Maximum voltage on a unipolar capacitor

[htg]

I need to place as much charge as possible on a metal ball of radius R (say 1 cm), in air.
What is the maximum voltage? Can I calculate it from air's dielectric strength ( 3kV/mm)?

 

[Dadface]

I need to place as much charge as possible on a metal ball of radius R (say 1 cm), in air.
What is the maximum voltage? Can I calculate it from air's dielectric strength ( 3kV/mm)?

Your method looks good.

 

[AJ Bentley]

You can't trust that 3kV/mm. It applies to spark gaps that are usually quite close together and deliberately designed to break down at more-or-less specific voltages

At high voltages, the propagation of 'streamers' from the electrode tends to take place by complex avalanche mechanisms. At something above 50 to 100kV streamers can start to grow to surprising lengths.

Take a look at the various Tesla Coil videos and photos on the web, you'll see what I mean.

 

[Dadface]

You can't trust that 3kV/mm. It applies to spark gaps that are usually quite close together and deliberately designed to break down at more-or-less specific voltages

At high voltages, the propagation of 'streamers' from the electrode tends to take place by complex avalanche mechanisms. At something above 50 to 100kV streamers can start to grow to surprising lengths.

Take a look at the various Tesla Coil videos and photos on the web, you'll see what I mean.

There are other problems the main one being that depending on the method of supporting the sphere other material(s) can be brought into contact with it and the curvature of the sphere can be comprimised at some places.I am thinking in particular about the Van De Graaff generator where discharge occurs mainly at the more pointed regions at the base and or at places where materials are brought close to the dome.Despite these difficulties the op needs to carry out a calculation and using a value of 3kV/mm gives an answer which is better than no answer at all.The important thing is that the op becomes aware of the difficulties and hopefully comes up with ways of minimising them.