Field between 2 conducting spheres in electric field

  • Thread starter oliverroth
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  • #1

Main Question or Discussion Point

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.
 

Answers and Replies

  • #2
clem
Science Advisor
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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.
 
  • #3
Thanx a lot. This matches qualitatively (although it still sounds odd to me). Can you tell me how you have derived this result?
 
  • #4
clem
Science Advisor
1,308
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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.
 
  • #5
Ok. Thank you.
 

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