I'm looking at redesigning a hydraulic solenoid valve with the aim of reducing the package size. The solenoid coil is by far the largest component of the device, with about 4000 coils arrayed in about 90 layers stacked on top of each other. I'm wondering if I can reduce the size by removing some of these layers of coils and pumping an increased current through the rest. However, given the 90 layers of coils there is a difference of about 30% in the radius of the coils in the inner layer vs the coils in the outermost layer. I am having trouble understanding how (or if ) the coils effect on the moving solenoid core varies with radial distance. My intuition is that the magnetic field generated by current passing through a coil in an outer layer is going to have less of an impact on the solenoid core than a coil in the innermost layer. In addition, the outermost coils have a larger circumference and thus higher coil resistance. However, none of the derivations i've seen of magnetic field within a solenoid seem to talk at all about the path length of the magnetic circuit induced by the coils. The closest I've come to an understanding is via this site, which indicates that I could rewrite the magnetic circuit with the reluctances of the moving core, the copper wiring of interior or exterior current loops, and a small air gap in series, but i have no idea what loop size I'm dealing with. Can anyone help me understand what's going on qualitatively? Or better yet, mathemetically?