Results 1 to 4 of 4

Math Help - Surface Integral of a Vector Field

  1. #1
    Newbie
    Joined
    Oct 2012
    From
    Singapore
    Posts
    4

    Surface Integral of a Vector Field

    Hi guys, need some assurance here in evaluating this surface integral.

    \iint_{S} \mathbf{F}\cdot d\mathbf{S}
    where

    \mathbf{F} = \left \langle x^2+y^2+z^2, -2xy+\sin(z), 2z  \right \rangle, (x,y,z)\in \mathbb{R}^3
    and

    S:x^2+y^2+(z-5)^2=1 with positive orientation (outward pointing normal).

    Here's what I did:
    Using Green's theorem (Divergence theorem)

    \textup{div }\mathbf{F}=2x-2x+2=2

    \iint_{S} \mathbf{F}\cdot d\mathbf{S}= \iiint_{E} \textup{div }\mathbf{F } dV
    =2\iiint_{E}  dV=2(\textup{volume of sphere})=2( \frac{4}{3} \pi r^3 )=\frac{8\pi}{3}

    Anything wrong with what I did?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Newbie
    Joined
    Oct 2012
    From
    Singapore
    Posts
    4

    Re: Surface Integral of a Vector Field

    Bump... Not even a 'OK' or 'Good' or 'Wrong'?

    Lol I've done the question already, only need someone to assure me this is the right way to go.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,412
    Thanks
    1328

    Re: Surface Integral of a Vector Field

    I thought I had responded to this, yesterday. Did you post on more than one forum?

    Yes, what you have done is completely correct. I considered suggesting you check by doing the surface integral directly but that "sin(z)" makes things horrible!
    Last edited by HallsofIvy; December 6th 2012 at 08:45 AM.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Oct 2012
    From
    Singapore
    Posts
    4

    Re: Surface Integral of a Vector Field

    Quote Originally Posted by HallsofIvy View Post
    I thought I had responded to this, yesterday. Did you post on more than one forum?

    Yes, what you have done is completely correct. I considered suggesting you check by doing the surface integral directly but that "sin(z)" makes things horrible!
    Thanks!
    Yes I posted on another forum, on which you replied as well. Thanks for both instances!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Flux of vector field through a surface.
    Posted in the Calculus Forum
    Replies: 1
    Last Post: May 8th 2011, 04:08 AM
  2. Conical surface and vector field
    Posted in the Calculus Forum
    Replies: 4
    Last Post: May 17th 2010, 05:31 AM
  3. Replies: 0
    Last Post: March 29th 2010, 06:17 AM
  4. Integral field vector
    Posted in the Calculus Forum
    Replies: 10
    Last Post: April 27th 2009, 11:38 AM
  5. vector field on surface
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: January 26th 2009, 10:35 AM

Search Tags


/mathhelpforum @mathhelpforum