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Electric dipole - derive torque from pot. energy

  1. Jul 2, 2011 #1
    1. The problem statement, all variables and given/known data

    Derive equation of torque: G = p X E from equation U = -p[itex]\cdot[/itex]E

    2. Relevant equations

    G = [itex]\int x \times \rho(x)E dV[/itex]

    U = [itex]\int \rho(x)x \cdot \nabla\varphi dV [/itex]


    3. The attempt at a solution
    I tried to figure how to represent G in a way that better express the nature of the problem. so I figured maybe G = r x F but then got stuck again...
     
  2. jcsd
  3. Jul 3, 2011 #2
    Use the relationship between the work and change of the energy.
     
  4. Jul 3, 2011 #3
    A shot:

    [itex]G = - \frac{\partial U}{\partial\theta}
    = - \frac{\partial(-p \cdot E)}{\partial\theta}
    = \frac{\partial(pEcos\theta)}{\partial\theta}
    = - pEsin\theta
    = - p \times E
    [/itex]


    did I get it all-right?
     
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