Inductance of a pair of concentric cylinders
A coaxial cable has an inner core of radius 1.0 mm and an outer sheath of internal radius of 4.0 mm. Determine the inductance of the cable per meter length.
Problem Type:
Plane problem of AC magnetics.
Geometry:
Given:
Inner radius a = 1 mm;
Outer radius b = 4 mm;
Current I = 0.001 A;
Analytical solution:
The total inductance per meter at low frequency is given by L = μ/2π · (1/4 + ln(b/a)) H/m
L = 4π·10-7 · (1/4 + ln(4)) = 3.27259·10-7 H/m
QuickField simulation results:
Note: QuickField calculates the total current and the total flux. To get RMS we should divide the corresponding amplitude value by root 2:
L = Flux / I = 3.272·10-10/1.4142 / 0.001/1.4142 = 3.272·10-7 H/m
L = 2·W / I2 = 2·8.181·10-14 / (0.001/1.4142)2 = 3.272·10-7 H/m
Mesh size |
QuickField |
Discrepancy with theory |
L = Flux / I |
L = 2·W / I2 |
251 (Student version) |
3.23·10-7 H/m |
3.22·10-7 H/m |
1% / 9.55% |
1301 (automatic refinement in Prof. version) |
3.267·10-7 H/m |
3.239·10-7 H/m |
0.17% / 1.03% |
4003 (automatic refinement 2) |
3.27·10-7 H/m |
3.263·10-7 H/m |
0.08% / 0.26% |
8814 (automatic refinement 3) |
3.271·10-7 H/m |
3.268·10-7 H/m |
0.05% / 0.14% |
26474 (automatic refinement 5) |
3.272·10-7 H/m |
3.271·10-7 H/m |
0.02% / 0.05% |
78585 (automatic refinement 10) |
3.272·10-7 H/m |
3.272·10-7 H/m |
0.02% / 0.02% |
 Download simulation files:
References:
- John Bird, "Electrical circuit theory and technology", p.520. ISBN-13: 978 0 7506 8139 1.
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