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Homework Help: Work done and limit of a vector field.

  1. Dec 1, 2011 #1
    1. The problem statement, all variables and given/known data
    Consider the vector field

    F = r/|r|^p = <x,y,z>/|r|^p

    where p>1. Let C be the line from point (1,1,1) to the point (a,a,a) for a>1.

    (a) Compute work done in moving an object along C.
    (b) Find the limit a->infinity (that is, the work done in moving an object to infinity). For what values of p is the work done finite?

    2. Relevant equations

    ∫[a,b] F(r(t))(dotted with)(r'(t))dt
    lim_a-infinity F = <lim_a-infinity x, lim_a-infinity y, lim_a-infinity z>

    3. The attempt at a solution

    r = <x,y,z>
    so does |r|^p = sqrt(x^2+y^2+z^2)^p?

    if so I have

    F = <x,y,z>/sqrt(x^2+y^2+z^2)^p

    What do I do next?
  2. jcsd
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