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Field between 2 conducting spheres in electric field

  1. Nov 8, 2011 #1
    Hi,
    I tried to make some simulations of two conducting spheres in a constant electric field. The simulations seem to indicate that the electric field in the gap increases with increasing diameter of the spheres at a constant gap distance. Does this make sense? I expected just the reverse. What is wrong? Does an analytical solution for this problem exist?
    I really appreciate any help.
     
  2. jcsd
  3. Nov 8, 2011 #2

    clem

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    If I approximate the added field at the center of the gap as due to two induced dipoles,
    I get [tex]E=\frac{4E_0}{(1+d/2R)^3}[/tex]. This agrees with what you found.
     
  4. Nov 8, 2011 #3
    Thanx a lot. This matches qualitatively (although it still sounds odd to me). Can you tell me how you have derived this result?
     
  5. Nov 8, 2011 #4

    clem

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    A conducting sphere in constant electric field E_0 gets an induced dipole moment
    [tex]p=E_0 R^3.[/tex]. The electric field a distance R+d/2 from a dipole is
    [tex]E=2p/(R+d/2)^3.[/tex] Put these together to get the answer.
     
  6. Nov 9, 2011 #5
    Ok. Thank you.
     
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