Measuring charge (or potential) with electroscope?

[David Anton]

I am trying to measure the charge(or voltage) of a positively charged sphere by touching it with a non- calibrated electroscope. I am getting consistent results in the separation(or angle) between the metal leaves, but I don´t know how to calculate the voltage between the leaves from there.

I thought of considering the point at the end of each metal leaf as a "point charge", as if my electroscope was made of two metallic spheres instead of two foils. That's the only method I have found in the internet. My question is, is there any method (or formula) that will give me the potential between two leaves in an electroscope given their material, mass, length and the angle they form?

 

[Simon Bridge]

You have to calibrate it.

What level does this need to be done at?
Recall that the charge won't be distributed only on the leaves, but over the entire conducting structure.

 

[lychette]

If you have access to a high voltage power supply (5kV ) you can connect it to the electroscope and note the deflection

 

[David Lewis]

The voltage between the leaves is zero.

 

[lychette]

The voltage between the leaves is zero.

The high voltage (5kV) is connected between the case (ground/earth) of the electroscope and the stem of the electroscope. The deflection is an indication of the potential between the leaf and ground/earth

 

[Simon Bridge]

@lychette : @David Anton asked how to calculate the voltage between the leaves.
@David Lewis has correctly pointed out that the voltage between the leaves is zero, which the rest of us kinda glossed over.
The electroscope needs to be calibrated - David A. wants to do this using maths. Better to do this using Nature... but maybe a quite sloppy approximation will be OK.

We need to hear back from David Anton I think.

 

[lychette]

@lychette : @David Anton asked how to calculate the voltage between the leaves.
@David Lewis has correctly pointed out that the voltage between the leaves is zero, which the rest of us kinda glossed over.
The electroscope needs to be calibrated - David A. wants to do this using maths. Better to do this using Nature... but maybe a quite sloppy approximation will be OK.

We need to hear back from David Anton I think.

I will be interested to hear the calibration technique using mathematics. We seem to be talking about different potentials ! The electroscope I am familiar with has a single leaf that diverges from a fixed stem when there is a potential difference between the stem and the grounded/earthed metal case. The stem and leaf are insulated from the metal case.
I can testify to the technique of calibrating this electroscope using a 0 to 5kV power supply...I have used this technique. If proof is needed I will photograph the set up and make it available for mathematical analysis.

 

[David Anton]

Yeah, I am sorry for the misleading post. I do not want to measure the potential between the leaves, but between the electroscope as a whole and a non charged reference. Want I really want to know is the charge/potential of the original sphere (in a sphere those 2 quantities are easily interchangable) and since I make contact between the electroscope and the sphere, I am assuming that the voltage is the same in the two.

Yes I was looking for a mathematical aproximation, it doesn't need to be perfect, just an aproximation, maybe calibrating the forces in the leaves (mg, electrostatic and tension), I don't know... I don't think I have easy access to a High voltage supply, so calibrating is not an option. I have access to a Van der Graaff if that helps :_)

 

[David Anton]

The best idea I have now is to take the end of the leave and assume that all the mass of the leave is there, as if the electroscope was made of two hanging spheres instead of 2 leaves. Then I could balance mg, tension and electrostatic repulsión using the angle, get the charge in one sphere, from it its potential and then assume that the potential in the original big sphere was the same

The sphere I make contact with is pretty heavy so the loss of charge it undergoes is negligible (I guess?)

 

[David Anton]

So what I am looking for is a mathematical approach that doesn't assume the electroscope is made of two spheres, but something that (somehow) balances the forces in the whole leave and assuming both leaves are the same mass length and material, and knowing those properties plus the angle they form, gets the charge per leave mass the electroscope must have had to achieve a certain deflection... Basically I just want to get rid of the assumption that the leaves act the same way as spheres

 

[lychette]

The best idea I have now is to take the end of the leave and assume that all the mass of the leave is there, as if the electroscope was made of two hanging spheres instead of 2 leaves. Then I could balance mg, tension and electrostatic repulsión using the angle, get the charge in one sphere, from it its potential and then assume that the potential in the original big sphere was the same

The sphere I make contact with is pretty heavy so the loss of charge it undergoes is negligible (I guess?)

I see what you are aiming to do. The only way I can help is to tell you that a voltage of about 5kV gives a 'good' deflection on a gold leaf electroscope...the typical school model. A voltage of about 100V gives hardly any deflection. If you want a very rough and ready technique I would say that if you get a noticeable deflection then the potential you are measuring is more than a few hundred volts and could be a few thousand volts. If you know the diameter of your sphere you could calculate the amount of charge present to produce this estimated potential...hope this helps

 

[David Anton]

I see what you are aiming to do. The only way I can help is to tell you that a voltage of about 5kV gives a 'good' deflection on a gold leaf electroscope...the typical school model. A voltage of about 100V gives hardly any deflection. If you want a very rough and ready technique I would say that if you get a noticeable deflection then the potential you are measuring is more than a few hundred volts and could be a few thousand volts. If you know the diameter of your sphere you could calculate the amount of charge present to produce this estimated potential...hope this helps

The angles of one leave to the vertical vary from 22 to 36 degrees in my experiment, so the deflection is large. I am getting a trend proportional to the time my sphere was exposed to a Van der Graaff, so I need to somehow mathematically translate angle into charge or potential.

I read in a Princeton University paper that this assumption (assuming that the electroscope is made of spheres instead of leaves) is "reasonably acceptable and accurate" so I guess I'll just go with that. However I am also going to see if there's any chance I can use a High Voltage generator to calibrate it.

Thank you!

 

[lychette]

The voltage between the leaves is zero.

The potential between the leaves and the (usually grounded) case is not zero

 

[Tom.G]

A different approach would be how close a grounded sphere needs to be to get a spark discharge.
Here is a graph of breakdown field strength for different gap widths. http://ethesis.nitrkl.ac.in/2875/1/Full_Thesis_Print_04.07.2011.pdf
I recommend reading the paper.

 

[David Lewis]

If you know the deflection versus charge function, and the capacitance of the electroscope then you can calculate the voltage.