1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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
    F=kqq/r^2
    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

    TSny

    User Avatar
    Homework Helper
    Gold Member
    2017 Award

    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.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted