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Homework Help: Surface Integral

  1. Dec 6, 2013 #1
    1. The problem statement, all variables and given/known data

    The problem asks to find the flux through a cylinder of radius R and height h.

    2. Relevant equations

    Flux = ∫∫FndS over S

    F = (ix + jy)*ln(x2+y2)

    3. The attempt at a solution

    After finding the unit normal vector (n) to the curved surface of the cylinder, the integral simplified down to:


    I'm wondering if it is ok to replace x2+y2 with R2. Then the integral would be:


    and since R is a constant


    = 4*pi*hR2ln(R). which is the correct answer
  2. jcsd
  3. Dec 6, 2013 #2


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    Gold Member

    Yeah,that's OK because you're computing [itex] \vec{F}\cdot\hat{n} [/itex] only on the surface of the cylinder!
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