Field Lines of an Electric Dipole?

[tade]

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?

 

[tade]

This is the DE I formulated: https://www.wolframalpha.com/input/...(y/((x+a)^2+y^2)^(3/2)-y/((x-a)^2+y^2)^(3/2))

So the separation of the two charges would be 2a.

 

[jasonRF]

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.

Jason