Permittivity and Permeability

Permittivity and Permeability

What is permittivity?

Permittivity Meaning: It is the property of every substance that determines the amount of resistance it provides to the production of an electric field. The Greek alphabet ε is used to represent it. It indicates how many charges are necessary to produce one unit of electric flux in a given material.

Permittivity formula:

Permittivity = Electric Displacement/Electric Field density

SI unit of permittivity is Farad/metre.

Relative permittivity

The vacuum represents the lowest possible Permittivity value. This is also known as the electric constant or Permittivity of Free Space. The value of 8.85 × 10-12 Farad/meter is denoted by the ε0. The resistance to the production of electric field lines can also be seen in dielectrics. A dielectric's permittivity is defined as the ratio of its absolute permittivity to its electric constant, which is referred to as relative permittivity. It is a dimensionless quantity that is expressed as:

Relative Permittivity, ε r = 0

Where ε – absolute permittivity of the material

ε0 – Permittivity of Free Space

εr – relative permittivity

Relative vacuum permittivity (εr) can be used to compute the amount of the electrostatic force between two point charges q1 and q2 separated by a distance r in free space using Coulomb's law. The electrostatic force (Fa) between two point charges separated by a specific distance in air or vacuum is compared to the electrostatic force (Fm) between the same two-point charges separated by the same distance in a medium. It's written like:

εr = FaFm

Where Fa =14Π0 q1q2r2

Fm = 14Π ε0rq1q2r2

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Dimensional formula of permittivity

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

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. 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." The Greek alphabet μ is used to represent it. The table below shows the mathematical representation of permeability, as well as the SI unit and dimensional formula: The value of permeabilityis given by:

FormulaPermeability = Magnitude of magnetic induction (B)/Intensity of magnetic field (H)
Dimension formula[MLT-2A-2]
SI UnitH/m or TmA-1

The Permeability constant measures the permeability of free space and has a value of μ0 = 4π× 10-7 H/m. Magnetic permeability is a key factor in classifying a material's magnetization property. If the magnetic permeability of a substance is less than μ0, it is said to be diamagnetic. Similarly, if the magnetic permeability of a substance is more than μ0, it is said to be paramagnetic.

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).

Magnetic permeability formula

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

μ = BH

Absolute permeability

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

μ0 = 4π× 10-7 H/m

Relative permeability

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

Relative Permeability, μr = 0

Where μr is a dimensionless quantity.

Comparison of permittivity and permeability

Comparison ParametersPermittivityPermeability
DefinitionIt is the measure of resistance offered by any material against the formation of an electric fieldIt is a measurement of how far magnetic field lines may penetrate a substance.
FormulaPermittivity = Electric DisplacementElectric Field densityPermeability = Magnitude of magnetic induction (B)Intensity of magnetic field (H)
Symbolεμ
SI UnitFarad/metre or F/mHenries/metre or H/m
Value in free spaceε0 = 8.85 × 10-12 F/mμ0 = 4π× 10-7 H/m
Principle InvolvedPolarisation of electric chargesMagnetisation
FieldElectric FieldMagnetic Field
ApplicationIn capacitorsIn transformer core and inductors

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