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.

Formula 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.

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 $(H / m)$

Formula 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 ( $\varepsilon_0$ ).

Applications of Permittivity and Permeability

Applications of Permittivity

1. Capacitors: Permittivity helps in finding the capacitance of a capacitor. Materials with high permittivity can store more electric charge.
2. Insulating Materials: It is used in the design of insulating materials to control and reduce electric field effects.
3. Communication Systems: Permittivity affects how radio and mobile signals travel through different materials like air or glass.
4. Optical Devices: It is used in lenses, sensors, and fibre optics to control how light passes through materials.

Applications of Permeability

1. Electromagnets: Permeability helps in making strong electromagnets used in motors, relays, and cranes.
2. Transformers and Inductors: It is used to select core materials that allow better magnetic flux and reduce energy loss.
3. Magnetic Storage Devices: Used in hard drives, magnetic tapes, and other data storage devices.
4. Wave Propagation: Permeability helps in understanding how electromagnetic waves move through air, metals, or water.

What is the Difference Between Permittivity and Permeability?

Permeability and Relative Permeability of Materials