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!

Flux Integral

  1. Jan 29, 2012 #1
    1. The problem statement, all variables and given/known data
    Find the flux of [itex]\vec{F}=(x, y, z)[/itex] outward across the sphere [itex]x^2+y^2+z^2=a^2[/itex].


    I am able to get it to this point:
    [tex]\int\int_Cadxdy[/tex] and I then convert it to polar coordinates, and integrate rdr from 0 to a, and theta from zero to 2pi. However, this does not give me the correct result, as the answer is 4a^3*pi, and Im getting a^3*pi.
     
  2. jcsd
  3. Jan 30, 2012 #2

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    hi sandy.bridge! :smile:
    it's the surface of a sphere …

    what does r have to do with it? :confused:

    (and why are you integrating? surely you know the surface area of a sphere? :wink:)
     
  4. Jan 30, 2012 #3
    Okay, well I know that once I get it to this point, it's right:
    [tex]\int\int_CadS=\int\int_Ca(1)dxdy[/tex]

    The projection of the sphere on the xy-plane is a circle, no? So why can I not use
    [tex]dxdy=rdrd\theta[/tex]?
     
  5. Jan 30, 2012 #4

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    projection? are you treating F as if it was a parallel field along one of the axes? :confused:

    in that case, yes, the projection perpendicular to the field would be a circle

    but the given F is radial ((x,y,z) = t), and constant in magnitude over the sphere,

    so you just need the amount of surface it cuts through, which is 4πa2
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Flux Integral
  1. Flux integral (Replies: 1)

  2. Flux integral (Replies: 7)

  3. Flux Integrals (Replies: 1)

  4. Flux Integral (Replies: 9)

  5. Flux Integrals (Replies: 4)

Loading...