I mean potential of any thing requires a reference point to be defined. Potential at a distance r from a point charge q is given by;
V=electrostatic constant × q/r
;but I dont understand how can I calculate potential of an isolated conductor or of any isolated object using this definition.
I have been trying to understand self-capacitance which is the amount of charge to raise the potential of an isolated conductor by one volt. But this needs me to understand what is potential of an isolated conductor. Means, I have got to know how is it defined? Don't direct me to the google or wikipedia for I have tried my best to find about it on these sites already. Although wikipedia got very close to defining the potential of isolated conductor. It also tries to tell about the reference point but I still don't understand the story. I want a very simple illustration.
Best Answer
If you have an isolated finite conductor (either charged or uncharged), its surface is an equipotential. The potential of this conductor you'll find by moving a small positive test charge $q$ along any path $\gamma$ from infinity to the surface of the conductor and determine the work $W$ done against the electrostatic force $\vec F$ in doing so. Then the electrostatic potential $\phi$ of the body is $$\phi=-W/q=-\frac{1}{q}\int_{\gamma}\vec F d\vec r=-\int_{\gamma}\vec E d\vec r$$ Depending on the net charge on the conductor and on induced charges and fields by nearby charges, the potential $\phi$ can be positive, negative or zero for example when there is no electric field.