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A charged spherical capacitor kept in air do not loose charge because air is a bad conductor and increase in charge results in Corona Discharge. Is it because the nucleus of air molecule repels the charge in sphere and after a limit the repulsion is less than the attraction by sphere leading to Corona Discharge. But if the same charged spherical capacitor is kept in vacuum, what would happen. Shouldn't charge repel each other and escape the spherical surface because now there is no nucleus of air molecule to repel those charges. Will the capacitance decrease or not.

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    $\begingroup$ Most real capacitors do slowly bleed charge off whether you want them to or not. $\endgroup$
    – Jon Custer
    Commented Jul 21, 2021 at 15:55
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    $\begingroup$ Do you mean a capacitor which has two conductive plates, or a single sphere which is only one conductor? $\endgroup$ Commented Jul 21, 2021 at 16:05
  • $\begingroup$ @GuyInchbald single spherical capacitor. I know this one is not a good capacitor but good enough for my question. $\endgroup$ Commented Jul 21, 2021 at 16:31
  • $\begingroup$ A single sphere is not a capacitor. Not at all. It can carry a charge but that does not make it a capacitor. Your question makes no sense until you can be absolutely clear which you mean; say to us either "sphere" or say "capacitor" but do not say both. $\endgroup$ Commented Jul 21, 2021 at 17:13
  • $\begingroup$ So a sphere which is charged and kept in vacuum loses charge due to inner repulsion and this does not happen in air due to bad conductivity $\endgroup$ Commented Jul 21, 2021 at 17:35

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A charged sphere stays charged in vacuum because it takes a minimum energy for an electron to exit the physical material. This is called the work function.

Indeed, if you would just have a spherical shell distribution of truly free charges this would fly apart.

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    $\begingroup$ But why the charge doesn't escape due to repulsion. $\endgroup$ Commented Jul 21, 2021 at 16:45
  • $\begingroup$ @SamyakMarathe A charged sphere stays charged in vacuum because it takes a minimum energy for an electron to exit the physical material. This is called the work function. Indeed, if you would just have a spherical shell distribution of truly free charges this would fly apart. $\endgroup$
    – my2cts
    Commented Jul 22, 2021 at 0:24
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It does escape - via a quantum tunnelling effect.

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If the charge of an object does not change, it means the net flux of charges to and from it is zero. It all depends on the environment and the object itself. It is normal that an object has some charge even in the near vacuum of space. Sunlit surfaces for instance become charged positively due to ultraviolet radiation knocking electrons out of the material. Surfaces in shadow become charged negatively due to the fact that the flux of plasma electrons in space is higher than that of protons (due their smaller mass and thus higher velocities). The material charges up to a value so that the net flux of charges is zero and thus a steady state is reached. See http://holbert.faculty.asu.edu/eee560/spc-chrg.html for more information.

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