the capacitance of two metal sphere system 1. The problem statement, all variables and given/known data What is the capacitance of the two metal sphere system. *The question has been attached shematically. All the variables are given in the attached file, there is no missing variable. thx for any help.
I thought that I could solve this problem by integration. I can divide two spheres to small circular plates as parallel to each other and consider them as parallel plates. Then, i can add them up. It ain't difficult, but it requires calculus knowledge.
You can't do it that way. It is a very difficult problem by any method. You could try image, but a large number of image charges would be needed.
Capacitance of two metal sphere system You can find the electric-field due to one sphere. Then, intagrate it from r to L-r to find the potential between spheres due to one sphere. I think the spheres must have a charge +Q and -Q, thus, potentials due to each sphere are same and total potential is two times the calculated one with integration. Once you have found an equality consists of Q and V, you can find the capacitancy by writing this equality in form of Q = C*V.
Because potential diffrence inside a sphere is zero, there is no potential difference between 0 and r, you do not need the to add potential difference between these points. And, of course, electric-field inisde sphere is zero, not depending on distance, so you can not even intagrate electric-field by choosing limits involving 0 to r and L-r to L intervals.