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One turn loop inductance

QuickField simulation example

Problem Type
Axisymmetric problem of DC magnetics

Geometry
One turn loop inductance Single turn is made of copper and carries direct current n R r I B

Given
Current I = 50 A,
Loop radius R = 40 mm,
Wire diameter 2r = 10 mm.

Task
Calculate one turn loop inductance.

Solution
One turn loop inductance can be calculated using equation:
L = μ0 R · ( ln(8R/R) - 1.75 )

Results
one turn loop magnetic field

Deviation from the analytic equation as a function or (R/r)

r, mm R/r L, uH Δ, %
QuickField Reference*
5 8 0.1213 0.1211 0.17%
10 4 0.0875 0.0862 1.51%
16 2.5 0.0605 0.0622 2.73%
20 2 0.0550 0.0514 7.00%

* Reference: Clayton R. Paul Inductance: Loop and Partial, p.130. ISBN-13: 978 0 4704 6188 4.