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Coulomb's Law and simple harmonic motion

  1. Jun 29, 2010 #1
    1. The problem statement, all variables and given/known data
    Two identical particles, each having a charge of +q are fixed in space and separated by a distance d. A third particle with charge -Q is free to move and lies initially at rest on the perpendicular bisector of the two fixed charges a distance x from the midpoint between the two fixed charges. Show that if x is small compared with d, the motion of -Q is simple harmonic along the perpendicular bisector. Determine the period of that motion. How fast will the charge -Q be moving when it is at the midpoint between the two fixed charges if it is initially released at a distance a << d from the midpoint?


    2. Relevant equations
    Fe= ke[tex]\frac{(q_1)(q_2)}{r^2}[/tex]
    -kx=max I'm not completely sure if I need this one, but the problem wants me to show that -Q is simple harmonic so I was thinking that I might need to set these equal to each other somehow, but I'm absolutely lost as to where to go.


    3. The attempt at a solution
     
  2. jcsd
  3. Jun 29, 2010 #2

    collinsmark

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    I believe your interim goal is to show that the net force is proportional to x, for small x. Because if that's the case, the force resembles that of a spring (force being proportional to x).

    I suggest first finding the equation for the net force on -Q. (First without making any assumptions.)

    Secondly, once you have your net force equation, make the assumption that x is small compared to d. See what happens. :wink:
     
  4. Jun 29, 2010 #3

    kuruman

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