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.

 

[sardar]

Your approach is correct. In order to avoid voltage breakdown between the cylinder and rod, you need to ensure that the electric field at the surface of the cylinder is below the breakdown strength of the material. This can be achieved by keeping the radius of curvature of the cylinder above a certain value.

To calculate the minimum radius, you can use the formula provided on the Physics website, which states that the electric field is inversely proportional to the radius of curvature. This means that as the radius decreases, the electric field increases. Therefore, to keep the electric field below the breakdown strength, you need to increase the radius of the cylinder.

You can use the following formula to calculate the minimum radius:

R_min = (V/d) * (1/E_max)

Where R_min is the minimum radius, V is the voltage, d is the distance between the 2 metal surfaces, and E_max is the maximum breakdown strength of the material.

For example, if the voltage is 1000 volts and the distance between the cylinder and rod is 1 cm, and the maximum breakdown strength of the material is 100 kV/cm, then the minimum radius would be:

R_min = (1000 V / 1 cm) * (1/100 kV/cm) = 10 cm

Therefore, in order to avoid voltage breakdown, the radius of the cylinder should be at least 10 cm.

It is important to note that this calculation only provides an estimate for the minimum radius and other factors such as surface roughness, material properties, and environmental conditions can also affect the breakdown voltage. It is always best to consult with a qualified engineer or conduct experiments to determine the exact minimum radius needed to avoid voltage breakdown in a specific situation.