## What is Magnetic Reluctance ?

All materials offer some opposition to being magnetized some materials require high magnetizing forces to align their atomic dipoles in the same direction, while others are readily magnetized by small forces the term used to describe this opposition is ‘magnetic reluctance

Magnetic reluctance or Magnetic resistance or Magnetic insulation is a property of magnetic material by which it offers opposition to the production of magnetic flux. It is denoted by “S”.

As electrical resistance is a opposition to the flow of current in electrical circuit similar magnetic reluctance is the opposition to the creation of magnetic flux. The resistance dissipates energy in the form heat whereas the magnetic reluctance stores magnetic energy.

The reluctance of a magnetic circuit depends upon its length (l), cross-sectional area (a) and permeability (μ) of the material. Thus, for a magnetic circuit.

- The reluctance is directly proportional to the mean length (in meter) of the magnetic circuit \\\;\\\;\;\;\;\;\;\;\;\;\;S ∝ l
- The reluctance is inversely proportional to the area of cross section (in meter
^{2}) of the magnetic circuit. \\\;\\\;\;\;\;\;\;\;\;\;\; S ∝ 1/A - The reluctance also depends upon the nature of material that makes up the magnetic circuit. i.e. permeability of material (µ=µ
_{0}µ_{r})\\\;\\\;\; where µ_{0}= permeability of free space = 4π 10^{-7}Henry/meter\\\;\\\;\;\;\;\;\;\;\;\;\; µ_{r}= relative permeability of magnetic material

Thus mathematically Magnetic reluctance can be expressed as \\\;\\\;\;\;\;\;\;\;\;\;\;S=\frac{l}{\mu_0 \mu_r A}

Magnetic reluctance is a scalar quantity. In both AC and DC magnetic reluctance is ratio of magnetomotive force to the magnetic flux in the magnetic circuit.\\\;\\Magnetic reluctance (S) = \; \frac{magnetomotive\;force}{magnetic\;flux}

** Unit of Magnetic Reluctance**\\The magnetic reluctance is given by\\\;\\ Magnetic reluctance (S) = \frac{magnetomotive\;force}{magnetic\;flux} =\frac{Ampere\; \times\; turns}{weber}\\\;\\ Magnetic reluctance = \; \frac{AT}{Wb}\\\;\\Thus unit of magnetic reluctance is AT/Wb

The reciprocal of the magnetic reluctance is known as the magnetic Permeance. It is given by the expression \\\;\\\;\;\;\;\;\;\;\;Permeance = \frac{1}{reluctance}\\ It is analogus to conductance in electric circuit.

In case of composite series magnetic circuit consisting of different magnetic materials of different permeability(µ), length(l) and area of cross section (A) has shown in figure. The total reluctance is the sum of individual reluctances \\\;\\\;\;\;\;\;\;\;\;\;\; \\\;\\Total reluctance =\sum \frac{l}{ \mu_{0} \mu_{r}A}\\\;\\Total Reluctance = \frac{l_1}{\mu_0 \mu_{r1} A_{1}} + \frac{l_2}{\mu_0 \mu_{r2} A_{2}} + \frac{l_3}{\mu_0 \mu_{r3} A_{3}} + \frac{l_4}{\mu_0 \mu_{r4} A_{4}}

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