Permittivity and Permeability - Meaning, Formula, Comparison, FAQs

What is Permittivity?

Permittivity is the property of every substance that determines the amount of resistance it provides to the production of an electric field. Permittivity is denoted by $\varepsilon$, It indicates how many charges are necessary to produce one unit of electric flux in a given material.

S.I. unit of permittivity is Farad/metre.

Mathematical Expression of Permittivity

$$
\varepsilon=\varepsilon_0 \cdot \varepsilon_r
$$

• $\varepsilon_0$ : Permittivity of free space $\left(8.854 \times 10^{-12} \mathrm{~F} / \mathrm{m}\right)$
• $\varepsilon_r$ : Relative permittivity or dielectric constant of the material.

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Unit of Permittivity

Derived Unit from$$
\mu=\frac{B}{H}
$$
$$
\mu(H / m)=\frac{T}{A / m}=\frac{\mathrm{N}}{\mathrm{~A}^2}
$$

Thus, the unit of permeability is also expressed as: Newton per Ampere squared (N/A ${ }^2$ ).

Dimensional Formula of Permittivity

The dimensional formula of permittivity of free space is [M^-1L^-3T⁴A²].

Types of Permittivity

Dielectric Permittivity: Describes the ability of a material to polarize in response to an electric field.
Expressed as:

$$
\varepsilon=\varepsilon_0 \cdot \varepsilon_r
$$

where:
$\varepsilon_0$: Permittivity of free space.
$\varepsilon_r$: Relative permittivity or dielectric constant.

Relative Permittivity $\left(\epsilon_r\right)$: A ratio of the material's permittivity to the permittivity of free space:

$$
\varepsilon_r=\frac{\varepsilon}{\varepsilon_0}
$$
Absolute Permittivity ( $\varepsilon$ ): The actual value of permittivity for a specific material, including contributions from free space and the material's properties.

What is Permeability?

Permeability is the ability of a material to allow the formation of magnetic lines of force or magnetic fields within it in electrostatics. It refers to a material's ability to magnetise in response to an applied magnetic field. Permeability is denoted by $\mu$.

In simpler terms, magnetic permeability can be defined as "the extent to which magnetic field lines can enter a substance." or "the power of a substance to conduct magnetic field lines."

S.I. unit of Permeability is Henry per meter $(H / m)$

Mathematical Expression of Permeability

$$
B=\mu \cdot H
$$
Where:

• $B$ : Magnetic flux density (in Tesla, $T$ or $\mathrm{Wb} / \mathrm{m}^2$ ).
• $H$ : Magnetic field strength (in $A / m$ ).
• $\mu$ : Permeability (in $H / m$ ).

Unit of Permeability

Derived Unit: Permeability is defined as:

$$
\mu=\frac{B}{H}
$$

Substituting the units:

$$
\mu=\frac{T}{A / m}=\frac{\text { Weber per square meter }}{\text { Ampere per meter }}=\frac{\text { Weber }}{\text { Ampere } \cdot \text { Meter }}=H / m
$$
Dimension formula of Permeability is $\left[\mathrm{MLT}^{-2} \mathrm{~A}^{-2}\right]$

Types of Permeability

Magnetic permeability

The magnetic permeability of a material is defined as the ability of the substance to enable a magnetic line of force to pass through it. Magnetic permeability is measured in Henry per metre (SI units).

The ratio of flux density to magnetic force, or magnetic permeability, is defined as:

$\mu=\mathrm{BH}$

Absolute permeability

Absolute permeability is a constant value that is related to the permeability of free space and is written as:

$\mu_0=4 \pi \times 10^{-7} \mathrm{H} / \mathrm{m}$

Relative permeability

The ratio of the absolute permeability of magnetic material to the absolute permeability of air is defined as the relative permeability of a magnetic material.

Relative Permeability, $\mu_{\mathrm{r}}=\mu / \mu_0$

It is a dimensionless quantity.

Relationship Between Permittivity, Permeability, and Speed of Light

Permittivity and permeability are interconnected through the speed of light ( $c$ ) in a vacuum:

$$
c=\frac{1}{\sqrt{\mu_0 \cdot \varepsilon_0}}
$$
This equation highlights that the speed of light depends on the fundamental constants of vacuum permeability ( $\mu_0$ ) and vacuum permittivity ( $\varepsilon_0$ ).

Difference Between Permittivity and Permeability

Permeability and Relative permeability of Materials