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Line integral

  1. Jan 24, 2006 #1
    i have a force field F = 2xy*(ux)+(x^2-z^2)(uy)-3xz^2(uz) where ux,uy,and uz are unit vectors in the direction indicated. I have to find the work done by the field on a particle that travels from A(0,0,0) to
    B(2,1,3) on a straight line. work is regarded as the integral from A to B of the dot product of F and dl = dx(ux)+dy(uy)+dz(uz). I'm not quite sure how to do this.
     
  2. jcsd
  3. Jan 24, 2006 #2

    siddharth

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    You can introduce a common vairable of integration to solve this.
    Since
    [tex] \int_{A}^{B} \vec{F}.d\vec{r} = \int_{t1}^{t2} \vec{F}.(\vec{\frac{dr}{dt}}) dt [/tex]

    Where [tex]\vec{r} [/tex] (and F) can be expressed as a function of t.
     
    Last edited: Jan 24, 2006
  4. Jan 24, 2006 #3
    ok, thanks
     
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