[theThinker (OP)]

I have a parallel plate capacitor 1 m x 1 m that is to be fully charged to 300 kV. The distance between the metal plates is 3 mm; the inner surface of one plate is to be coated with 1 mm ceramic (permittivity >=1000) leaving an air gap of 2 mm.   
1) Can such a capacitor be charged to 300 kV without dielectric failure.
2) Is there ways to experimentally measure the charge by discharging the the fully charged capacitor. Is such a method common practice. The accuracy needed is only about 5%.
3) Would a good experimental physicist be able to work with such a capacitor.
4) would there be significant charge leakage if left for 2 hr.

[Kryptid]

Please rewrite the title in the form of a question, in order to comply with our rules.

[alancalverd]

No problem measuring the charge on a capacitor, though in this case you could calculate it quicker than you could measure it.

However the breakdown gradient for air is around 30 kV/cm so the air gap may as well not exist - it's effectively a short circuit at 300 kV!

Charge leakage depends on the resistivity (and indeed the breakdown gradient) of the dielectric, the quality of the finish of the perimeter, and in this case the nature of the environment and supporting insulators.

A good experimental physicist would find another way of doing whatever it is you are trying to achieve!

[Bored chemist]

leaving an air gap of 2 mm.   

That's a catastrophically bad design fault.

[theThinker (OP)]

No problem measuring the charge on a capacitor, though in this case you could calculate it quicker than you could measure it.

However the breakdown gradient for air is around 30 kV/cm so the air gap may as well not exist - it's effectively a short circuit at 300 kV!

Charge leakage depends on the resistivity (and indeed the breakdown gradient) of the dielectric, the quality of the finish of the perimeter, and in this case the nature of the environment and supporting insulators.

A good experimental physicist would find another way of doing whatever it is you are trying to achieve!

So no way to reach 300 kV.

Many thanks.

[Bored chemist]

No problem measuring the charge on a capacitor, though in this case you could calculate it quicker than you could measure it.

However the breakdown gradient for air is around 30 kV/cm so the air gap may as well not exist - it's effectively a short circuit at 300 kV!

Charge leakage depends on the resistivity (and indeed the breakdown gradient) of the dielectric, the quality of the finish of the perimeter, and in this case the nature of the environment and supporting insulators.

A good experimental physicist would find another way of doing whatever it is you are trying to achieve!

So no way to reach 300 kV.

Many thanks.

300 KV is quite possible- even "common",
https://en.wikipedia.org/wiki/High-voltage_substations_in_the_United_Kingdom#400_kV_substations

but not with your design.

[theThinker (OP)]

No problem measuring the charge on a capacitor, though in this case you could calculate it quicker than you could measure it.

However the breakdown gradient for air is around 30 kV/cm so the air gap may as well not exist - it's effectively a short circuit at 300 kV!

Charge leakage depends on the resistivity (and indeed the breakdown gradient) of the dielectric, the quality of the finish of the perimeter, and in this case the nature of the environment and supporting insulators.

A good experimental physicist would find another way of doing whatever it is you are trying to achieve!

I can't think of any alternative design setup.

I think the air gap may be ok as it is not between two conducting plates; there is the 1 mm ceramic insulation. The question is whether the 1 mm ceramic can withstand the 300 kV voltage. Also we need the dielectric to have permittivity in the > 1000 range for high capacitance.

There would be less charge leekage if the the ceramic fully insulates one plate. A leekage of 5% is allowed in 2 hours. 

[Bored chemist]

I can't think of any alternative design setup.

Find someone who can.

I think the air gap may be ok

Well, Alan and I agree that you are wrong, and it's not because we like agreeing with eachother...


it might be better if you tell us what you are trying to achieve

[theThinker (OP)]

I can't think of any alternative design setup.

Find someone who can.

I think the air gap may be ok

Well, Alan and I agree that you are wrong, and it's not because we like agreeing with eachother...


it might be better if you tell us what you are trying to achieve

I understand an air gap of 2mm between parallel plates without insulation would not work. It should be different when there is strong insulation; it should be ok as long as the insulation is not broken by the high voltage. 

