Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    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

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    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

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    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

    User Avatar
    Science Advisor
    Gold Member

    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.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Cross Product Polar Coor
  1. Cross product (Replies: 15)

  2. Cross product! (Replies: 3)

Loading...