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[Electromagnetism] How much work is required in moving Q3 to infinity?

  1. Jan 30, 2012 #1
    1. The problem statement, all variables and given/known data

    How much work is required in moving Q3 to infinity while Q1 and Q2 remain in their positions?

    |-----------------| b

    a = 16.0 cm
    b = 6.0 cm
    Q1 = 5.70 μC
    Q2 = -5.70 μC
    Q3 = 1.8 μC

    2. Relevant equations


    3. The attempt at a solution

    Just added the potential energies associated with Q3 which is the work needed to move Q3 to infinity (i.e. bring said potential energies to 0).
    kQ1Q3/r13 + kQ2Q3/r23
    =(8.9875e9)(5.7e(-6))(1.80e(-6))/0.06 + (8.9875e9)(-5.7e(-6))(1.8e(-6))/sqrt(0.06^2 + 0.16^2)
    =0.997 J

    Also tried calculating ΔPE = final - initial (I think I messed up the formula, but somehow I got the negative of the first one)
    (8.9875e9)(5.7e(-6))(-5.7e(-6))/.16 + 0.827790168702400828475759973771078927721678492943077184393)
    = -0.997 J

    Trying ΔPE again:
    kQ1Q2/r12 - (kQ1Q3/r13 + kQ2Q3/r23 + kQ1Q2/r12)
    =-kQ1Q3/r13 - kQ2Q3/r23
    =-(8.9875e9)(5.7e(-6))(1.8e(-6))/0.06 - (8.9875e9)(-5.7e(-6))(1.8e(-6))/sqrt(0.06^2 + 0.16^2)
    = -0.997 J

    What am I supposed to do? Neither of these work.
  2. jcsd
  3. Jan 30, 2012 #2


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper

    Yes. And you realize ΔPE is PEfinal - PEinitial, right?

    No, the work needed is ΔPE, which is PEfinal - PEinitial.
    You have calculated PEinitial here. You want PEfinal-PEinitial.
    Your second answer (the negative one) looks correct to me. However if I use a rounded-off version of k, 8.99e9 N*m2/C2, then the answer rounds off to -0.998 J.

    p.s. please don't report results, even intermediate calculations, to 50 significant figures. It just clutters up your work unnecessarily for people who are trying to follow your calculation.
  4. Jan 30, 2012 #3


    User Avatar
    Gold Member

    Are you submitting this to a computer? I'm not sure how many significant digits your answer should have, but have you tried -1.0?
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