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The capacitance of the two metal sphere system

by Indis Nenhrma
Tags: capacitance, metal, sphere
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Indis Nenhrma
Mar16-08, 05:28 AM
P: 8
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.
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File Type: bmp two metal sphere.bmp (230.4 KB, 120 views)
Attached Files
File Type: doc two metal sphere.doc (23.5 KB, 84 views)
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Indis Nenhrma
Mar17-08, 03:22 PM
P: 8
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.
Mar17-08, 04:03 PM
Sci Advisor
P: 1,266
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.

Mar18-08, 05:24 AM
P: 2
The capacitance of the 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.
Indis Nenhrma
Mar18-08, 05:52 AM
P: 8
Quote Quote by Porter View Post
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?
Mar18-08, 06:48 AM
P: 2
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.
Indis Nenhrma
Mar18-08, 05:39 PM
P: 8
thx dude.
Mar18-08, 07:29 PM
P: 455
But the surface charge density on each sphere is not uniform.

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