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Coulomb's law three points on a line

  1. Jun 20, 2014 #1
    1. The problem statement, all variables and given/known data
    Three point charges, q1, q2 and q3 all on x-axis (i.e y=0 and z=0)
    +q1 at x = 0
    -q2 at dist from origin x = a
    +q3 at dist from origin x = -2a
    where q1, q2 and q3 are magnitudes of the charges.

    Assuming q1 = q2 derive magnitude of q3 in order for there to be zero net force on q1.


    2. Relevant equations
    Coulombs law
    F12 = (q1 * q2) / (r12)2 rhat12



    3. The attempt at a solution
    attempt 1
    in order for there to be no force on q1 then,
    -q2(a) = q3(2a)
    so
    q3 = (-q2*a)/2a = -q2/a

    bit too simplistic?

    or attempt 2
    F12 = 1/4*∏*ε0 * (q1*q2) / (r12)2 rhat12 .
    F12 = 1/4*∏*ε0 * (q1*q2) / (a2) ex

    F13 = 1/4*∏*ε0 * (q1*q3) / (r13)2 * rhat12
    F13 = 1/4*∏*ε0 * (q1*q3) / (-2a2) -ex


    Resultant
    magnitude F1 = 0 = 1/4*∏*ε0 * ((q1*q2) / (a2) ex + (q1*q3) / (-2a2) -ex

    agh, run out of input time, will be back
    Am I on the right track?
     
  2. jcsd
  3. Jun 20, 2014 #2

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    What does that mean? Charge as function of distance?

    That equation cannot be true.

    In attempt 2, there are many missing brackets. Apart from that, it looks good.
     
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