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I'm trying to calculate the minimum voltage needed create a spark across 2 electrodes (needle shaped) in open air at normal ambient pressure.

Usually, I would use the figure of 3000V /mm as the breakdown for air, which gives these figures:

  • 300V for 0.1 mm gap
  • 30V for 0.01 mm gap

I found this page which talks about the Paschen curve.

It states:

Using Paschen's Law, the minimum breakdown in air is calculated to be 327 V at standard atmospheric pressure. This occurs at a distance of 7.5 µm.

I got a bit confused because with regular math I get around 300V for 100um.

How did they arrive to the figure 327V for 7.5um (microns)?

How to I correctly calculate the minimum voltage required to create a spark across a 50 micron air gap?

JRE
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Anchovy
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1 Answers1

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Usually i would use the figure of 3000V /mm as the breakdown for air. and I arrived at the figure of 300V for 0.1 mm gap 30V for 0.01 mm gap

That's the figure for sphere-sparking where the diameter of the sphere is much bigger than the gap between them. For needle-points the voltage breakdown figure is significantly smaller. See this graph from Jochen's High Voltage Page: -

enter image description here

So, that's a 3:1 reduction in voltage when needles are used compared to spheres.

Andy aka
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  • 1. I was also interested in why the site I linked contradicts it by saying " 327V for 7.5um", can you please. 2. Also the graph ends at 1mm would it be a linear relationship down to 50micron – Anchovy Mar 02 '23 at 15:31
  • That's the best data I have and I don't really know how linear it will be below those numbers. What I can say is that the smaller the gap, the more variable would be any experimental results due to atmospheric conditions. – Andy aka Mar 02 '23 at 15:44
  • @Anchovy 2. The voltage increases again as the gap drops below the minimum, which has to do with the mean free path of ions in the gas, they don't get to ionise the gas as well as with a longer run-up. – Neil_UK Mar 02 '23 at 15:58
  • @Neil_UK I don't understand the `Torr-cm `part on the x axis, also are there any graphs for air at standard atmospheric pressure? For the wiki article you linked to regarding `Paschens Curve` – Anchovy Mar 02 '23 at 16:29
  • @Andyaka Do you have any data for the breakdown voltage and air gap relationship (graph) for air at standard atmospheric pressure? – Anchovy Mar 02 '23 at 16:34
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    @Anchovy suggest you google this phrase 'paschen curve atmospheric pressure' and work your way through the hits – Neil_UK Mar 02 '23 at 17:15
  • @Neil_UK Regarding the wiki page you linked for breakdown voltage calculation using `paschen law` we need the ` secondary-electron-emission coefficient ` to calculate it. Do you by change know the ` secondary-electron-emission coefficient` for air? – Anchovy Mar 03 '23 at 12:16