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Homework Help: Using Coulomb's Law

  1. Apr 6, 2009 #1
    1. The problem statement, all variables and given/known data

    Given: Two similar tiny balls of mass M are hung from silk threads of length L and carry equal charges q. An angle is formed where the two threads meet which we'll call [tex]\phi[/tex] (This angle is actually divided in half and each half is called [tex]\theta[/tex])

    Assume that [tex]\theta[/tex] is so small that tan [tex]\theta[/tex] can be replaced by its approximate equal, sin [tex]\theta[/tex].

    I'm supposed to show that, for the following approximation, the distance between the two charges, x, in equilibrium, is equal to:

    x = [((q^2)L) / 2 [tex]\pi[/tex] [tex]\epsilon[/tex]sub 0 (m)(g)]^(1/3)

    2. Relevant equations

    Obviously, Coulomb's Law plays a major role in determining the outcome of this problem, but I'm yet unsure of where and how I actually apply it...

    Since mass is given to us, I assume that I'll have to use F = ma or some derivation of it to find the force that will be used in Coulomb's Law...

    3. The attempt at a solution

    Since they give the length of the thread, I figure that 1/2 x is going to be equal to the tangent of [tex]\theta[/tex], but since tan is to be replaced with sin, I'm not exactly sure where this leaves me...

    I really didn't know where to start with this one, so, even if you can offer direct advice, even a point in the right direction would be nice...
  2. jcsd
  3. Apr 6, 2009 #2


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    Homework Helper

    In equilibrium position, the ratio of the forces to the sin of opposite angle are constant.
    In the problem the forces are tension T, electrostatic force F and weight of the balls mg.
    Identify the angles opposite to these forces and apply above rule.
  4. Apr 7, 2009 #3
    Thanks, I was able to get the right answer, I appreciate the helpful tip.

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