A description of the magnetic reluctance, also discussing a way to calculate it
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Overview
Key facts
The magnetic reluctance is defined as:
where is the magnetomotive force, and the magnetic flux.
For a magnetic circuit of length , cross-sectional area , and relative magnetic permeability , the magnetic reluctance can be calculated with:
where is the magnetic permeability of free space.
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Constants
The magnetic reluctance of a magnetic circuit can be regarded as the formal analog of the resistance in an electrical circuit. The magnetic reluctance can be expressed as:
where is the magnetomotive force (mmf), and is the magnetic flux.
In order to calculate the magnetic reluctance, consider a magnetic circuit of length and cross-sectional area , as diagramed in Figure 1.
Figure 1
We know that the magnetic field strength can be written as:
where is the current in the coil, and is the number of turns (for a more detailed discussion on the magnetic field strength see Field Strength ). Furthermore, can be related to the magnetic flux density with the equation:
Example - Magnetic flux and flux density of a toroid
Problem
Consider a toroid with the mean length of , the cross section of , and the relative magnetic permeability of . What is the magnetic flux and the magnetic flux density if the coil has 10 turns and the current is 2 amperes ?
As a side note, if the toroid has an air gap of length , then its total magnetic reluctance, , would be the magnetic reluctance of the toroid plus the magnetic reluctance of the air gap: