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Harmonic oscillations and electric dipoles

  1. May 23, 2004 #1
    Hi there, I was hoping that someone would be kind enough to help me out with this question. I don't even know where to start :yuck:

    Use T=Ia (where T=torque) to show that if an electric dipole with dipole moment of magnitude p and moment of inertia I is oriented with its dipole moment making a small angle theta with the direction of an external electric field of magnitude E, the dipole will execute simple harmonic oscillations about the field direction with a frequency v given by:

    v= [1/(2pi)] [(pE)/I]^1/2
     
  2. jcsd
  3. May 24, 2004 #2

    turin

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    Homework Helper

    The dipole moment and electric field will give you the torque, which is the L.H.S. of the equation τ = I α. (Big hint: it will involve orientation as a function of time, θ(t))

    For the R.H.S., you need to replace angular acceleration α with a second order derivative. (Big hint: it will involve orientation as a function of time, θ(t))

    Then, solve the diff. eq. The solution should be sinusoidal (with a frequency, ν).
     
    Last edited: May 24, 2004
  4. May 24, 2004 #3
    I'm sorry... I'm still lost. I have no idea how to do any of that. How do you take the derivative if you don't know the value?
     
  5. May 25, 2004 #4
    ok I figured it out!!! Thanks for your help!!!

    :biggrin:
     
  6. May 25, 2004 #5

    turin

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    Very cool. However, I am curious:


    How did you go from:
    to:
    ?
     
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