# Why do we take $V$ of surface of spherical conducting uniformly charged sphere when we find it's capacitance?

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?

• 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 Commented Jul 6, 2023 at 10:44

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.