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# What is Permeance â€“ Definition, Formula, Units, Coefficient and Example

In this article, we shall learn about Permeance in magnetic circuits, its definition, formula, unit of measurement, and coefficient.

## What is Permeance?

The measure of the ease with which the magnetic flux can flow through a magnetic material is called **Permeance**. It is denoted by the symbol P and given by the following expression,

$$\mathrm{Permeance,\, P=\frac{1}{Reluctance}\: \: \cdot \cdot \cdot \left ( 1 \right )}$$

Hence, the Permeance may also be defined as the reciprocal of **magnetic reluctance**. Where, magnetic reluctance is the measure of opposition that a magnetic material or a magnetic circuit offers in the path of magnetic flux.

It is experimentally observed that the Permeance of a magnetic material is directly proportional to the magnetic flux passing through it, and inversely proportional to the MMF (magnetomotive force). Therefore, we have,

$$\mathrm{P=\frac{\phi }{NI}\: \: \cdot \cdot \cdot \left ( 2 \right )}$$

This expression shows that if the Permeance of a magnetic circuit is low, then it requires a large MMF to establish a certain amount of magnetic flux in it.

The Permeance of a magnetic circuit can also be expressed in terms of the physical parameters of the circuit as,

$$\mathrm{P=\frac{\mu A }{l}=\frac{\mu_{0}\mu_{r} A }{l}\: \: \cdot \cdot \cdot \left ( 3 \right )}$$

Where,

- A is the area of cross-section of the circuit,
- l is the mean length of the magnetic circuit,
- $\mathrm{\mu_{0}}$ is the permeability of free space, which is equal to 4Ï€ Ã— 10
^{-7}H/m, and - $\mathrm{\mu_{r}}$ is the relative permeability of the magnetic material

Thus, from this equation, it can be observed that the Permeance of a magnetic circuit increases with the increased cross-sectional area and decreases with the increase in length of the magnetic circuit.

## What is the Unit of Permeance?

As the Permeance is given by the ratio of magnetic flux in the magnetic circuit to the MMF required to establish this flux, i.e.,

$$\mathrm{P=\frac{Magneti\: Flux }{MMF}=\frac{Weber }{Ampere \: Turn}}$$

Therefore, the Permeance is measured in **weber per ampere turn (Wb/AT)**.

Also,

$$\mathrm{1\: Wb/AT = 1\: Henry (H)}$$

## What is Permeance Coefficient?

The ratio of magnetic flux density to the magnetic field intensity at the operating point of the B-H curve is called the **Permeance coefficient**. It is usually represented by the symbol *P _{C}*.

$$\mathrm{Permeance\: coefficient,P_{c} = \frac{B_{0}}{H_{0}}\: \: \:\cdot \cdot \cdot \left ( 4 \right )}$$

Where, *B _{0}* is the magnetic flux density, and

*H*is the magnetic field intensity at the operating point of the B-H curve.

_{0}The Permeance coefficient is one of the important parameters in the magnetic circuit design as it is used to determine the operating point of the magnetic circuit on the B-H curve.

A typical B-H curve is shown in the figure. Here, the straight line *OA* passing through the origin cuts the B-H curve at point *A*, which is called the operating point of the magnetic circuit. The line *OA* is known as the *Permeance line*, and the slope of the Permeance line *OA (i.e. B _{0} / H_{0})* is known as the

**Permeance coefficient**.

## Numerical Example

A magnetic circuit is built up of an iron core of 9 cm^{2} cross-sectional area. The mean length of the magnetic circuit is 20 cm, and the relative permeability of the core material is 1000. Find the Permeance of the magnetic circuit.

## Solution

Given data,

$$\mathrm{Area\: of\: cross\: section, A = 9\, cm^2 = 9 \times 10^{-4}\, m}$$

$$\mathrm{Mean\: length\: of\: the\: circuit, l = 20\, cm = 20 \times 10^{-2} m}$$

$$\mathrm{Relative\: permeability, \mu _{r} = 1000}$$

Then, the Permeance of the magnetic circuit is given by,

$$\mathrm{P=\frac{\mu _{0}\mu _{r}A}{l}}$$

$$\mathrm{\Rightarrow P=\frac{(4\pi \times 10^{-7}) \times (1000) \times (9 \times 10^{-4})}{(20 \times 10^{-2})}=5.652 \times 10^{-6} \: Wb/AT}$$

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