Coil shot current, high fill factor

A high fill factor coil is one whose bore is barely larger than the part - the coil cross-section is less than twice the part cross-section. The part sits right inside the windings where the flux is densest, so a given field is reached with fewer ampere-turns than the same part would need in an oversized coil. That is why the high fill constant (35 000) is smaller than the low fill constant (45 000), and why the denominator carries the extra +2.

The field produced is longitudinal, running along the axis of the part, so it reveals discontinuities lying transverse to that axis. Ampere-turns, not amperes, set the magnetomotive force: doubling the turns halves the current needed for the same result.

As with any coil shot, the part's own end poles generate a demagnetising field that opposes the applied one, and that opposition grows as the part gets shorter and stubbier. The length-to-diameter ratio L/D quantifies it. The formula is valid between L/D = 2 and L/D = 15; shorter parts need ferromagnetic pole pieces butted against the ends to lengthen the magnetic circuit, and anything above 15 is treated as 15.

Fill factor is not a detail you can eyeball. If the coil bore area is between two and ten times the part area you are in the intermediate band and neither the high nor the low fill formula applies on its own. Whichever formula is used, verify the tangential field at the surface with a Hall-effect gaussmeter or an artificial flaw shim before accepting the technique.

L/D ratio = part length / part diameter, limited to the range 2 to 15
NI = 35 000 / ((L/D) + 2)   ampere-turns, ±10%
I = NI / N
High fill factor: coil bore area < 2 x part cross-sectional area