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Math Help - Work

  1. #1
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    Work

    If  \bold{F}(x,y) = \frac{k(x \bold{i} + y \bold{j})}{x^{2}+y^{2}} find the work done by  \bold{F} in moving a unit charge along a straight line segment from  (1,0) to  (1,1) .

    So  \bold{F}(1,y) = \frac{k(\bold{i} + y \bold{j})}{1 + y^{2}} . Then  x = 1, \ y = y .

     k \int_{0}^{1} \frac{y}{1+y^{2}} \ dy

     u = 1+y^{2}

     du = 2y \ dy

     \frac{k}{2} \int \frac{du}{u}

     = \frac{k}{2} \int_{0}^{1} \ln|1+y^{2}|

     = \frac{\ln 2}{2} .

    Is this correct?
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  2. #2
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    Essentially it the work is just in the y-direction right?
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  3. #3
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    Quote Originally Posted by shilz222 View Post
    Essentially it the work is just in the y-direction right?
    Yes it is, because the displacement is also in the +y direction. (Typically we'd have to take a component of the force along the y direction and wind up with a cosine term, but the force was conveniently in coordinate form to begin with.)

    -Dan
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