Results 1 to 2 of 2

Math Help - finding potential function of F(x,y,z)

  1. #1
    MHF Contributor
    Joined
    Nov 2008
    Posts
    1,401

    finding potential function of F(x,y,z)

    F(x,y,z)=(4xe^z )i +(cosy)j+[(2x^2+cos^2z)e^z]k

    what is the general theory for finding the potential of this.

    i know only how to find on 2d functions
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor chisigma's Avatar
    Joined
    Mar 2009
    From
    near Piacenza (Italy)
    Posts
    2,162
    Thanks
    5

    Re: finding potential function of F(x,y,z)

    Quote Originally Posted by transgalactic View Post
    F(x,y,z)=(4xe^z )i +(cosy)j+[(2x^2+cos^2z)e^z]k

    what is the general theory for finding the potential of this.

    i know only how to find on 2d functions
    The potential function W, if exists, satisfies the conditions...

    \frac{\partial{W}}{\partial{x}} = - 4 x e^{z} (1)

    \frac{\partial{W}}{\partial{y}} = - \cos y (2)

    \frac{\partial{W}}{\partial{z}} = - (2 x^{2}+ \cos^{2} z) e^{z} (3)

    The (1), (2) and (3) can be integrated independently. The (1) and (2) have no problem, for (3) You take into account that ...

    \int e^{z}\ \cos^{2} z\ dz = \frac{e^{z}}{5}\ (\cos^{2} z + 2 \sin z\ \cos z + 2) + c (4)

    ... so that is...

    W(x,y,z)= - \sin y - \frac{e^{z}}{5}\ (10 x^{2} + \cos^{2} z + 2 \sin z\ \cos z + 2) + c (5)

    Kind regards

    \chi \sigma
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Finding the potential to draw phase planes
    Posted in the Differential Equations Forum
    Replies: 1
    Last Post: June 4th 2012, 07:33 AM
  2. Finding a Potential for a field
    Posted in the Calculus Forum
    Replies: 2
    Last Post: November 23rd 2009, 03:12 AM
  3. potential finding proccess question..
    Posted in the Calculus Forum
    Replies: 1
    Last Post: August 12th 2009, 05:57 AM
  4. Finding a scalar potential.
    Posted in the Calculus Forum
    Replies: 4
    Last Post: May 6th 2009, 12:25 PM
  5. [SOLVED] Potential Zero's and finding the zeros
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: February 7th 2009, 12:40 PM

Search Tags


/mathhelpforum @mathhelpforum