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Line integral around a circle, using polar coordinates

  1. Oct 5, 2014 #1
    Given the force (derived from a potential in planar polar coordinates)

    [tex]F(p,w) = 2p+sin(w)e_p+cos(w)e_w [/tex] Where e_p and e_w are unit vectors

    How do I calculate the line integral over a circumference that is defined as:
    p = 2
    0 ≤ w ≤ 2pi

    Using the definition of a line integral [tex] \int_0^{2pi} \! F(p,w) . \, \mathrm{d}r [/tex]

    What confuses me though is what the "dr" term would be in this case? Do I need to do some form of parametrisation, in that case, how?

    Thank you!
  2. jcsd
  3. Oct 5, 2014 #2


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    I am confused by your use of "p" and "w" for both the parameters and the unit vector subscripts. In particular, does e_w change when w changes? Or is it fixed?

    In any case, since e_p and e_w are unit vectors, you can write them as (cos_p, sin_p) and (cos_w, sin_w). The values of (cos_w and sin_w) may be functions of w.

    I think you will have to parameterize the path in order to define the line integral. Since w runs from 0 to 2*pi, I think that is a good parameter to use.
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