Magnetic permeability is a fundamental property of materials that describes how easily they get magnetized when subjected to a magnetic field. To describe the magnetic properties of a given substance, we require some quantities which include a quantity called magnetic permeability denoted as $\mu$ which is pronounced as the mew symbol or mu or meu sign. Hence in magnetism, mu means magnetic permeability. It quantifies the ability of a material to support the formation of the magnetic field within itself. In this article, we will come across three types of magnetic permeability. Also, we will learn about topics like basic principles, mathematical descriptions, and factors affecting magnetic permeability in this article.
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Magnetic permeability ($\mu$) is the ability to measure the degree of penetration of the magnetic field through the medium, It also measures the capacity of the substance to take magnetism. However, to define magnetic permeability, we must know about magnetic field strength/ magnetic induction denoted by ‘B’, and magnetic field intensity denoted by ‘H’.
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We know that $\mathrm{B} \propto \mathrm{H}$
$\mathrm{B}$=$\mu$$\mathrm{H}$, where is $\mu$ the constant of proportionality and stands for magnetic permeability.
Thus, we can define magnetic permeability as the ratio of magnetic field induction (B) to the magnetic intensity (H).
$$\mu=\frac{\text{Total magnetic field inside the material}}{\text{Magnetising field}}$$
$$\mu=\frac{B} {H} $$
where,
$\mu$ is the permeability
$\mathrm{B}$ is the magnetic flux density
$\mathrm{H}$ is the magnetic field strength
The S.I. unit of $\mu$
$\mathrm{B}$ $=\mathrm{Wb} / \mathrm{m}^ 2$
$\mathrm{H}$ $= \mathrm{A}/\mathrm{m}$
The unit of magnetic permeability is
$\mu=\frac{B} {H} $
Unit of $\mu$ $=\frac{\mathrm{Wb} / \mathrm{m}^ 2}{\mathrm{A}/\mathrm{m}}$
simplifying
Unit of $\mu$ $=\frac{\mathrm{Wb}}{\text{A m}}$
2. Another unit is Henry per meter ($\mathrm{Hm}^{-1}$)
$\mathrm{B}$ $=T$
$\mathrm{H}$ $=\mathrm{A}/\mathrm{m}$
Now, the unit of $\mu$ $=\frac{\mathrm{T}}{\mathrm{A}/ \mathrm{m}}$
$=\frac{\left(\mathrm{kg} \cdot \mathrm{m} /\left(\mathrm{s}^2 \cdot \mathrm{A}\right)\right.}{\mathrm{A} / \mathrm{m}}$
The unit of $\mu$ $=\mathrm{H} / \mathrm{m}$
3. Another unit of $\mu$ is Newton per ampere square (NA-2) or Telsa meter per ampere(TmA-1).
$\mathrm{B}$ $=T$
$\mathrm{H}$ $=\mathrm{A}/\mathrm{m}$
Now the unit of $\mu$ $=\mathrm{T} \cdot \mathrm{m} / \mathrm{A}$
OR
$\mathrm{1T}=\frac{1 \mathrm{~N} \cdot \mathrm{m}}{\mathrm{A} \cdot \mathrm{m}^2}=\frac{1 \mathrm{~N}}{\mathrm{~A} \cdot \mathrm{m}}$
Unit of $\mu=\frac{\mathrm{T}}{\mathrm{A} / \mathrm{m}}$
Unit of $\mu=\frac{\frac{1 \mathrm{~N}}{\mathrm{Am}}}{\mathrm{A} / \mathrm{m}}$
Unit of $\mu=\frac{1 \mathrm{~N}}{\mathrm{~A}^2}$
The magnetic permeability in vacuum Charges Magnetism, or free space , $\mu_0=4 \pi \times 10^{-7} \mathrm{H} / \mathrm{m}$
Dimensional formula,
$1 \mathrm{H}=\frac{1 \mathrm{~kg} \cdot \mathrm{m}^2}{\mathrm{~s}^2 \cdot \mathrm{A}^2}$
We know that,
$\mu_0=\frac{1 \mathrm{H}}{\mathrm{m}}=\frac{\frac{1 \mathrm{~kg} \cdot \mathrm{m}^2}{\mathrm{~s}^2 \cdot \mathrm{A}^2}}{\mathrm{~m}}=\frac{\mathrm{kg} \cdot \mathrm{m}}{\mathrm{s}^2 \cdot \mathrm{A}^2}$
The dimensional formula of magnetic permeability of free space,
$$\mu_0=\mathrm{M} \cdot \mathrm{L} \cdot \mathrm{T}^{-2} \cdot \mathrm{I}^{-2}$$
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We will come across three types of magnetic permeability i.e. magnetic permeability in vacuum (μ0)or permeability of free space, the magnetic permeability of medium (μ) and relative magnetic permeability (μr).
