Poisson's Equation in Cylindrical Coordinates

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Homework Help Overview

The discussion revolves around Poisson's Equation in cylindrical coordinates, focusing on boundary conditions and the application of Gauss's Law. Participants are exploring the implications of these concepts in solving the problem.

Discussion Character

  • Mixed

Approaches and Questions Raised

  • Participants discuss the application of boundary conditions and question the correctness of their derived solutions. There is mention of constants in the general solution and the need to verify results using Gauss's Law.

Discussion Status

The discussion is ongoing, with some participants providing feedback on attempts and suggesting areas for clarification. There is an acknowledgment of progress, but also recognition of misunderstandings that need to be addressed.

Contextual Notes

Participants note challenges in applying boundary conditions and the need for clarity on constants in the solution. There is also a mention of time constraints affecting the ability to explore the problem fully.

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Homework Statement



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Homework Equations



Possions Equation and boundary conditions...


The Attempt at a Solution



First Part that I think is right...

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However when I try and apply the boundary conditions ie V(a)=V(r)=0... I can't get the answer!

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And for the last part I need to use Gauss's Law in integral form. Any help on where I am going wrong?
 
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What happened to part (d)? I guess they want you to use your V(r) rather than the easy (Gaussian surface) way.

parts a and b are correct. Nicely done in fact.

In part c you have your A and B as functions of r. They are supposed to be constants. Why don't you solve for A and B using the general solution you derived in (b)? How did you come by the 3rd equation on your second sheet?

(A an aside, you realize you can derive everything using Gauss' law. You should do it to check your Poisson's equation solution.)
 
Got there in the end... Sort off. I've just submitted this so any help now is more for my understanding rather than me getting a better mark.

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And this part is wrong... Couldn't do it and didn't have time to try and more.

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I have a harder time reading these pages than before, but you seem to be on the right track.
 

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