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Cross Product Polar Coor

  1. Oct 23, 2008 #1
    I would like to know how to perform a cross product on polar coordinates.

    Thank You
  2. jcsd
  3. Oct 23, 2008 #2


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    Hi tekness! :smile:

    Can you give us an example of two vectors you're trying to cross-product?
  4. Oct 23, 2008 #3

    Hi tim,

    I am just looking for a general way to perform the operation. I will perform a cross product between E and H fields that are in polar coordinates. I don't want to go through the hassle of converting back and forth :).

    I hope this explains it, if not please let me know what else I can add.
  5. Oct 23, 2008 #4


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    Well, so long as the vectors are expressed in terms of perpendicular unit vectors such as ihat and jhat or rhat and thetahat, you just cross-product them the usual way.

    The only problem might be converting into unit vectors. :smile:
  6. Oct 23, 2008 #5
    so for example.
    I have |i j k|
    |rcos() rsin() Z1|
    |r2cos()2 r2sin()2 Z2|

    the 2 is for a different value/angle.
    So just perform the same cross product operation as rectangular coordinates would require?
  7. Oct 23, 2008 #6


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    Hi tekness! :smile:

    (have a theta: θ :smile:)

    I'm a little confused … those look like vectors from the origin. :confused:

    You will generally want to cross-product the fields at a general point.
  8. Oct 23, 2008 #7
    I will try to verify exactly what I need and respond back. Looks like I need to rethink my question.
    Thank you for your help! I will be back asap.
  9. Oct 23, 2008 #8

    Ben Niehoff

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    The confusion is that the cross product is an operation in the tangent space, not in the coordinate space. At a particular point, your field has components in the r-hat, phi-hat, and theta-hat directions. These three vectors constitute an orthonormal basis. So you simply take the cross product without any modification at all. For example,

    [tex]\hat r \times \hat \theta = \hat \phi[/tex]

    and the rest are similar.
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