Calculator of inductance of a straight elliptical non-magnetic wire
 | Stan Zurek, Calculator of inductance of a straight elliptical magnetic wire, Encyclopedia Magnetica, https://www.e-magnetica.pl/doku.php/calculator/inductance_of_straight_elliptical_wire, {accessed: 2025-03-13} |
 See more: Calculators of inductance |
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Inductance of a straight wire or conductor made from nonmagnetic material with elliptical cross-section can be calculated with the the equation as specified below.
Equations
Note: Several assumptions are made for all these equations: 1) The return path is not considered so the total inductance of the complete circuit can be significantly different. 2) The length of the wire is assumed to be significantly longer than its diameter(s) (a,b « l), otherwise the calculation errors might be excessive. 3) The wire and the surrounding medium is assumed to be non-magnetic (μr = 1). 4) The current is uniformly distributed inside the wire (no skin effect). 5) The equations were converted here to be consistent with SI units.
| Inductance of a straight round magnetic wire or conductor | ||
|---|---|---|
| Source: [2] F.W. Grover, Inductance Calculations: Working Formulas and Tables, ISA, New York, 1982, ISBN 0876645570 | ||
| (1) [2] Grover, eq. (10), p. 36 | $$ L = \frac{μ_0 ⋅ l}{2⋅π}⋅\left( ln \left( \frac{4⋅l}{a+b} \right) - 0.05685 \right) $$ | (H) |
| where: $μ_0$ - magnetic permeability of vacuum (H/m), $l$ - wire length (m), $a$, $b$ - shorted and longer diameters of ellipse (m) | ||
| The original Grover's equation is expressed by “semiaxes” α, β of the ellipse, with the under-logarithm coefficient as 2·l/(α+β), hence if the full “diameters” are used then this becomes 4·l/(a+b), as written above. | ||
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