Long solenoid inductance

QuickField simulation example

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;

Task
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.

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

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