In my textbook I came across the capacitance of a certain body (i.e. a sphere, not two different spheres as in a spherical capacitor) and in it the formula,

$$Q = CV$$

where $V$ is the potential of the body with respect to the Earth. Now in a parallel plate capacitor, why do we choose the potential difference and not the potential of a single plate to the Earth?

  • $\begingroup$ |It's just a matter of experimental observation that POTENTIAL DIFFERENCE for two conductors is found to be directly proportional to the charge. It is as similar as coeffcient of mutal in ductance. And by the way exact potential has no meaning. you are automatically taking potential difference by assuming nilpotent earth. $\endgroup$ – Prayas Agrawal Apr 4 '17 at 15:22

V in th either situation is potential difference but in the case of an isolated sphere as written in Halliday/Resnick ( Indian edition)

We can assign a capacitance to a single isolated spherical conductor of radius R by Assuming that the " missing plate " is a conducting sphere of infinite radius

So the potential on single sphere comes out to be potential difference

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  • $\begingroup$ So that means by definition capitance is charge by potential difference and not potential right $\endgroup$ – user150854 Apr 4 '17 at 15:22
  • $\begingroup$ Yes that is correct $\endgroup$ – Utkarsh futous Apr 4 '17 at 15:24
  • $\begingroup$ So if we try to find capacitance of any isolated surface we take it with respect to another at infinity $\endgroup$ – user150854 Apr 4 '17 at 15:25
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    $\begingroup$ And capacitance is not of a singular surface but for a pair .....right $\endgroup$ – user150854 Apr 4 '17 at 15:30
  • $\begingroup$ I am not sure if that is true while it makes sense for spherical body for plate at d = infinity C will get infinity so I would say it depends on the body we are talking about....and yeah for pair of course $\endgroup$ – Utkarsh futous Apr 4 '17 at 15:31

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