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One turn loop inductance

Problem type:
Axisymmetric problem of DC magnetics

Geometry:

one turn loop inductance

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

Problem:
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

r, mm

R/r

L, uH

Δ, %

QuickField

Theory

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%

Deviation from the analytic equation as a function or (R/r)
one turn loop inductance value

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References:

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