# I Field Lines of an Electric Dipole?

1. Oct 11, 2016

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. Oct 11, 2016

3. Oct 12, 2016

### 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