Magnetic Reluctance (Rm)

The concept of magnetic resistance or reluctance is used in the study of circuits. It refers to the ratio of the magnetomotive force to the magnetic flux. It can be expressed as the opposition to magnetic flux depending on the composition and geometry of the object.

Resistor is a measure of resistance in an electrical circuit, and the concept of magnetic reluctance refers to the opposition of current to magnetic flux. The dissipation of heat from a magnetic flux through a reluctance does not occur as much as it does from resistance.

The concept of magnetic reluctance cannot be used in the design of systems where the energy flows between the electrical and magnetic domains. Instead, it can be modeled using the gyrator-capacitor model.

When magnetized, the atomic dipoles of some materials must be subjected to large forces while those of others can be aligned with relatively weak magnetic fields. Magnetic reluctance is the resistance a material has to being magnetized.

Magnetic Reluctance Formula

Like resistance in an electric circuit, reluctance is a function of a number of variables.

1.In a magnetic circuit, the length is measured in turns. It is similar to electrical resistance in that reluctance varies directly with the mean length of a magnetic circuit.
figure 1
2.Dimensional measure of a magnetic circuit’s cross-section. There is a negative relationship between the cross-sectional area of a magnetic circuit and its reluctance.
figure 2
3.Circuit material permeability. Material permeability refers to the ease with which a material can be magnetized again. However, reluctance quantifies the resistance to change. Comparing permeability to the resistivity of a circuit:

figure 3

Rm = reluctance in ampere-turns per weber
l = length of circuit in meters
A = cross-sectional area in square meters
µo = permeability of free space
µr = relative permeability

Magnetic Permeability Example

An iron core travels an average of 200 mm along its path. Cross-sectionally, the core is 15 mm 10 mm in size. Determine the core’s reluctance if its relative permeability is 830 at the targeted flux density. (Don’t forget to do the metric conversion!)

figure 1 magnetic reluctance
figure 1 magnetic reluctance