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Magnetic Permeability

Magnetic Permeability (μ) :- The property of a medium by which it allows magnetic field lines to pass through it is called magnetic permeability of that medium.

Types of Magnetic Permeability

Magnetic permeability can be divided into 2 parts :-

Absolute Magnetic Permeability μ
Relative Magnetic Permeability μ_r

(1) Absolute Magnetic Permeability (μ)

The ratio of magnetic induction (B) and magnetizing field (H) in a medium is called absolute magnetic permeability (μ).

$\displaystyle \mu =\frac{B}{H}$ …..(1)

The value of μ is always positive and depends on the nature of the substance.

Unit of Absolute Magnetic Permeability

$\displaystyle \mu =\frac{B}{H}=\frac{T}{A{{m}^{-1}}}=Tm{{A}^{-1}}$

$\displaystyle \mu =Tm{{A}^{-1}}=\left( \frac{Wb}{{{m}^{2}}} \right)m{{A}^{-1}}=Wb{{A}^{-1}}{{m}^{-1}}$

As $\displaystyle Wb{{A}^{-1}}=henry(H)$ , So

$\displaystyle \mu =H{{m}^{-1}}$

Hence unit of absolute magnetic permeability are $\displaystyle Tm{{A}^{-1}}$ अथवा $\displaystyle Wb{{A}^{-1}}{{m}^{-1}}$ or $\displaystyle H{{m}^{-1}}$ .

Value of magnetic permeability of vacuum is $\displaystyle {{\mu }_{0}}=4\pi \times {{10}^{-7}}Wb{{A}^{-1}}{{m}^{-1}}$

(2) Relative Magnetic Permeability (μ_r)

The relative magnetic permeability of a medium is expressed as the ratio of the number of magnetic field lines per unit area (i.e., flux density B) of that medium to the number of magnetic field lines per unit area that would be present, if the medium were replaced by vacuum (i.e., flux density B₀).

In other words, the extent to which magnetic field lines can penetrate a medium is called the relative magnetic permeability of that medium.

Or the relative magnetic permeability of a medium is defined as the ratio of the magnetic permeability of that medium (μ) and the magnetic permeability of vacuum (μ₀).

$\displaystyle {{\mu }_{r}}=\frac{B}{{{B}_{0}}}$

$\displaystyle {{\mu }_{r}}=\frac{\mu }{{{\mu }_{0}}}$

$\displaystyle \Rightarrow \mu ={{\mu }_{0}}{{\mu }_{r}}$

μ_r is a positive, unitless and dimensionless quantity and for vacuum μ_r = 1.

Magnetic Permeability

Types of Magnetic Permeability

Unit of Absolute Magnetic Permeability

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