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A problem about surface element

  1. Feb 16, 2013 #1
    I really don't know how to do this question as it asks me to write the surface element of a hemisphere in xyz coordinates. I know how to answer if it is asked in spherical coordinates.

    I think this is a tricky question because it asks for the portion da near (0, A, 0) (in xyz) where A is the radius.

    I guess da = dydz.
     

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    Last edited by a moderator: Feb 16, 2013
  2. jcsd
  3. Feb 16, 2013 #2

    SammyS

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    That doesn't look very vector-like.

    attachment.php?attachmentid=55804&d=1361038640.png

    You say you know the answer in spherical coordinates. What is the answer in spherical coordinates?
     
  4. Feb 16, 2013 #3
    it should be r^2sin(θ)dθdϕ (unit vector r)
     
  5. Feb 16, 2013 #4

    SammyS

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    What is the value of θ at (x,y,z) = (0,A,0) ? ... the value of r ?
     
  6. Feb 16, 2013 #5
    it is equal to 90 degree or pi/2
    so i should plug this valve to the expression?
    i have tried but the question needs me to express it in xyz coor,
    how to deal with (unit vector of r)?
     
  7. Feb 16, 2013 #6

    SammyS

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    At the point, (0,A,0), what is [itex]\ \hat{r}\ [/itex] in terms of [itex]\ \hat{i},\,\hat{j},\,\hat{k}\ ?[/itex]
     
  8. Feb 16, 2013 #7
    O, I get what u mean

    at (0 A 0) , the r is along the y axis, so 0i, 1j , 0k ?
     
  9. Feb 16, 2013 #8

    SammyS

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    Just put this with dydz.
     
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