Results 1 to 4 of 4

Math Help - Finding Flux

  1. #1
    Newbie
    Joined
    Jul 2009
    Posts
    9

    Finding Flux

    Another question I'm having trouble with is:

    "Find the flux of F(x,y,z) = -yi + xj + (6z^2)k out of the closed surface S, bounded by the paraboloids z = 4 - x^2 - y^2 and z = x^2 + y^2."

    I can get the graph drawn easily enough, I just can't figure out what the limits of my integration should be.

    Any assistance would be much appreciated.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Jan 2009
    Posts
    715
    Quote Originally Posted by Katzenjammer View Post
    Another question I'm having trouble with is:

    "Find the flux of F(x,y,z) = -yi + xj + (6z^2)k out of the closed surface S, bounded by the paraboloids z = 4 - x^2 - y^2 and z = x^2 + y^2."

    I can get the graph drawn easily enough, I just can't figure out what the limits of my integration should be.

    Any assistance would be much appreciated.

    the domain is  D = [(x,y,z)\in \mathbb{R}^3 |  x^2 + y^2 \leq z \leq 4 - x^2 - y^2 , x^2 + y^2 \leq 2 ]

    or cylinder coordinates :

     D = [(r,\theta,z) \in \mathbb{R}^3 | r^2 \leq z \leq 4 - r^2 ~, 0 \leq r \leq \sqrt{2} ~, 0 \leq \theta \leq 2\pi ]
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Jul 2009
    Posts
    9
    This may sound dumb, but can I break this into two separate flux integrals? Since they are two paraboloids that meet at z=2, is that a good way to go about it?

    And I'm thinking the top paraboloid would be "oriented upward" and the bottom paraboloid would be "oriented downward", yes?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor Calculus26's Avatar
    Joined
    Mar 2009
    From
    Florida
    Posts
    1,271
    you have to break it into 2 parts

    if the orientation is outward

    the upper part has formula z= 4 - x^2 -y^2

    with Normal N = 2x i +2y j + k

    For the bottom z = x^2 + y^2

    With N = 2x i +2 y j - k

    The domain of integration however is the same in both cases
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [Electric Power] Solenoid, finding Flux
    Posted in the Math Topics Forum
    Replies: 1
    Last Post: November 17th 2011, 01:16 AM
  2. finding outward flux of the field
    Posted in the Calculus Forum
    Replies: 3
    Last Post: July 18th 2011, 01:07 PM
  3. Finding total outward flux?
    Posted in the Calculus Forum
    Replies: 3
    Last Post: December 13th 2009, 11:03 AM
  4. finding flux through a surface
    Posted in the Calculus Forum
    Replies: 0
    Last Post: November 17th 2009, 05:41 PM
  5. Magnetic Flux & Magnetic Flux Density
    Posted in the Calculus Forum
    Replies: 2
    Last Post: December 2nd 2006, 05:20 PM

Search Tags


/mathhelpforum @mathhelpforum