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Derivation of PEcos(θ) for diploles in constant Efield?

  1. Jul 23, 2013 #1
    I know that the potential energy of a dipole in a constant electric field is

    P(dot)E=PEcos(θ), but I cant seem to find how they got here; its not in my textbook.

    If anyone knows why please tell me.
     
  2. jcsd
  3. Jul 23, 2013 #2

    vanhees71

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    A straight-forward way is to just use two charges of the same magnitude [itex]Q[/itex] and opposite sign located at the origin and at [itex]\vec{r}_0[/itex] (negative charge in the origin). The total potential energy of this charge distribution in the homogeneous electric field is
    [tex]V=-Q \vec{r}_0 \cdot \vec{E}.[/tex]
    Now the dipole moment is given for the limit [itex]\vec{r}_0 \rightarrow 0[/itex] such that [itex]Q \vec{r}_0=\vec{P}=\text{const}.[/itex] This leads to
    [tex]V=-\vec{P} \cdot \vec{E}.[/tex]
    QED.
     
    Last edited: Jul 23, 2013
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