Following the IEEE paper, we turned our interest to other attributes, with the first being rectangular stock. We were able to obtain sample strips of Alfenol and Galfenol, and turned to other materials that are more readily available in rectangular cross sections. From an analysis perspective, while it is relatively trivial to compute the magnetic field produced by conducted current within a circular wire (at DC), it is another matter on a rectangular member. As easy to use equations weren’t available, I had to turn to vector potential, which can be expressed for various geometries and then differentiated by taking the partial derivative to find the magnetic field. The vector potential for a rectangle can be expressed as:
Expanding this was not a trivial task. The field appeared as might be predicted, in which the largest axial field was at the center of the rectangular beam and would fall towards the ends as the flux reorients into the orthogonal direction.
The field at several specific locations on the conductor could be computed, in which the expansion was greatly simplified, ultimately resulting in:
Although an aside, these equations made it much easier to calculate how much field could be produced as a function of applied current for a given rectangular cross section.