Field between 2 conducting spheres in electric field

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Discussion Overview

The discussion revolves around the behavior of the electric field between two conducting spheres placed in a constant electric field. Participants explore the relationship between the diameter of the spheres and the electric field in the gap, questioning the expected outcomes and seeking analytical solutions.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • One participant notes that simulations suggest the electric field in the gap increases with the diameter of the spheres, contrary to their expectations.
  • Another participant proposes an approximation involving induced dipoles to explain the observed behavior, providing a formula for the electric field in the gap.
  • A later reply expresses gratitude and seeks clarification on the derivation of the proposed formula.
  • Further explanation is provided regarding the induced dipole moment and its effect on the electric field at a specific distance from the dipole.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the initial expectations versus the simulation results, as one participant finds the outcome odd while another provides a mathematical framework that aligns with the simulation findings.

Contextual Notes

The discussion includes assumptions about the behavior of induced dipoles and the specific conditions under which the electric field is analyzed, but these assumptions are not fully resolved.

Who May Find This Useful

Individuals interested in electrostatics, particularly those studying the effects of induced charges in conducting materials within electric fields, may find this discussion relevant.

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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