Results 1 to 3 of 3

Math Help - Vector field -> rotational

  1. #1
    Super Member
    Joined
    Jun 2008
    Posts
    829

    Vector field -> rotational

    Show that any vector field of the form:
    F(x,y,z) = f(x) i + g(y) j + h(z) k where f, g and h are differentiable, is not rotational
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member Random Variable's Avatar
    Joined
    May 2009
    Posts
    959
    Thanks
    3
    Find the curl of F.

    Curl F =  \Big( \frac { \partial}{\partial y} h(z) - \frac {\partial}{\partial z} g(y) \Big) \hat{i} - \Big( \frac { \partial}{\partial x} h(z) - \frac {\partial}{\partial z} f(x) \Big) \hat{j} + \Big( \frac { \partial}{\partial x} g(y) - \frac {\partial}{\partial y} f(x) \Big) \hat{k}

    And you can clearly see that Curl F = 0.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member
    Joined
    Jun 2008
    Posts
    829
    Quote Originally Posted by Random Variable View Post
    Find the curl of F.

    Curl F =  \Big( \frac { \partial}{\partial y} h(z) - \frac {\partial}{\partial z} g(y) \Big) \hat{i} - \Big( \frac { \partial}{\partial x} h(z) - \frac {\partial}{\partial z} f(x) \Big) \hat{j} + \Big( \frac { \partial}{\partial x} g(y) - \frac {\partial}{\partial y} f(x) \Big) \hat{k}

    And you can clearly see that Curl F = 0.
    Ok. Thank you
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Ring, field, Galois-Field, Vector Space
    Posted in the Advanced Algebra Forum
    Replies: 4
    Last Post: November 15th 2012, 03:25 PM
  2. Vector Field
    Posted in the Calculus Forum
    Replies: 9
    Last Post: March 24th 2012, 01:50 AM
  3. Vector field help
    Posted in the Calculus Forum
    Replies: 5
    Last Post: March 16th 2010, 05:49 PM
  4. Vector Field
    Posted in the Calculus Forum
    Replies: 2
    Last Post: June 1st 2009, 01:44 PM
  5. vector field
    Posted in the Calculus Forum
    Replies: 0
    Last Post: May 1st 2009, 07:34 PM

Search Tags


/mathhelpforum @mathhelpforum