[alancalverd]

Why do you want  the air gap?

If you want to stand off 300 kV/mm you will need a fused silica dielectric - I can't find any other practical engineering material that comes close. But it only has a relative permittivity of about 4!

[theThinker (OP)]

Why do you want  the air gap?

If you want to stand off 300 kV/mm you will need a fused silica dielectric - I can't find any other practical engineering material that comes close. But it only has a relative permittivity of about 4!

The experimental  setup need the air gap, very high capacitance and high Q charge storage that may be achieved only near 300 kV.

I have read some ceramic has relative permittivity of > 1000. What about barium titanate?

[alancalverd]

Barium titanate can be fabricated with a very high dielectric constant but its breakdown field is around 30 kV/mm, a factor of 10 below your requirement. Obtaining a consistent deposition over a square meter would be technically challenging and you would have problems bonding it to your substrate as it is piezoelectric so tends to distort at high field strengths.     

With ε₀ ≈ 10^-11 F/m your capacitor (without the air gap) would be around 10 picofarad. You shouldn't have a problem getting a 10 pF 300 kV capacitor stack from a high voltage laboratory equipment supplier, or use a few meters of x-ray HT cable.

[theThinker (OP)]

Barium titanate can be fabricated with a very high dielectric constant but its breakdown field is around 30 kV/mm, a factor of 10 below your requirement. Obtaining a consistent deposition over a square meter would be technically challenging and you would have problems bonding it to your substrate as it is piezoelectric so tends to distort at high field strengths.     

Just a correction. The field strength is uniform throughout the 3 mm
(1 mm ceramic + 2 mm air); so the rough requirement is 100 kV/ mm.

I do expect that such an experimental setup is difficult to realize. Our setup cannot do with dielectric relative permittivity below 1000.

Wonder if there could be other suitable "wonder" material if we have the money to throw at the experiment. 

[theThinker (OP)]

Barium titanate can be fabricated with a very high dielectric constant but its breakdown field is around 30 kV/mm, a factor of 10 below your requirement. Obtaining a consistent deposition over a square meter would be technically challenging and you would have problems bonding it to your substrate as it is piezoelectric so tends to distort at high field strengths.     

With ε₀ ≈ 10^-11 F/m your capacitor (without the air gap) would be around 10 picofarad. You shouldn't have a problem getting a 10 pF 300 kV capacitor from a high voltage laboratory equipment supplier. 

The problem is that we cannot do without the 2 mm air gap. 

[alancalverd]

At 100 kV/mm the air will ionise and perform like a conductor. And I've played with some awful conductors.

[Bored chemist]

Just a correction. The field strength is uniform throughout the 3 mm

No, it is not.
Because physics.

And that's why you can't have the air gap.
So, you can either abandon the idea, or tell us what you are trying to achieve.

[theThinker (OP)]

At 100 kV/mm the air will ionise and perform like a conductor. And I've played with some awful conductors.

I think it is correct. The air is connected to the atmosphere. But within a high vacuum chamber, the 300 kV may hold if the ceramic insulation can withstand the high field strength.

[Bored chemist]

In a vacuum chamber you will probably still fail.
The metal bits will spray electrons at each-other.
You will have an interesting xray generator.

So, you can either abandon the idea, or tell us what you are trying to achieve.

[Bored chemist]

With ε₀ ≈ 10^-11 F/m your capacitor (without the air gap) would be around 10 picofarad.

I think you may have lost track of a few zeroes.

ε₀ ≈ 10^-11 F/m
means that a 1 metre cube capacitor with a vacuum in it would be about 10pF
The plates here are 1mm apart so that's about 10 nF
And then he's using magic to get a dielectric constant of 1000 so that means he's looking for about 10µF

Which means (If I got the arithmetic right) he's looking at a stored energy of roughly a MJ
That's the stored energy of a candy bar.
Do you think he can be trusted with it?

[alancalverd]

Divide, multiply....it's Friday, for heavens' sake.

Anyway, a partial vacuum is worse than air.