Magnetic permeability - Revision history

Rational Point: /* Calculating the magnetic permeability of a toroid core */

2026-04-21T15:48:48Z

Calculating the magnetic permeability of a toroid core

← Older revision		Revision as of 15:48, 21 April 2026
Line 19:		Line 19:

	Problem: calculate the magnetic permeability of the material of which this core is made.		Problem: calculate the magnetic permeability of the material of which this core is made.

			=== The Biot–Savart Law for air-core inductors and coils in free space ===

			...

Rational Point: Example problem

2026-04-12T15:01:22Z

Example problem

← Older revision		Revision as of 15:01, 12 April 2026
Line 11:		Line 11:

	:''μ'' = ''Lℓ'' / ''N''<sup>2</sup>''A''		:''μ'' = ''Lℓ'' / ''N''<sup>2</sup>''A''

			=== Example ===

			[[File:Inductor 20260412~2.jpg\|thumb\|alt=Measuring inductance\|Measuring inductance\|none]]

			For this example, L=1.813mH, ''Φ''=102mm, ''φ''=65.5mm, A=18.25mm×19.5mm, and N=23.

			Problem: calculate the magnetic permeability of the material of which this core is made.

Rational Point: harmonic mean path length

2026-04-11T22:37:14Z

harmonic mean path length

New page

== Calculating the magnetic permeability of a toroid core ==

:''L'' = ''μN''<sup>2</sup>''A'' / ''ℓ''

where ''L'' is the inductance of a winding of wire about a magnetic core, ''μ'' is the magnetic permeability of the core, ''N'' is the number of turns of wire, A is the (constant) cross-sectional area of the core and ''ℓ'' is the harmonic mean path length of magnetic flux through the core. If ''Φ'' is the outer diameter and ''φ'' is the inner diameter of a toroidal core with a rectangular cross section, then the harmonic mean path length is calculated:

:<math>\ell = \pi\cdot\frac{\Phi-\phi}{\int_{\phi}^{\Phi} \frac {dx}x} = \pi\cdot\frac{\Phi-\phi}{\log\Phi-\log\phi}</math>.

Now

:''μ'' = ''Lℓ'' / ''N''<sup>2</sup>''A''