How much induced voltage on sphere?

[johne1618]

Hi,

Assume that one has a pair of metal spheres, A and B, some distance apart.

A is connected to, say, a small van der Graaf generator and B is connected to a voltmeter which is then connected to ground.

I expect charge to be induced on sphere B.

How would one calculate the voltage one would expect to measure on sphere B?

Would it depend on the radius of sphere B?

Actually thinking about it I guess I should connect sphere B to the ground first to let induced charges run onto it, disconnect it, and then measure its voltage relative to ground. Is that right?

Basically, what is the best way to measure the strength of a static electric field electronically?

A field-effect transistor maybe?

 

[mfb]

Actually thinking about it I guess I should connect sphere B to the ground first to let induced charges run onto it, disconnect it, and then measure its voltage relative to ground. Is that right?

The result will depend on your method. Those are two different experiments, there is no "right" or "wrong" one.

In the second case, the measured potential difference is zero, as you let current flow to get exactly this value.
There are purely electrostatic ways to measure a potential difference - and unless you have very sensitive equipment, that is probably the best method, otherwise you discharge B too quickly.

How would one calculate the voltage one would expect to measure on sphere B?

I'm not sure if there are analytical formulas for that setup. If not, with a numerical simulation or with good approximations. I would expect a weak dependence on the radius (if the spheres are not too close to each other), but that is just a guess.

 

[voko]

http://en.wikipedia.org/wiki/Capacitance , pay especial attention to self-capacitance.

Note that the induced voltage will appear on B only when it is isolated from the Earth; note also that your voltmeter must have a very high internal impedance, which is not the case in most ordinary voltmeters. Specially-built high-impedance voltmeters are known as electrometers. An electrometer is generally a device for measuring charge; other designs are possible, see http://en.wikipedia.org/wiki/Electrometer