Dimensions of Permeability

Dimensions of Permeability: Permeability was indeed outlined as the amount of magnetization that a material obtains in response to an applied magnetic field in electromagnetism. The Greek letter μ is commonly used to represent permeability. Oliver Heaviside invented the term in September 1885. Magnetic reluctance is indeed the reciprocal of permeability.

Permeability has always been measured in SI units of henries per metre (H/m), or in newtons per ampere squared (N/A²). The permeability constant μ0 is the proportionality between magnetic induction and magnetising force when forming a magnetic field in a classical vacuum. It is often known as the magnetic constant or the permeability of free space.

Magnetic susceptibility is said to be a material property that is closely related to magnetism and it is a dimensionless proportionality factor that indicates the degree of magnetization of a substance or material in response to an external magnetic field.

Materials may be classified magnetically on the basis of their permeabilities. When compared to a vacuum, diamagnetic materials end up causing the lines of flux to move farther apart, resulting in a decrease in magnetic flux density. Components that concentrate magnetic flux by a factor greater than one but less than or equal to ten are referred to as paramagnetic; substances that concentrate flux by a factor greater than ten are referred to as ferromagnetic. A few substances’ permeability factors change as the temperature rises or falls, or as the intensity of the applied magnetic field changes. The relative permeability rises as the magnetising field increases reach a maximum and then decreases. The optimum relative permeability of pure iron and many magnetic alloys is 100,000 or higher. Let us learn about the dimensional formula of permeability.

Dimensional Formula of Permeability

The dimensional formula of permeability can be represented as,

[M¹ L¹ T^-2 I^-2]

Here,

M = Mass

I = Current

L = Length

T = Time

Derivation

We have, Magnetic Permeability (μ) = Magnetic flux density × [Magnetic field strength]^-1 . . . . (1)

As because, Force = magnetic flux density × current × length

Thus, magnetic flux density = Force × [Current × Length]^-1 . . . . (2)

Now, The dimensional formula of,

Force = [M¹ L¹ T^-2] . . . (3)

Current = [M⁰ L⁰ T⁰ I¹] . . . (4)

Length = [M⁰ L¹ T⁰] . . . . . (5)

When substituting equation (3), (4) and (5) in equation (2) we get,

Magnetic flux density = Force × [Current × Length]^-1

= [M¹ L¹ T^-2] × [M⁰ L⁰ T⁰ I]^-1 × M⁰ L¹ T⁰]^-1

Thus, the dimensional formula of magnetic flux density = [M¹ L⁰ T^-2 I^-1] . . . . (6)

Similarly, the dimensions of Magnetic field strength = [M⁰ L^-1 T⁰ I¹] . . . . . (7)

When substituting equation (6) and (7) in equation (1) we get,

Magnetic Permeability = Magnetic flux density × [Magnetic field strength]^-1

That is, μ = [M¹ L⁰ T^-2 I^-1] × [M⁰ L^-1 T⁰ I¹]^-1 = [M¹ L¹ T^-2 I^-2]

Thus, the magnetic permeability has been dimensionally represented as [M¹ L¹ T^-2 I^-2].