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Calculus 3: Work

  1. Dec 16, 2013 #1
    1. The problem statement, all variables and given/known data

    An electric dipole with dipole moment p = 4 × 10−5 C-m sets up
    an electric field (in newtons per coulomb)

    F(x,y,z) = [itex]kp/r^5[/itex] <3xz, 3yz, 2z[itex]^{2}[/itex] - x[itex]^{2}[/itex] - y[itex]^{2}[/itex]>

    where r = (x[itex]^{2}[/itex] + y[itex]^{2}[/itex] + z[itex]^{2}[/itex])[itex]^{1/2}[/itex] with distance in meters and k = 8.99 ×
    109 N-m[itex]^{2}[/itex]/C[itex]^{2}[/itex]. Calculate the work against F required to move a particle
    of charge q = 0.01 C from (1,−5, 0) to (3, 4, 4). Note: The force on
    q is qF newtons.

    2. Relevant equations

    ∫[itex]^{b}_{a}[/itex] F(c(t)) * c'(t) dt

    3. The attempt at a solution

    I know that I need to set ∇f = F and find a potential function. I'm not sure what the parametric equation should be.
     
  2. jcsd
  3. Dec 18, 2013 #2
    Perhaps you don't need to calculate the potential at all. Seems like you get work directly from the force, according to your formula.

    The path parametrization depends on the path of course. It seems a path is not specified in the problem. Why is it not needed to solve the problem?
     
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