# How to distribute static charges evenly on a finite plate?

There are several ways to make charges on an object evenly distributed. For example, if the surface of the object is infinite or the object is a sphere. There is one more way which I am not sure if it is a good way: if the object is made out of an insulating material.

I would like to know if there are other ways to make the charges on a finite charged plate evenly distributed over the surface? Also, how efficient is the idea of using an insulating material?

• Can someone help me? – Starior Aug 28 '14 at 14:48

A charged conducting material in the form of a sphere or an infinite plane can only be uniformly charged in the absence of external charges. Any other shape of charged conducting material can be induced to be uniformly charged by the placing the right external charge density around it. A conducting infinite cylinder is also uniformly charged (in the absence of external charges). All these shapes share a common property: they lack corners - in a corner, the electrical field produced by cations is stronger, and the electrons can not order themselves spontaneously in a uniform manner.

In an insulating material, there is no problem since the electrons lack the mobility they have in a conducting material and can't redistribute themselves, so it can be uniformly charged regardless of it's shape or of external charge distribution.

• Wouldn't chages on a cylinder accumulate on top or bottom since they are like corners? – Starior Aug 28 '14 at 17:46
• @Starior You've got it - for a finite cylinder - That's why it has to be an infinite cylinder (as it is in my answer). – Mr.WorshipMe Aug 28 '14 at 18:02
• Oh okay sorry. I didn't see that. Thanks for your answer. Are there another ways other than these you mentioned in your answer? – Starior Aug 28 '14 at 18:04
• @Starior I guess you're interested in another shape of metal which, with no external field, would have a uniform charge? (since I've mentioned that in all other cases, any shape would do). There are no more shapes that would fit the uniform curvature condition I have mentioned in my answer... in a 3d space, the maximum number of degrees of freedom one can use to describe a curvature on a surface is two: the sphere has two degrees. The next form would have one degree - that's the cylinder. And the final one has zero - a plane. – Mr.WorshipMe Aug 28 '14 at 18:13
• I mean with external charges. Is there any way to evenly distribute the charges on the object with external field? – Starior Aug 28 '14 at 18:28