, and very safe. If at least some of the energy
required to move the leaf comes from the voltage supplying the electric
field, then a small value capacitor will be no use.

This is a fairly low priority task for me at the minute, as I need to do
some real work until Friday evening. But over the weekend I will play with
this.

Dave

On 8 March 2018 at 07:19, Andre <Andre@lanoe.net> wrote: > Hi, re. capacitors it might be worth mentioning that the normal equation > assumes charge and discharge through a constant current. > What 'normal equation' do you mean? > Don't forget that the equation includes a non linear term so you'll need > to take that into account (Q=CV2 iirc) where Q is Coulombs, C is > capacitance. > I am puzzled by CV2. The energy (joules) stored in a capacitor is 1/2 C V^2, where C is the capacitance and V the voltage. I don't know if that's what you mean. > If this is done using something like an LM317T in CC mode or even a string > of them (my idea) with anti-overload circuitry added externally then this > may well work. > Any series resistance will cause problems so you'd need quite a lot of > regulators but there are ways to use JFETs selected by hand if you really > wanted to > make a test setup. > I am totally lost here! If anyone has an explanation of whether any of the energy to move the leaf comes from the battery/capacitor, or does it all come from the charge applied to the unit, I would like to know. If no energy (apart from leakage) comes from the device applying the electric field, a small capacitor is suitable, and very safe. If at least some of the energy required to move the leaf comes from the voltage supplying the electric field, then a small value capacitor will be no use. This is a fairly low priority task for me at the minute, as I need to do some real work until Friday evening. But over the weekend I will play with this. Dave
EB
ed breya
Fri, Mar 9, 2018 3:17 AM

Here's a simplistic view that may be sufficient. Some energy (in the
form of charge redistribution, which includes current flow) has to come
from the capacitor, and some from the input signal, to do the work
needed to push the leaf against gravity. When the input signal is
removed, some of the energy (charge) stored on the leaf is returned to
the cap as gravity restores the initial position - roughly the same
amount of work, depending on leakage and mechanical loss, and heating of
the protective series resistor.

With a quick review of electrostatics, you could estimate up a simple
model and the field equations to get a more satisfying, detailed answer.
It may be more straightforward to look at it from a circuit perspective.
Picture it as as a very small, non-linear capacitor (the leaf structure)
in series with a much much larger regular capacitor charged up to a
constant DC voltage. Any actual series resistance is just resistance,
and the mechanical loss can be represented as more resistance added in
series. Presuming the leaf never actually touches or emits particles* or
arcs to the reference capacitor node, it's basically a capacitive
voltage divider, and the applied signal may be considered to be
transient, or even AC - it steps to the applied voltage, then returns to
zero (or open), then the cycle may be repeated. Each experiment is
adding or subtracting charge, then reversing the process. Ideally, the
cap would never lose its DC bias if there were no losses.

The problem is that figuring out all these details may not be trivial.
It may be more fun to just try some experiments and see how it goes -
you'll get some idea of how the real thing holds up, and figure what
amount of C is OK.

*You shouldn't have to worry too much about corona discharge if the
maximum voltage on anything is below 3 kV or so. Beyond that, it could
cause problems.

Ed

Here's a simplistic view that may be sufficient. Some energy (in the form of charge redistribution, which includes current flow) has to come from the capacitor, and some from the input signal, to do the work needed to push the leaf against gravity. When the input signal is removed, some of the energy (charge) stored on the leaf is returned to the cap as gravity restores the initial position - roughly the same amount of work, depending on leakage and mechanical loss, and heating of the protective series resistor. With a quick review of electrostatics, you could estimate up a simple model and the field equations to get a more satisfying, detailed answer. It may be more straightforward to look at it from a circuit perspective. Picture it as as a very small, non-linear capacitor (the leaf structure) in series with a much much larger regular capacitor charged up to a constant DC voltage. Any actual series resistance is just resistance, and the mechanical loss can be represented as more resistance added in series. Presuming the leaf never actually touches or emits particles* or arcs to the reference capacitor node, it's basically a capacitive voltage divider, and the applied signal may be considered to be transient, or even AC - it steps to the applied voltage, then returns to zero (or open), then the cycle may be repeated. Each experiment is adding or subtracting charge, then reversing the process. Ideally, the cap would never lose its DC bias if there were no losses. The problem is that figuring out all these details may not be trivial. It may be more fun to just try some experiments and see how it goes - you'll get some idea of how the real thing holds up, and figure what amount of C is OK. *You shouldn't have to worry too much about corona discharge if the maximum voltage on anything is below 3 kV or so. Beyond that, it could cause problems. Ed