The capacitance of the two metal sphere system

  1. 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.

    Attached Files:

    Last edited: Mar 16, 2008
  2. jcsd
  3. 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.
    Last edited: Mar 17, 2008
  4. clem

    clem 1,276
    Science Advisor

    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.
  5. 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.
  6. Why did you choose limits as r and L-r?
  7. 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.
  8. thx dude.
  9. But the surface charge density on each sphere is not uniform.
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