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# Long solenoid inductance

Problem type:
Axisymmetric problem of DC magnetics.

Geometry:

R1 = 30 mm, R2 = 35 mm.

Given:
Current in the conductor i = 10 A;
Number of turns N = 100,
Length l = 0.5 m;

Calculate inductance of the long solenoid, side effects are neglected.

Solution:
Inductance of the long solenoid can be obtained from the equation:
L = N ² · μ0 A / l,
where A is a cross-section area of the core (m²).

To calculate the inductance in QuickField you should divide magnetic flux by the source current.

L = N · Φ / i

Results:
Cross-section area of the core
A = π * ( (R1 + R2)/2 )² = 3.142 * ( (0.03+0.035)/2 )² = 0.00332 m².

Inductance of the long solenoid
L = 100² · 4e-7 · 3.142 * 0.00332 / 0.5 = 83.45 μH. QuickField Theory Δ, % Inductance L, μH 83.55 83.45 0.12%

* Reference: John Bird, Electrical circuit theory and technology, p.77. ISBN-13: 978 0 7506 8139 1.

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