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Potential of ring with sphere inside it

  1. Jun 13, 2013 #1
    1. The problem statement, all variables and given/known data
    Hi,

    I'm trying to find the potential of conducting grounded sphere with radius Rs which located in the center of charged ring with Rr (>Rs) with charge density λ, h meters up to the z axis (see the attached images)


    Rs=4.3[cm]
    Rr=6.6[cm]
    h=13.1[cm]
    λ=1.0[esu/cm]

    The answer should be 0.81023024

    2. The attempt at a solution

    The sphere potential is easy one -
    [itex]\Phi ring=\frac{2\pi Rr\lambda}{\sqrt{z^2+Rr^2}}[/itex]
    But how do I get the potential of the sphere?
    I've tried to use the image charged method, but I can't get to the right answer.
    Can somebody help me?

    Thanks,
    Adam
     

    Attached Files:

    • temp.jpg
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    Last edited: Jun 13, 2013
  2. jcsd
  3. Jun 13, 2013 #2

    haruspex

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    Doesn't sound too hard :wink:. Am I missing something?
     
  4. Jun 13, 2013 #3
    Can you give me some clue about the calculation of the sphere's potential?
     
  5. Jun 13, 2013 #4
    I don't know how to calculate the sphere's potential but the problem can be easily done by method of image charges. Did you try that?
     
  6. Jun 13, 2013 #5
    Yes.

    I know how to replace a grounded sphere near to a single particle, but don't know how to replace a grounded sphere with surrounded ring.
    I have only the ring’s potential on the Z axis, and it makes it harder.
     
  7. Jun 13, 2013 #6
    Like a point charge, you can replace the grounded sphere with a ring here in this case.
     
  8. Jun 13, 2013 #7
  9. Jun 13, 2013 #8
    Do you mean ##\displaystyle q'=-\frac{R_s}{R_r}Q## where ##Q=\lambda \cdot 2\pi R_r##?

    Correct!
     
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