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Electric Charge and Coulomb's Law

  1. Jan 15, 2008 #1
    Coulomb's Law Problem - Please Help

    1. The problem statement, all variables and given/known data
    Two positive charges +Q are held fixed a distance d apart. A particle of negative charge -q and mass m is placed midway between them, then is given a small displacement perpendicular to the line joining them and released. Show that the particle describes simple harmonic motion of period sqrt((epsilon not)m((pi)^3)(d^3))/(qQ).


    2. Relevant equations



    3. The attempt at a solution

    SO I calculated the resultant force on the Q charge at any point and found it to be [((sqrt(2))qQ)]/[4pi(epsilon not)(r^2)). I then saw that F=-kz and T = 2pi*sqrt(m/k).
    After plugging everything in and seeing that z was neglible when compared to d/2, I came up with several different answers all the same as sqrt((epsilon not)m((pi)^3)(d^3))/(qQ) only I had coefficients in the numerator and denominator. I have no idea what I am doing wrong? Also, how do you prove it is simple harmonic motion?

    Here's what I did:

    I said that r is approx. equal to d/2. and z is rsin(theta). After I pug this all in to T = 2p*sqrt(m/k) I get T = sqrt([16(pi^3)(epsilon not)m(r^3)sin(theta)]/[sqrt(2)qQ]).
    I don't get what I am doing wrong. Plz help...thx.
     
    Last edited: Jan 15, 2008
  2. jcsd
  3. Jan 16, 2008 #2

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