Poisson's Equation in Cylindrical Coordinates

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smileandbehappy
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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!

Handwritten derivation on squared paper solving for the potential V(r) in a cylinder, applying boundary conditions V(a) = V(r) = 0 to find constants A and B and arriving at a final expression for V(r) with terms involving rho, r, a, epsilon and ln(r/a).


And for the last part I need to use Gauss's Law in integral form. Any help on where I am going wrong?
 
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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