Results 1 to 2 of 2

Math Help - Divergence and Curl

  1. #1
    Newbie
    Joined
    Mar 2008
    Posts
    1

    Exclamation Divergence and Curl

    Hey guys ive been asked to calculate the divergence and curl of the vector function:
    V(x,y,z)= (xi + yj + zk)/r^2

    where r^2=(x^2)+(y^2)+(z^2)

    Any help would be great i dont know where to begin with this one!!!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by marz_cro View Post
    Hey guys ive been asked to calculate the divergence and curl of the vector function:
    V(x,y,z)= (xi + yj + zk)/r^2

    where r^2=(x^2)+(y^2)+(z^2)

    Any help would be great i dont know where to begin with this one!!!
    How about beginning by looking at the definitions? What do they suggest you need to do ....?

    Finding \frac{\partial V_1}{\partial x} is hackwork much better left for you to do. But once found, you can use symmetry to easily write down:

    \frac{\partial V_2}{\partial y} (just swap x and y around in your answer for \frac{\partial V_1}{\partial x}), and

    \frac{\partial V_3}{\partial z} (just swap x and z around in your answer for \frac{\partial V_1}{\partial x}).


    Of course, you could always recognise that \boldsymbol{V} = \frac{\boldsymbol{r}}{r^2} = \frac{\hat{\boldsymbol{r}}}{r} and find div and curl in an appropriate alternative coordinate system ...


    PS. I assume you're OK with the level curve question doing the rounds from this assignment .......
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Divergence and Curl
    Posted in the Calculus Forum
    Replies: 5
    Last Post: July 6th 2010, 02:42 PM
  2. Curl and Divergence
    Posted in the Calculus Forum
    Replies: 5
    Last Post: November 18th 2009, 04:25 PM
  3. Divergence and Curl???
    Posted in the Advanced Applied Math Forum
    Replies: 2
    Last Post: November 10th 2009, 03:09 AM
  4. Differentiation Equation Curl, Divergence
    Posted in the Calculus Forum
    Replies: 4
    Last Post: July 12th 2009, 12:00 PM
  5. del operator, divergence , and the curl
    Posted in the Calculus Forum
    Replies: 1
    Last Post: May 23rd 2009, 05:18 AM

Search Tags


/mathhelpforum @mathhelpforum