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Poisson's Equation in Cylindrical Coordinates

  1. Jun 3, 2014 #1
    1. The problem statement, all variables and given/known data

    14337265752_076851f371_z.jpg

    2. Relevant equations

    Possions Equation and boundary conditions...


    3. The attempt at a solution

    First Part that I think is right...

    14152244848_7a90f60d3c_b.jpg

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

    14152443677_11d23676d0_z.jpg

    And for the last part I need to use Gauss's Law in integral form. Any help on where I am going wrong?
     
  2. jcsd
  3. Jun 4, 2014 #2

    rude man

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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.)
     
  4. Jun 5, 2014 #3
    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.

    14353752092_8a8ec8ff79_z.jpg [/url]

    14375489963_6d9d731866_z.jpg


    14168824657_60a2f81056_z.jpg [/url]


    14168638389_db40465fd8_z.jpg [/url]

    14168639439_71a12413ef_z.jpg [/url]

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

    14168676288_55f9a71f73_z.jpg [/url]
     
  5. Jun 5, 2014 #4

    rude man

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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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