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Converting to cylindrical and then taking div and curl

  1. Feb 22, 2008 #1
    1. The problem statement, all variables and given/known data
    Change to cylindrical coordinates and find the divergence

    F = <x, y, 0>/(x^2 + y^2)


    2. Relevant equations


    [tex]\nabla[/tex] . F = [tex]\frac{1}{\rho}[/tex][tex]\frac{\partial\rho F}{\partial\rho}[/tex]+[tex]\frac{1}{\rho}[/tex][tex]\frac{\partial F}{\partial\theta}[/tex]+[tex]\frac{\partial F}{\partial z}[/tex]

    3. The attempt at a solution

    i changed into cylindrical by simply having x = [tex]\rho[/tex]cos[tex]\theta[/tex]
    y =[tex]\rho[/tex]sin[tex]\theta[/tex] and x^2 +y^2 = [tex]\rho[/tex]^2. THen, using the above formula I get cos(theta)/rho^2. The answer is 0 however. Can someone please tell me what i could have messed up?
     
  2. jcsd
  3. Feb 22, 2008 #2
    Wait, must I also convert the i,j,k unit vectors to e(rho), e(theta), and ez before I can use vector operations? If i do this i get the right answer, but I'm still not sure -- my book doesn't have a single example excersise so I dont have too much to work off of. If someone could help me out that would be appreciated greatly. Thank you
     
  4. Feb 22, 2008 #3

    Dick

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    Sure. You have to convert the basis vectors as well. You should get F_r=1/r and the other components zero, so div(F)=0.
     
  5. Feb 22, 2008 #4
    that is in fact what I got. Thank you very much for the help -- unfortunately my book offers only theory and no examples.
     
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