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One turn loop inductance

wire loop inductance, wire loop magnetic field simulation

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.

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