1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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:

    ∫∫((x2+y2)/√(x2+y2))*ln(x2+y2)dS

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

    ∫∫Rln(R2)dS

    and since R is a constant

    Rln(R2)∫∫dS

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

    ShayanJ

    User Avatar
    Gold Member

    Yeah,that's OK because you're computing [itex] \vec{F}\cdot\hat{n} [/itex] only on the surface of the cylinder!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Surface Integral
  1. Surface integrals (Replies: 10)

Loading...