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Electrostatics Question

  1. Jan 13, 2017 #1
    1. The problem statement, all variables and given/known data
    In the figure particles 1 and 2 are fixed in place on an x axis, at a separation of L = 7.30 cm. Their charges are q1 = +e and q2 = -27e. Particle 3 with charge q3 = +3e is to be placed on the line between particles 1 and 2, so that they produce a net electrostatic force on it.
    At what coordinate should particle 3 be placed to minimize the magnitude of that force?

    The figure shows particle 1 at x=0 and particle 2 at x=7.30 cm.

    2. Relevant equations
    Setting x equal to the x coordinate where q3 would be.

    3. The attempt at a solution
    F = k3e^2(x^-2+[27]/[L^2 - 2Lx + x^2]) (factored out k, q3 [3e], and then e from the two charges)
    So from here you want to find the critical points. So I took the derivative and set it equal to 0 (also got rid of 3ke^2):
    0 = -2x^-3 + (0 - 27[-2L+2x])/(L^2 - 2Lx + x^2)^2
    I rearranged it to this (assuming I made no mistakes):
    0 = x^-3 * [56x^4 - (62L)x^3 + (12L^2)x^2 - (8L^3)x + 2L^4]
    I have no idea how to solve for x in this case and we're not permitted graphing calculators, so how would you attempt this question?
  2. jcsd
  3. Jan 13, 2017 #2


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    I recommend not squaring out the ##(L-x)^2## in the denominator of the second force. Thus, you want to minimize the function ##f(x) = \frac{1}{x^2} + \frac{27}{(L-x)^2}##.
  4. Jan 14, 2017 #3
    Thanks, now I got it.
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