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Inductance of A Toroid

This document describes how to calculate the inductance of a toroid. It provides an equation that relates the inductance to the number of turns in the toroid, the radius of the toroid, the radius of the coil, the permeability of the core material, and other parameters. The document also notes that inductors are commonly made with air cores for electronics and iron cores for larger inductances and in transformers, due to iron's higher permeability. The calculation provided is an approximation that gets more accurate when the toroid radius is much larger than the coil radius.

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1K views2 pages

Inductance of A Toroid

This document describes how to calculate the inductance of a toroid. It provides an equation that relates the inductance to the number of turns in the toroid, the radius of the toroid, the radius of the coil, the permeability of the core material, and other parameters. The document also notes that inductors are commonly made with air cores for electronics and iron cores for larger inductances and in transformers, due to iron's higher permeability. The calculation provided is an approximation that gets more accurate when the toroid radius is much larger than the coil radius.

Uploaded by

geralt
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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11/27/2020 Inductance of a Toroid

Index
Approximate
Magnetic
Inductance of a field
concepts
Toroid
Finding the magnetic field inside a toroid
is a good example of the power of
Ampere's law. The current enclosed by
the dashed line is just the number of
loops times the current in each loop.
Amperes law then gives the magnetic
field at the centerline of the toroid as

The inductance can be calculated in a


manner similar to that for any coil of
wire.

The application of Faraday's law to calculate the voltage induced in the toroid is of the form

This can be used with the magnetic field expression above to obtain an expression for the
inductance.

Toroidal radius r = cm with N = turns,

Coil radius = cm gives area A = cm2.

Relative permeability of the core k = ,

Then the inductance of the toroid is approximately

L= Henry = mH.
hyperphysics.phy-astr.gsu.edu/hbase/magnetic/indtor.html 1/2
11/27/2020 Inductance of a Toroid

This is a single purpose calculation which gives you the inductance value when you make
any change in the parameters.

Small inductors for electronics use may be made with air cores. For larger values of
inductance and for transformers, iron is used as a core material. The relative permeability of
magnetic iron is around 200.

This calculation is approximate because the magnetic field changes with the radius from the
centerline of the toroid. Using the centerline value for magnetic field as an average
introduces an error which is small if the toroid radius is much larger than the coil radius.

Inductance of a solenoid

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HyperPhysics***** Electricity and Magnetism R Nave

hyperphysics.phy-astr.gsu.edu/hbase/magnetic/indtor.html 2/2

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