Magnetic permeability of free space (mu not)- It is the ratio of magnetic induction in free space to magnetic intensity,
i.e. $\mathrm{B}_0=\mu_0 \mathrm{H} \Rightarrow>\mu_0=\mathrm{B}_0 / \mathrm{H}$
The value of $\mu_0$ is $4 \pi \times 10^{-7} \mathrm{WbA}^{-1} \mathrm{~m}^{-1}$
Permeability of medium (μ)- It is the ratio of magnetic field induction in the medium to the magnetic intensity.
$$\mu=B / H$$
Relative permeability (r)- It is defined as the ratio of the magnetic permeability of a medium ($\mu$) to the magnetic permeability of free space or vacuum.
$$\mu_{\mathrm{r}}=\mu / \mu_0$$
Relative permeability of a material can also be defined as the ratio of the number of magnetic field lines per unit area (flux density i.e. B) in that material to the number of magnetic field lines per unit area that would be present if the material is replaced by vacuum ( flux density in a vacuum i.e. B0).
As both the quantities involved in the above equations have the same unit, therefore relative permeability has no units and is a dimensionless quantity. It is just a number.
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Based onbased on magnetic property, Faraday classified materials into three categories. These are-
Diamagnetic materials
Paramagnetic materials
Ferromagnetic materials
Let us briefly understand each of these on the basis of their mu values.
Hence, $\mu_r$ =-ve and it is less than 1.
This is because ->
$\begin{aligned} & B<B_0 \\ & B / B_0<1\end{aligned}$
$ \mu$<1 ($\mu$ value (relative) for diamagnets is always less than 1)
2. Paramagnetic materials-
Thus, $\begin{aligned} & B>B_0 \\ & B / B_0>1\end{aligned}$
$\mu_r$>1 ( $\mu_r$ value for paramagnetic are always greater than 1).
3. Ferromagnetic materials
Thus, the $\mu_r$ value is very high in these materials i.e. $\mu_r$=103 to 105.
Note: there is a B-H graph for all magnetic materials discussed above, the slope of which gives us the curve’s incremental permeability. Hysteresis loops are also plotted in the B-H graph for ferromagnetic materials. The B-H graph for all three magnetic materials is given below.
NCERT Physics Notes:
$$\chi_m=\frac{I}{H}$$
Now, when a magnetic material is placed in an external magnetic field of magnetic intensity H, it gets magnetized.
Then, total magnetic field induction is-
$B=B_0+B_m$
Therefore, $B=\mu_0(H+I)$ ------(1)
We know that, $\mathrm{I}=\mathrm{\chi}_{\mathrm{m}} \mathrm{H}$.
Therefore putting this value in equation (1)
$B=\mu_0 H\left(\chi_m+1\right)$
But, $B=\mu H$
$\Rightarrow \mu \mathrm{H}=\mu_0 \mathrm{H}\left(\mathrm{\chi}_{\mathrm{m}}+1\right)$
$=>\mu / \mu_0=\chi_m+1$
$$\mu_{\mathrm{r}}=\mathrm{\chi}_{\mathrm{m}}+1$$
This is the relationship between $\mu_r$ and $\chi_m$.
Also read -
Magnetic permeability is the ability of a material to allow magnetic lines to pass through it. Relative magnetic permeability ($\mu_r$) quantifies how a material influences the magnetic field compared to the vacuum. It is used in devices such as electric motors, generators, transformers, etc.. to provide better efficiency. High $\mu_r$ materials are used for magnetic shielding, reducing interference in sensitive electronics and magnetic recording media. Understanding and utilizing relative permeability is essential for technological applications.
This is because permeability and susceptibility of ferromagnetic materials are very high.
Para and ferromagnetic materials have relative mu value greater than 1.
Zero
No, every material is at least diamagnetic
Relative permeability
It is the ratio of the permeability of a material to the permeability of the vacuum.
S.I unit of magnetic permeability is Henry per meter (H/m).
$\mu_{\mathrm{r}}=\mu / \mu_0$
$\mu_0=4 \pi \times 10^{-7} \mathrm{H} / \mathrm{m}$
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