Effective L/D ratio for coil magnetisation
Every coil ampere-turn formula is driven by the length-to-diameter ratio L/D, because that ratio governs how strongly the part’s own end poles oppose the applied longitudinal field. A long slender bar has widely separated poles and a weak demagnetising field; a short fat one has strong opposition and needs far more ampere-turns.
For a hollow part the outside diameter overstates the problem. What matters magnetically is the amount of iron in the cross-section, not the outline. The standards therefore replace D with an effective diameter: the diameter of a solid bar having the same metal cross-sectional area. Generally D_eff = 2 sqrt((A_total - A_hollow)/pi), which for a plain tube reduces to D_eff = sqrt(OD² - ID²). A 100 mm tube bored to 60 mm behaves like an 80 mm solid bar, not a 100 mm one, so it needs fewer ampere-turns than its outside diameter suggests.
The empirical coil formulas are only valid between L/D = 2 and L/D = 15. Above 15 there is no further reduction in required ampere-turns, so 15 is used. Below 2 the demagnetising field swamps the applied field and the formula fails; the usual fix is to butt ferromagnetic pole pieces of similar diameter against the ends of the part to lengthen the magnetic circuit until the effective L/D reaches at least 2.
The same effective diameter is used for the fill factor decision, since fill factor compares the coil bore area with the part’s true cross-sectional area.
Worked example
| Outside diameter | 100 mm |
| Inside diameter | 60 mm |
| Part length | 400 mm |
| Effective diameter | 80 mm |
| Metal cross-sectional area | 5026.5 mm² |
| L/D as calculated | 5 |
| L/D to use in the coil formula | 5 |
| Length needed for L/D = 2 | 160 mm |
| Pole piece length per end | 0 mm |
A 400 mm length of 100 mm OD tube bored to 60 mm. D_eff = sqrt(100² - 60²) = sqrt(10 000 - 3 600) = sqrt(6 400) = 80 mm, so it magnetises like an 80 mm solid bar. Metal area = pi(100² - 60²)/4 = 1 600 pi = 5 026.5 mm². L/D = 400/80 = 5, comfortably inside the 2 to 15 band, so no clamping and no pole pieces. Had the outside diameter been used naively, L/D would have read 4 and the calculated ampere-turns would have been too high.
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