Permittivity and Permeability

Permittivity

The property of the material that measures the resistance offered to the formed electric field or an ongoing electric field is known as permittivity. It is represented by the Greek letter epsilon, ϵ. It informs about the number of charges needed to generate a unit of electric flux for a given medium.

Permittivity = electrical displacement / electric field intensity

SI unit of electrical permittivity = Farad/meter

The least value of permittivity is found in a vacuum. This permittivity in a vacuum is known as the permittivity of free space or electric constant and is denoted by ϵ0 with the value 8.85✕ 10-12 Farad/meter. Dielectric materials also possess permittivity properties as they have an electric field. Permittivity in dielectrics is dimensionless, represented by the ratio of absolute permittivity to the electric constant, and is denoted by-

εr = ε / εo

where, ϵr is the relative permittivity

ϵ is the absolute permittivity of that material

ϵ0 is the electric constant

Coulomb’s law states that the two-point charges q1 and q2 separated by distance r in free space have some magnitude of the electrostatic force between them. This force can be calculated by using relative permittivity. Using the ratio of the electrostatic force between these two-point charges to the vacuum electrostatic force between the same two-point charges is given by-

Fa = q1 q2 / 4 π εo r2

Fr = q1 q2 / 4 π εo εr r2

Permeability

Permeability of the material is the ability to allow the formation of magnetic fields or magnetic field lines of force. Thus, it tells about the material’s magnetizing properties when subjected to the magnetic field. In simpler words, we can define permeability as the extent of penetration of a magnetic field in a material or the conducting power of a material to conduct magnetic field lines. It is denoted by the Greek letter mu, μ.

SI unit of permeability = H/m or TmA-1, where H is Henry

The dimensional formula of permeability = MLT-2A-

Permeability = magnitude of magnetic induction (B) / intensity of magnetic field (H)

The free space permeability is referred to as the permeability constant, given by μ0 = 4𝝅×10-7 H/m. It is a second rank tensor for anisotropic medium and is a scalar quantity. Permeability plays a significant role in classifying the magnetizing property of a medium. For example, if the magnetic permeability is less than μ0, the material is diamagnetic. Similarly, if the magnetic permeability is greater than μ0, then the material is said to be paramagnetic.

Definitions

Magnetic permeability – The property exhibited by a material due to which magnetic lines of force can pass through it is magnetic permeability. The SI unit of magnetic permeability is Henry per meter. It is the ratio of flux density to the magnetic force-

Μ = B (Tesla) / H ((A-t)/m)
Absolute permeability – The permeability of free space is called absolute permeability. It is a constant value, denoted by-

μ0 = 4π × 10-7 H m-1

It is given by-

μ = μ0 μr

Where, μr is the relative permeability and a dimensionless quantity
Relative permeability – The ratio of absolute permeability to the absolute permeability of air is known as relative permeability.

Permeability of different materials

Material	Permeability (μ) (H m^-1)	Relative Permeability (μ_r)
Air	1.257 × 10^-6	1.000
Copper	1.257 × 10^-6	0.999
Vacuum	4π × 10^-7	1
Water	1.256 × 10^-6	0.999
Wood	1.257 × 10^-6	1.00

Difference between permittivity and permeability

In physics, permittivity and permeability both are significant in the electrical field and magnetic field respectively. They difference between them is described as under-

Permeability	Permittivity
The ability to allow the formation of magnetic field or magnetic field lines of force	The property of the material that measures the resistance offered to the formed electric field or an on-going electric field
Permeability = magnitude of magnetic induction (B) / intensity of magnetic field (H)	Permittivity = electrical displacement / electric field intensity
It is represented by μ.	It is represented by ϵ.
SI unit of permeability = H/m or TmA^-1, where H is Henry.	SI unit of electrical permittivity = Farad / meter
The permeability constant is given by μ₀ = 4𝝅×10^-7 H/m.	The permittivity of free space ϵ₀ possesses the value 8.85✕ 10^-12 Farad/meter.
The field in permeability is the magnetic field.	The field in permittivity is the electric field.
The principle involved in permeability is magnetization.	The principle involved in permittivity is the polarisation of electric charges.
It is used in inductors and cores of transformers.	It is used in capacitors to store energy.