# How much voltage should be applied to an object to create a certain amount of charge?

I am curious as to how much voltage should be applied to create a specific charge. Is there a formula to calculate it, and what are the parameters that can affect the relation between voltage and charge created in that object?

P.S: I haven't taken course on this subject, so I don't know the details of this subject.

## 2 Answers

Voltage has absolutely nothing to do with charge. I can "move" an infinite amount of charge trough a superconductor with zero voltage. Are you asking about the relationship of charge to voltage on a capacitor? That's a linear relationship: Q=C*U. The charges, in that case, are not "created" but merely separated. If you want more charge for the same amount of voltage, all you have to do, is to increase the capacitance of the capacitor.

Now, if you want to actually create new charges out of "nothing", you would have to create electron-positron pairs, which requires an energy of approx. 1MeV per pair. In that case a simple accelerator would have to operate on a voltage of over one MV, to overcome the threshold of pair production in particle collisions. Even so that would be a very inefficient process, to say, the least, and a detailed analysis of the kinematics shows, that a multiple of that threshold energy is needed. Practical positron sources use multi-MeV photons, which are derived from GeV beam lines and ultrashort laser pulses focused on heavy nuclei, like gold, in which case the emission is caused by complex multi-photon processes.

• Then what is the easiest way to create static charges in an object made out of insulating material? – user57144 Aug 23 '14 at 14:24
• I think what you mean is what's the easiest way to separate charges? That's exactly what a battery, or any voltage source does. The question is really, what do you want to do with those charges? – CuriousOne Aug 23 '14 at 14:32
• I mean is there a way to charge insulators other than by friction. I just want the information for a project not that I will create charges. – Starior Aug 23 '14 at 14:47
• Yes, it's called a voltage source. You can use a battery, if you like. But, again, the question is: what, exactly, does your project do with the separated charges? It's kind of hard to measure the few ten to hundred pC separated by a battery on an insulating rod. I could show you how, but it requires some serious electronics expertise to make it work in practice. That's why high school experiments use much higher voltages of tens of kV, which you get by simply rubbing appropriate materials. Alternatively, you can use a voltage source of 10kV or more... but that's seriously dangerous. – CuriousOne Aug 23 '14 at 14:52
• @ThePhoton I know it since an electron can't be created from nowhere which is supported by fundamental laws of physics. I just used the word "create" in the wrong place I guess. Moreover I would be happy if my question on the other comment was answered. Thanks in advance. – Starior Aug 23 '14 at 16:30

It is very hard to use a voltage source to induce charge on an insulator. The reason is that by definition, an insulator does not conduct electricity - so if you apply an electrode at one place, you will not move electrons elsewhere, and so you cannot induce a net charge (the best you can hope for is to create polarization, and maybe pull off a handful of electrons at the point of contact).

People make high voltage generators (for example, Van de Graaff generators) that are used to charge conductors - for example this one which you can buy from xump: A large voltage (up to 350 kV) is generated by the moving insulator band that runs up and down the insulating tube on the left, and a differential charge is induced on the two conducting spheres. When the potential difference is large enough you get a nice lightning bolt. But this only works because the charge can distribute itself along the surface, which is conducting.

The induction of charge on an insulator happens when you "steal away" electrons one at a time. When you touch two dissimilar insulators against each other (say silk and glass), then the molecules of one tend to have higher electron affinity than the other. As a result, when the two surfaces are separated, it is possible that an electron is transferred from one material to the other. Rubbing is a way to do a large number of "stick-unstick" operations millions of times per second, and this results in charge buildup. And since the insulator does not conduct electricity, when electrons are "stolen" from the surface, they do not get replenished from elsewhere. This is a fundamental difference between charged insulators and charged conductors.

Finally - the relationship between voltage and charge is given by the capacitance of the object. For a sphere, the capacitance, usually denoted by $C$, is given by

$$C = 4\pi\epsilon_0 R$$

and the relationship between voltage $V$, charge $Q$ and capacitance $C$ is given by

$$Q = C V$$

So for a sphere of 10 cm radius, $C = 11.1 pF$ (picoFarad), and a voltage of 350 kV (above generator) would induce a charge of $3.9 \mu C$ according to the formula.

For larger spheres, the charge would be larger - the answer scales linearly with both radius and voltage. But it's awfully hard to get a measurable amount of charge this way.

UPDATE

It is possible to charge an insulator without rubbing. Imagine the following setup:

A conducting sphere coated in an insulator. Apply a large voltage to the sphere. This results in an electric field normal to the surface of the insulator.

Now water molecules in air are partially ionized. The molecules with the appropriate charge will be attracted by the sphere, and on contact will neutralize, taking a bit of charge with them. This creates an apparent "leakage current" and results in surface charging of the insulating sphere. Note that in this case the charge is NOT coming from conduction through the insulator - it is coming from the air. It would require an experiment in a good vacuum chamber to prove whether conduction through an insulator can result in charge buildup. The answer is "probably, somewhat". But it's not a good mechanism to rely on for your experiments.

• Thanks for the answer. What I understand is there isn't any way to make an insulator get charged other than by friction. However, as far as I know there is not a thing suc as perfect insulator so all insulators can conduct electricity but at much slower rate. Thus, wouldn't the insulator eventually get charged after a long time staying in contact with the voltage source? – user57144 Aug 23 '14 at 18:58
• @FarStar - I have added a description of how one might charge an insulator without rubbing. – Floris Aug 23 '14 at 19:13
• It seems like a not so efficient mechanism. However, as I mentioned on the other comment is it possible to make an insulator get charged by making it to stay in contact with the voltage source for a long time since the insulator still conducts electricity? – user57144 Aug 23 '14 at 19:18
• When you are in contact with the voltage source your voltage source acts the same way as the silk: it "pulls" electrons off the surface. This is actually part of the mechanism in a Van de Graaff generator (there is a "charge pickup" on the moving insulator). So in that sense, the answer is "yes". But you need huge voltages to generate an appreciable charge accumulation. – Floris Aug 23 '14 at 19:24
• Ok thanks. Also is there a formula(like 4pi*epsilon_0*r) to calculate the capacitance of other geometrical objects like tube(cylinder with no top and bottom? – user57144 Aug 23 '14 at 19:48