How Does the Method of Images Determine Potential Inside a Grounded Sphere?

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Homework Help Overview

The discussion revolves around a problem involving a grounded conducting sphere and the method of images to determine the electrostatic potential inside the sphere due to a point charge placed outside it. The context includes concepts from electrostatics and the application of Legendre polynomials.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the potential calculation using the method of images and express confusion regarding the application of Legendre polynomials in this context. There are attempts to relate the problem to Laplace's Equation and questions about the relevance of the Legendre equations to the solution.

Discussion Status

The discussion is ongoing, with participants seeking clarification and guidance on how to incorporate Legendre polynomials into their approach. Some participants are exploring the connection between the method of images and the required mathematical framework, while others are looking for additional resources to aid their understanding.

Contextual Notes

There is an indication that the problem is part of a homework assignment focused on Legendre equations and polynomials, which may influence the approach participants feel they should take. Some participants express a need for a clearer connection between the problem and the required mathematical tools.

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Homework Statement


We have a grounded conducting sphere of radius R and a charge q is placed a distance a from the center of the sphere. Show that the potential in the interior produced by q and the distributed induced charge is the same as that produced by q and its image charge q'.The image charge is at a distance a'=R^2/a fro the center collinear with q and the origin. Calculate the electrostatic potential for a<R<a'. Show that potential vanishes for r=R if we take q'=-qR/a


Homework Equations


In the course we are investigating legendre equations, legendre polynomials etc.


The Attempt at a Solution


I can find potential by simply using V=Sum (1/4pieps)q/r however there is no legendre polynomial or legendre series in it. I tried Laplace's Equation however I got confused. Because in Laplace's eqn I can only deal with r. Where have I gone wrong? How should i think?
 
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I know that solution, however there is nothing related to legendre in it. The question was given to me as a homework for Legendre equation/polynomials topic. I should o something related to that I suppose.
 

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