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Show that the vector has zero divergence

  1. Sep 9, 2011 #1
    1. The problem statement, all variables and given/known data
    Show that the vector
    v = [itex]\frac{\hat{r}}{r2}[/itex] (not sure why formatting isn't working?)

    v = (r-hat) over (r squared)

    has zero divergence (it is solenoidal) and zero curl (it is irrotational) for r not equal to 0


    2. Relevant equations
    div(V) = (d/dx)V_x + (d/dy)V_y + (d/dz)V_z


    3. The attempt at a solution

    I used del operator in spherical (the r component being (d/dr)) and it didn't seem to work?
    for curl i was able to get curl(v) = 0
    I've tried converting v to cartesian and using the cartesian del operator but it didn't work either
    I'm stuck at this point =\
     
  2. jcsd
  3. Sep 9, 2011 #2

    Mute

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  4. Sep 9, 2011 #3

    vela

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    Don't use the BBcode tags within LaTeX mark-up.

    Also, if you're going to use LaTeX, use it for the whole equation instead of bits and pieces. It's easier to type, and it'll look better.
     
  5. Sep 9, 2011 #4

    HallsofIvy

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    Also, you might need to refresh your screen to get the LaTeX to work.
     
  6. Sep 12, 2011 #5
    thanks everyone!

    few questions though,
    1) where can I find a guide on posting LaTeX code on the forums?

    2) does the 1/(r^2) * (r^2 * v_r): does the r^2 come from metric coefficients?
     
  7. Sep 14, 2011 #6

    Mute

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    1) See https://www.physicsforums.com/showthread.php?t=386951 [Broken] to get started.

    2) I'm not sure what you mean by metric coefficients. These factors show up for similar reasons as to why the volume element in spherical coordinates is r2 sin(theta). A vector calculus book should explain it in the section about grad, div and curl in different coordinate systems. Maybe even the wiki page I linked to earlier explains it?
     
    Last edited by a moderator: May 5, 2017
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