Results 1 to 5 of 5
Like Tree1Thanks
  • 1 Post By romsek

Math Help - Gauss's Theorem

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

    Gauss's Theorem

    Hello.

    Greetings,

    How is the following solved:

    In exercises 1-4, use Divergence Theorem to calculate the flux of the given vector field out of the sphere ("sign that looks like &, I am not sure what it is called") with equation x2+ y2 = a2 , where a > 0.

    1. F = (x2 + y2)i + (y2 - z2)j + zk

    div F = 2x + 2y + 1

    I am aware that Ill need to use the formula for a volume of a sphere:

    V = (4/3)πr3

    But to calculate this triple integral or flux I might need bounds of integration - how are they found if required?

    Sincere regards from user, Kaemper
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Nov 2013
    From
    California
    Posts
    2,485
    Thanks
    961

    Re: Gauss's Theorem

    did you forget a $z^2$ in the equation for your sphere? You've described an infinite cylinder.
    Follow Math Help Forum on Facebook and Google+

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

    Re: Gauss's Theorem

    I did forget to tell you this:

    "With equation x2 + y2 + z2 = a2, where a > 0".
    Last edited by kaemper; March 20th 2014 at 12:46 AM.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Joined
    Nov 2013
    From
    California
    Posts
    2,485
    Thanks
    961

    Re: Gauss's Theorem

    take your expression for $\nabla \cdot F$ and convert it to spherical coordinates and do the 3D integral in spherical coordinates over

    $0\leq \rho \leq a$

    $0\leq \theta \leq \pi$

    $0 \leq \phi \leq 2\pi$
    Thanks from kaemper
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Junior Member
    Joined
    Mar 2014
    From
    Denmark
    Posts
    55

    Re: Gauss's Theorem

    I did as requested and got following result:

    Gauss's Theorem-scan_april-1-2014-6-57-01-290-pm.png

    Please notice I have two versions of the convertion from cartesian coordinates to spherical coordinates. I think the last one is the correct one.

    Best regards
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Gauss bonnet theorem
    Posted in the Differential Geometry Forum
    Replies: 3
    Last Post: May 7th 2013, 06:43 AM
  2. Gauss's theorem, gradient
    Posted in the Calculus Forum
    Replies: 0
    Last Post: April 1st 2011, 10:43 AM
  3. A theorem of Gauss
    Posted in the Math Challenge Problems Forum
    Replies: 1
    Last Post: June 7th 2010, 04:01 PM
  4. Gauss Divergence Theorem
    Posted in the Calculus Forum
    Replies: 3
    Last Post: May 13th 2010, 05:04 AM
  5. Gauss' Theorem
    Posted in the Calculus Forum
    Replies: 2
    Last Post: May 7th 2010, 03:38 PM

Search Tags


/mathhelpforum @mathhelpforum