calculator:solenoid_single_layer_circular_with_insulation_inductance
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Calculator of inductance of a single-layer thin round solenoid, with insulated wire
 | Stan Zurek, Calculator of inductance of a single-layer thin round solenoid, with insulated wire, Encyclopedia Magnetica, https://www.e-magnetica.pl/doku.php/calculator/solenoid_single_layer_circular_with_insulation_inductance, {updated: 2026/02/21 23:07} |
 See more: Calculators of inductance |
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* This page is being edited and may be incomplete or incorrect.
Toroidal coil dimensions: a - mean diameter (to the centre of the wire), c - wire diameter, b - solenoid length (including insulation of the wire), N - number of turns
S. Zurek, E-Magnetica.pl, CC-BY-4.0
Inductance of an ideal straight “thin” round solenoid (circular cross-section) can be calculated from the equations as specified below. Various equations apply for “long” and “short” solenoids, with limited range of validity, because there are no closed-form solutions to elliptic integrals (only their limited approximations).
The wire of the coil is assumed to be infinitely thin, and the current distribution is uniform (equivalent to the ideal current sheet configuration, with the skin effect ignored). The medium is assumed non-magnetic (permeability is unity, as it is for vacuum).
Equations
| Approximate inductance of a straight “thin” solenoid (with a circular cross-section) | ||
|---|---|---|
| Source: [1] V.G. Welsby, The theory and design of inductance coils, Macdonald & Co., London, 1950 | ||
| Formula (1) with correction for insulation thickness or wire pitch [1], eq. (28)-(32), p. 25-26 | $$ L = L_0 · K_N · K_{AB} $$ | (H) |
| where: $μ_0$ - permeability of vacuum (H/m), $a$ - mean diameter (m) of solenoid measured to the centre of the wire, $b$ - solenoid length (m), $N$ - number of turns (unitless), $A = π · a^2/4 $ - cross-sectional area of the solenoid (m2), $c$ - wire diameter (m), $p = b/N$ - winding pitch (m) as measured between the centres of the consecutive wire turns for a uniformly wound single-layer coil, and: | ||
| $$ L_0 = \frac{ μ_0 · π · a^2 · N^2 }{4·b} = \frac{ μ_0 · A · N^2 }{b} $$ | (H) | |
| $$K_N = \frac{1}{ 1 + 0.45 · (a/l) - 0.005 · (D/l)^2 } $$ | (unitless) | |
| $$K_{AB} = 1 - \frac{2·l · (A+B)}{π·a·N·K_N}$$ | (unitless) | |
| $$A = 2.3 · log_{10} \left( 1.73 · \frac{c}{p} \right) $$ | (unitless) | |
| $$B = 0.336 · \left( 1 - \frac{2.5}{N} + \frac{3.8}{N^2} \right) $$ | (unitless) | |
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calculator/solenoid_single_layer_circular_with_insulation_inductance.1771711626.txt.gz · Last modified: 2026/02/21 23:07 by stan_zurek