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I Field Lines of an Electric Dipole?

  1. Oct 11, 2016 #1

    It isn't difficult to find the electric field of a dipole.

    However, it is tricky to find the field lines. All points of a field line have to be parallel to the electric field at those points. A tangent, which is the derivative, is parallel.

    We can hence formulate the equation for a field line as the solution to a first order differential equation.

    I have already done so, but I haven't been able to solve it. Google has not been my friend either.

    Does anyone know of the equations that describe the field lines?
  2. jcsd
  3. Oct 11, 2016 #2
  4. Oct 12, 2016 #3


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    Science Advisor
    Gold Member

    If you show the approach you are taking it will be easier to help you. In any case, I have a couple of suggestions:

    1) use the `far-field' approximation, which means in the denominator of your electrostatic potential, let ##a \rightarrow 0##. This also provides the first term of the multipole expansion, and is what people often mean when talking about a dipole field.

    2) align your dipole with the z axis and use spherical coordinates.

    When I do these two things I get an ODE that is elementary.

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