How Do You Calculate the Charge Between Two Asymmetric Cylinders?

[jleahy]

Hey all,

I'm trying to calculate the charge that forms on two adjacent and asymetrical cylinders when a voltage is put between them. The figures I was using was something like 1mm radius for one and 10mm radius for the other, a voltage of about 20kV and a separation of a few cm.

I thought of using Q=CV, but I couldn't find the revelant equation for capacitance; that is, if there is one. As they are asymetric I'm not expecting for +Q to form on one and -Q on the other, so I'm unsure as to whether this even applies.

I've also tried using the electric field calculations, using work for voltage and all that, but can't quite work out how to tie all the maths together. Has anybody seen a problem like this before?

Thanks in advance,

Josh

 

[kuruman]

If you have two uncharged asymmetric cylinders and you hook them up to a battery, the battery will move charge from one cylinder to the other in order to maintain a constant potential difference across its terminals. Whatever amount leaves one cylinder must accumulate on the other. So Q=CV is still applicable and the size of Q depends on C which is purely a quantity that depends on the geometry, the length and radius of each cylinder, the separation between them and their relative orientation. A calculation from first principles is usually fraught with assumptions and approximations even if the cylinders are equal in length and aligned with each other to fit inside a plane rectangle. Your best bet would be to measure the capacitance using something like a capacitance meter or bridge. You don't need a formula unless you are in the design stage and you want to optimize some relevant quantity to your application.