Minimum radius to avoid voltage breakdown?

[rwiebe89]

I am trying to figure out the minimum radius needed to avoid voltage breakdown. I found this from a Physics website:

"The electric field near a conductor is inversely proportional to the radius of curvature of the surface."

So if I know the voltage and the distance between the 2 metal surfaces (a cylinder and rod), how would I calculate the minimum radius needed on the cylinder to keep from arcing between the cylinder and rod? Am I going about this wrong? Help?

 

[SpectraCat]

http://en.wikipedia.org/wiki/Paschen's_law

That site and the links on it should get you started. Come back and ask more questions if you get stuck.

 

[rwiebe89]

I guess I should have specified. I'm looking for at the difference a radius has on a voltage breakdown. Right now I have a square edge, but needed know the minimum radius needed to avoid a breakdown.

 

[SpectraCat]

I guess I should have specified. I'm looking for at the difference a radius has on a voltage breakdown. Right now I have a square edge, but needed know the minimum radius needed to avoid a breakdown.

The minimum radius will depend on the voltage, the separation and the pressure and chemical identity of the gas in between your two electrodes. That is why I pointed you towards the Paschen curve data. If you know 3 of the 4 quantities above, then you can calculate the 4th. The radius of curvature is not generally one of the input quantities .. I *think* this is because it is generally assumed to be effectively infinite (i.e. the ratio of the radius to the separation between electrodes is large enough that the field inhomogeneity induced by the curvature is negligible.