Charge transfer within a dielectric

[Calvin Cox]

Hi,
this simple principle is proving difficult to resolve.
We need a concise formula to describe the following:
An air dielectric is formed between two fixed electrodes.
When a charged polymer is passed between them the containment field is modulated.
We require an elegant formula to resolve Vout = ??

Thanks
Calvin

 

[stevenb]

Hi,
this simple principle is proving difficult to resolve.
We need a concise formula to describe the following:
An air dielectric is formed between two fixed electrodes.
When a charged polymer is passed between them the containment field is modulated.
We require an elegant formula to resolve Vout = ??

Thanks
Calvin

The simplest thing to do is take measurements and fit a function.

No doubt you can derive a simple approximate formula, but the geometry is probably too complicated to get the accuracy you want from a derivation.

Still, if you post the geometry and details, someone might come up with something for you.

 

[dgOnPhys]

Please provide more details:
what are the parameters of this problem?
is the polymer much larger or much smaller than the electrodes?
is the polymer moving at constant distance from the electrodes or is it moving away from one towards the other?
...

 

[Calvin Cox]

The electrodes are 6mm apart and 5mm sq.
The applied voltage is 200V fed via a 1M resistor.
The polymer rotates producing a 100mV sinewave output.
I would like to show parameters of: permittivity/charge density and capacitance.
It is intended as part of the technical review that will be scrutinised by cynics.

Thanks again
Calvin

 

[dgOnPhys]

I am still not getting the size of the polymer:
is it a large disc? a tiny fragment? a long thread?

If you cannot go into details for proprietary reasons, from what I gather you are interested in induction from charges moving between electrodes: look up Ramo-Shockley theorem

 

[Calvin Cox]

OK - this is the situation. I came up with an idea for measuring rotational speed for a plastic impeller wheel. The idea is attractive because it is embedded and therefore causes no turbulance. I have been designing electronics since before the transistor, I am 66, but this level of theory is beyond me. The senior managers at my company have dissmissed the concept as techno-********. I need to show them that the principles are sound, going back to Coulomb and Faraday. If I had a concise formula, with some explanation, it would give validity to the project and prevent it from being cancelled.
I have some knowledge of electrostatic formula but it is bringing capacitance and charge transfer together into an elegant description that is defeating me.
I hope this helps
Calvin

 

[dgOnPhys]

Interesting but I am still not getting the geometry of this setup: can you have a look at the attachment and let us know if A or B are somewhat close to your design?

Is the plastic disc uniformly charged or only in a specific location?

PS I left out the resistor in series with the supply; I am guessing you measure your signal across this resistor, right?

 

[Calvin Cox]

A is the closest. I didn't want to complicate matters by providing the actual wheel geometry as it is complex. By measuring the surface charge of the wheel we can see that the charge density and polarity varies significantly with the highest concentration of charge appearing at the blade edges. That is why we get a good signal (across the resistor) representing each blade pass. I am surmising that air turbulace around the blade tips liberates electrons from the friction. What I need is a formula to describe the interchange mechanism that occurs between the static sensing dielectric and the modulation caused by the dynamic charge influence of the passing blade. The Ramo-Shockley theorem is over complex as it covers all charge points. I just need the basic: charge = V*C +/- (blade charge).
Thank you for your patience.

 

[dgOnPhys]

Man this site, I just lost my message... here I go again

I am guessing you are thinking that your supply is providing an intermittent current to compensate for the charge induced by the localized wheel charge. Your resistor converts that current into voltage.

If that were the case I would expect the signal not to depend on the voltage on the electrodes but since you are using 200V I am guessing that you need to apply a large potential to get a decent signal. I would also expect that you would get more signal by having the electrodes plane (assuming your electrodes are plane) tilted wrt the wheel plane

Anyway if you need high voltage, it means you need to polarize the wheel to get a signal, in that case your signal comes from introducing a dielectric of variable thickness (blades, cavities,etc) between the electrodes of a capacitor.

We could model this as:
$Q=C(\phi) V_0; \phi=\omega t$
$i=dQ/dt=\omega C'(\omega t) V_0$
$V_s= \omega C'(\omega t) V_0 R$

C(phi) could be measured with a capacimeter with the wheel at different angular positions but all that matters is probably just that (assuming the wheel has a regular structure) C(phi) is periodic and so will be C'(phi)

In summary both the amplitude of the signal and its frequency would be proportional to the angular velocity $\omega$.

Is this anywhere close to what you observe?

 

[Calvin Cox]

I am greatly indebted to you dgonPhys.
This is precisely what I have been looking for.
You have got it spot on in every event.
All the research I have been doing resulted in overcomplication because the assumption is always that you should know all the basics already. The most instructive information came from the work of Cavendish and Faraday.
Thanks again for your patience.

 

[dgOnPhys]

You are welcome Calvin, it was an interesting problem after all. Let us know how your technical review goes and good luck with it.