Results 1 to 4 of 4

Math Help - DivF, Flux integral, centroid

  1. #1
    Junior Member
    Joined
    Mar 2014
    From
    Denmark
    Posts
    55

    DivF, Flux integral, centroid

    DivF, Flux integral, centroid-fluxintegral3.png
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,713
    Thanks
    1472

    Re: DivF, Flux integral, centroid

    In the first problem you are given \vec{F}= x^2\vec{i}+ y^2\vec{j}+ z^2\vec{k} and are asked to find it flux out of the ball (x- 2)^2+ y^2+ (z- 3)^2\le 9. div F= \nabla\cdot F= 2x+ 2y+ 2z (you have 2x\vec{i}+ 2y\vec{j}+ 2z\vec{k} but that is corrected in the integral so I assume that was a typo).

    You do the integral by writing it as 2V\overline{x}+ 2V\overline{y}+ 2V\overline{z} and then try to calculate \overline{x}, \overline{y}, and \overline{z}. You realize, do you not that those are just the coordinates of the center of the figure? Here that figure is a sphere with center at (2, 0, 3) so you should be able to write down, with no calculation at all, that \overline{x}= 2, \overline{y}= 0, and \overline{z}= 3.

    I have no idea at all how you got " \overline{x}= x^2"! You understand, don't you, that the x coordinate of the centroid of a figure is a number not a function of x? And it certainly is NOT the case that \int\int\int xdV= x^2V!
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Mar 2014
    From
    Denmark
    Posts
    55

    Re: DivF, Flux integral, centroid

    I give sincere thanks to HallsofIvy who has generously presented me with the most promising answer imaginable. I address you directly, HallsofIvy:

    I do have received teaching in pre-calculus math: I was just insecure about the term "centroid".

    Yours,

    Student, Chemistry (Bachelor) at University of Southern Denmark (SDU).
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Junior Member
    Joined
    Mar 2014
    From
    Denmark
    Posts
    55

    Re: DivF, Flux integral, centroid

    So the flux out of the ball is the following:

    DivF, Flux integral, centroid-flux3.png
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: September 15th 2012, 12:18 PM
  2. Flux integral
    Posted in the Calculus Forum
    Replies: 2
    Last Post: June 23rd 2012, 01:12 PM
  3. Flux integral
    Posted in the Calculus Forum
    Replies: 0
    Last Post: July 13th 2010, 06:03 PM
  4. divF
    Posted in the Calculus Forum
    Replies: 0
    Last Post: December 8th 2009, 12:01 PM
  5. estimate divF
    Posted in the Calculus Forum
    Replies: 3
    Last Post: April 22nd 2009, 05:57 PM

Search Tags


/mathhelpforum @mathhelpforum