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We all have seen experiments where an electric arc is created. Sometimes arcs of four inches are created with pretty rudimentary devices. When two electrodes are brought close together, a spark flashes. Then the arc is created an the experimenter moves the electrodes further apart. My question is about the distance between two electrodes. What exactly should the distance be for a spark to flash? How is it related to the voltage?

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    \$\begingroup\$ This image of Nikola Tesla comes to mind when I read this question \$\endgroup\$
    – Ron Beyer
    Oct 27 '17 at 5:16
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    \$\begingroup\$ The larger the voltage, the wider the gap it can arc across. Sometimes, if there is something in place to limit the short circuit current, you may be able to actually touch the electrodes together. As you then separate them, an arc will likely form, assuming the voltage is high enough. \$\endgroup\$
    – mkeith
    Oct 27 '17 at 5:50
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it depends on many things, assuming you are working with air there is a set number for breakdown at normal atmospheric pressure which is 3kV/mm

For breakdown on gases

atmospheric pressure will affect this(known as pashchen's law) humidity also will divert this value also remember this not a certain thing and usually the value given is for 50% chance of an arc happening.

Now the relation with voltage is mostly a limit of electric field that can be applied to the air before it becomes conductive.

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