# The capacitance of the two metal sphere system

the capacitance of two metal sphere system

1. Homework Statement

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.

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## Answers and Replies

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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.

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clem
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.

Then, intagrate it from r to L-r to find the potential between spheres due to one sphere.
Why did you choose limits as r and L-r?

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.

thx dude.

pam
But the surface charge density on each sphere is not uniform.