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Is there a way to make the charges of a charged conductor evenly distributed over the surface? I know the charges of a charged insulator are evenly distributed but I want to know that if there is a way to make the charges of a charged conductor evenly distributed too.

Starior
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  • If you want to create a certain charge distribution to shape an electric field, relying on the electrostatic interactions of charges is not enough. The proper method is to use an active power source and a voltage divider connected to a segmented conductor, to force the potential to whatever value you want. This is usually done along linear structures to achieve a linear potential distribution, e.g. in photomultiplier tubes and linear accelerator tubes. – CuriousOne Aug 25 '14 at 19:55
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    @CuriousOne - PMTs usually don't want a uniform voltage distribution (you put more voltage across the first stage to improve the probability of photo-electrons being amplified at the first dynode, and lowering the excess noise). But the trick you describe is used in many high voltage applications, for example to prevent flash-over on MV electrostatic accelerators. – Floris Aug 25 '14 at 19:59
  • @Floris: You are technically right, but many simple PMT bases (especially home built ones!) use a linear distribution of voltages. I have seen this more often than I wanted to and had to modify quite a few designs for better performance. – CuriousOne Aug 25 '14 at 20:04
  • @CuriousOne fair enough - I have seen those diagrams. Let's agree that the dissemination of misinformation stops here :-) – Floris Aug 25 '14 at 20:08
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    @Floris: I am more than happy to agree with you on that! – CuriousOne Aug 25 '14 at 20:09
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    Detail: charges on a charged insulator are not evenly distributed over the surface. – garyp Aug 25 '14 at 20:29
  • @garyp What do you mean? – Starior Aug 25 '14 at 20:30
  • In general, when charges are placed on an insulator they don't migrate too far. Charges do not move and become evenly distributed. If you wait long enough, perhaps. A greasy insulator, perhaps. But generally, no. – garyp Aug 25 '14 at 20:37
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    @garyp: In reality it's far worse than that. One can simply not rely on what charges on insulators will do (especially not if the insulator is surrounded by a low pressure gas). In cases in which it matters, technical designs will always make surfaces or the bulk of the material slightly conductive or, at the very least, add surfaces of well defined potential (that's what electrostatic guards are). – CuriousOne Aug 25 '14 at 21:23
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    Completely agree with @CuriousOne's last comment - insulators are notorious for getting uneven charge / potential; evening this out is a major design task to ensure high voltage stability of larger systems. And yes, semiconducting coatings (where a tiny current acts as a "voltage divider") can play a role in evening things out. This stabilizes insulators and can prevent flashover. – Floris Aug 25 '14 at 21:29

1 Answers1

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The only way to have the charges on a charged conductor evenly spread is to make sure that there is no horizontal component of electric field in the case of "evenly spread". The only two solutions for that are

  • things with infinite dimensions: planes, cylinders
  • spheres

For any other shape of conductor, there comes a point where the evenly distributed charge would feel an asymmetrical force - more charge on one side than on the other. The charge, which can flow freely because it's in a conductor, will respond to this by moving - until the forces even out. At that point you have the usual boundary condition (electric field perpendicular to the conductor surface) but no longer a uniform charge distribution.

update I just found a relevant earlier answer - this shows a bit of the mathematics of the above, but otherwise agrees exactly.

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Floris
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