In the previous article we introduced the Vortex ring and derived the governing equations. We found that the voltage developed on the sense coil could be described by the following equation:

We also defined a rough process for designing the ring.

### Ring Parameters

The first step is to select the material and dimensions of the ring itself. For a proof of concept, it is unnecessary and expensive to create a custom ring and so instead I looked online for existing solutions. Luckily, toroidal ferrite cores are a common component for creating inductors and transformers. These are effectively just a ring of a high permeability material which is exactly what I need – although they aren’t generally made to fit on a finger. The best solution I found was the TDK Electronics B64290L0647X038 which has an inner diameter of 17.7mm, an outer diameter of 31.0mm and a length of 16.1mm. The magnetic permeability is about 10000 which is pretty good. This is definitely a chunky ring and barely fits on my finger, but it was the best off-the-shelf compromise I could find for now. The effective area and effective magnetic length can be read from the data sheet as 76.98mm^{2} and 73.78mm.