Capacitance $=Q/|∆V|$ and we take $|∆V|$ of the surface of uniformly charged conducting sphere when we are dealing with a capacitor consisting a system such as one sphere is positively charged and the other is negatively charged and the negatively charged sphere is placed at infinity so that potential due to negatively charged sphere on the surface of positively charged surface will be zero and even on the points surrounding the positively charged sphere. While finding capacitance of the positively charged sphere we take |V|(i.e.|V|=|∆V|=V due to -ve sphere - V on the surface of positive sphere)but why don't we take ∆V between other points outside the sphere in the electric field of the positively charged sphere as we take in the parallel capacitor to find the capacitance?
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$\begingroup$ Your last sentence is hard for me to understand, but I suspect the answer might be this: A conductor, by definition, has the same potential everywhere. So it doesn't matter which point on the conductor you use to define the "voltage of the conductor." And if there isn't a conductor somewhere, you wouldn't call it a capacitor $\endgroup$– AXensenCommented Jul 6, 2023 at 10:44
1 Answer
The original text of the question remains hard for me to understand, but you clarified what was confusing you in the comments and now I can attempt to answer.
Capacitance is always defined as a relationship between two objects. It's not one object that "has a capacitance" it's two objects that "have a capacitance between them." If I have two conductors called $A$ and $B$, the capacitance between them $C_{AB}$ tells us how much voltage we produce when we put a charge $Q$ on conductor $A$. It might help for you to go a few pages forward in your textbook and learn about capacitance matrices - I think that helps with conceptual understanding of capacitance.
However, sometimes we talk about "self capacitance," with only one object in question... so what is that? It's the capacitance between the object and the ground. So first you assume that the ground is the definition of zero voltage. Then you say that the ground is very far from your object. To a good approximation, instead of adding a flat plane of zero voltage to your system far below your conductor, you can instead calculate the voltage difference between your conductor and points that are very far away.
So ultimately in your problem you're imagining putting a charge Q on a spherical conductor. You're asking what is the voltage between that sphere and a point that's very far away. The experimental situation is that you have a spherical conductor floating (or sitting on an insulating stand) pretty far from the ground (relative to its radius). Then to a good approximation, you calculate the voltage difference between the spherical conductor and the ground.