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The capacitance of the two metal sphere system 
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#1
Mar1608, 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. 


#2
Mar1708, 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.



#3
Mar1708, 04:03 PM

Sci Advisor
P: 1,261

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. 


#4
Mar1808, 05:24 AM

P: 2

The capacitance of the two metal sphere system
You can find the electricfield due to one sphere. Then, intagrate it from r to Lr 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.



#5
Mar1808, 05:52 AM

P: 8




#6
Mar1808, 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, electricfield inisde sphere is zero, not depending on distance, so you can not even intagrate electricfield by choosing limits involving 0 to r and Lr to L intervals.



#7
Mar1808, 05:39 PM

P: 8

thx dude.



#8
Mar1808, 07:29 PM

P: 455

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



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