Field between 2 conducting spheres in electric field

AI Thread Summary
The discussion focuses on the behavior of the electric field between two conducting spheres placed in a constant electric field. Simulations indicate that the electric field in the gap increases with the diameter of the spheres while maintaining a constant gap distance, which contradicts initial expectations. An analytical solution is derived using the concept of induced dipoles, resulting in a formula that aligns with the simulation results. The induced dipole moment of a conducting sphere in an electric field is calculated, leading to a specific expression for the electric field at a certain distance from the dipole. The conversation concludes with a confirmation of the derived results and their qualitative agreement with the simulations.
oliverroth
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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.
 
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If I approximate the added field at the center of the gap as due to two induced dipoles,
I get E=\frac{4E_0}{(1+d/2R)^3}. This agrees with what you found.
 
Thanx a lot. This matches qualitatively (although it still sounds odd to me). Can you tell me how you have derived this result?
 
A conducting sphere in constant electric field E_0 gets an induced dipole moment
p=E_0 R^3.. The electric field a distance R+d/2 from a dipole is
E=2p/(R+d/2)^3. Put these together to get the answer.
 
Ok. Thank you.
 
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