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Work done by moving unit charge along straight line segment

  1. Nov 26, 2007 #1
    If [tex] \bold{F}(x,y) = \frac{k(x \bold{i} + y \bold{j})}{x^{2}+y^{2}} [/tex] find the work done by [tex] \bold{F} [/tex] in moving a unit charge along a straight line segment from [tex] (1,0) [/tex] to [tex] (1,1) [/tex].

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

    [tex] k \int_{0}^{1} \frac{y}{1+y^{2}} \ dy [/tex]

    [tex] u = 1+y^{2} [/tex]

    [tex] du = 2y \ dy [/tex]

    [tex] \frac{k}{2} \int \frac{du}{u} [/tex]

    [tex] = \frac{k}{2} \int_{0}^{1} \ln|1+y^{2}| [/tex]

    [tex] = \frac{k\ln 2}{2} [/tex].

    Is this correct?
     
    Last edited: Nov 26, 2007
  2. jcsd
  3. Nov 27, 2007 #2

    HallsofIvy

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    Looks perfectly good to me.
     
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