Why does the method of images work?

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Discussion Overview

The discussion centers around the method of images in electrostatics, specifically regarding its application to calculate the electric field distribution of a charge near a conducting surface. Participants explore the theoretical underpinnings and implications of this method.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • One participant asks for clarification on which method is being referenced, indicating a need for specificity in the discussion.
  • Another participant specifies that the discussion pertains to the method of image charges in electrostatics and its application to electric field calculations near conducting surfaces.
  • A further contribution references Wikipedia articles to provide background information, mentioning the uniqueness theorem for Poisson's equation as a foundational concept that supports the method of images.
  • This participant suggests that if a solution for the electric potential meets the boundary conditions and charge density, it is the unique solution, implying that the method of images leverages this principle to find solutions effectively.
  • The idea of using symmetries to simplify the problem and find solutions is also introduced, highlighting a strategic aspect of applying the method of images.

Areas of Agreement / Disagreement

Participants have not reached a consensus on the explanation of why the method of images works, and multiple perspectives on its theoretical basis are present.

Contextual Notes

The discussion does not fully explore the implications of the uniqueness theorem or the specific conditions under which the method of images is applicable, leaving some assumptions and limitations unaddressed.

Shreyas Shree
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Why does the method of images work?
 
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Which method ?
 
Method of image charges in electrostatics to calculate the distribution of the electric field of a charge in the vicinity of a conducting surface.
 
Have you read the relevant Wikipedia articles?

https://en.wikipedia.org/wiki/Method_of_image_charges
https://en.wikipedia.org/wiki/Uniqueness_theorem_for_Poisson's_equation

In short, if you can find a solution for the electric potential that satisfies your boundary conditions for the electric potential, and the charge density within the considered region, you've found the unique solution. This is due to the uniqueness theorem.

That fact allows you to cleverly pick an arrangement of charges outside your considered region that satisfies your electric potential boundary conditions (usually by taking advantage of/introducing symmetries) and know that you've found the only solution that exists for your configuration.
 
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