Permittivity And Permeability

What is Permittivity?

It is the property of every material, which measures the opposition offered against the formation of an electric field. Represented by the Greek alphabet ϵ. It tells the number of charges required to generate one unit of electric flux in the given medium. Following is the table for its mathematical form and SI unit:

Mathematical expression \(Permittivity=\frac{Electric\;displacement}{Electric\;field\;intensity}\)
SI unit of permittivity Faraday/meter

The vacuum characterizes the least possible value of Permittivity. This is commonly referred to as Permittivity of Free Space or electric constant. Denoted by ϵ0 and has the value 8.85✕ 10-12 Faraday/meter. The opposition against the formation of electric field lines is evident in dielectrics too. The permittivity of a dielectric is represented by the ratio of its absolute permittivity to electric constant and is commonly called relative permittivity. It is a dimensionless quantity and is given as:

\(\varepsilon_{r} =\frac{\varepsilon }{\varepsilon _{0}}\)

Where,

  • ϵ0 is the electric constant
  • ϵr is the relative permittivity
  • ϵ is the absolute permittivity of that material

Using Coulomb’s law, The magnitude of the electrostatic force between two point charges q1 and q2 separated by a distance r in free space can be calculated using relative permittivity(ϵr). By taking “the ratio of electrostatic force(Fa) between two point charges separated by a certain distance in air or vacuum to the electrostatic force(Fm) between the same two point charges separated by the same distance in a medium.” It is expressed as:

\(\varepsilon_{r} =\frac{F_{a}}{F_{m}}\)

Where,

  • \(F_{a}=\frac{1}{4\pi \varepsilon _{0}}\frac{q_{1}q_{2}}{r^{2}}\)
  • \(F_{r}=\frac{1}{4\pi \varepsilon _{0}\varepsilon _{r}}\frac{q_{1}q_{2}}{r^{2}}\)

What is Permeability?

In electrostatics, the permeability is the measure of the ability of the material to allow the formation of magnetic lines of force or magnetic field within. It speaks on the ability of magnetization that a material possesses for the applied magnetic field. In simpler words, we can define magnetic permeability as “the extent to which magnetic field lines can enter substance.” or “The power of conducting magnetic field lines by a substance.” It is denoted by the Greek alphabet μ. Following is the table with the mathematical representation of permeability, SI unit, and dimensional formula:

Mathematical representation \(Permeability=\frac{Magnitude\;of\;magnetic\;induction(B)}{Intensity\;of\;magnetic\;field(H)}\)\(\mu =\frac{B}{H}orB=\mu H\)
SI unit H/m or TmA-1 where H is Henries
Dimension formula [MLT-2A-2]

The permeability of free space is called Permeability constant and has the value μ0 = 4𝝅×10-7 H/m It is a scalar quantity of isotropic medium and second rank tensor for anisotropic medium. Magnetic permeability plays an important role in classifying the magnetization property of a material. The material is said to be diamagnetic if its magnetic permeability is less than μ0. Similarly, the material is said to be paramagnetic if its magnetic permeability is greater than μ0.

Magnetic Permeability

The magnetic permeability is defined as the property exhibited by the material where the material allows the magnetic line of force to pass through it. The SI unit of magnetic permeability is Henry per metere.

Magnetic Permeability Formula

Magnetic permeability is defined as the ratio of flux density to magnetic force which is given as:

\(\mu =\frac{B (Tesla)}{H (\frac{A-t}{m})}\)

Absolute Permeability

Absolute permeability is related to permeability of free space and is a constant value which is given as:

μ0 = 4Π × 10-7 H.m-1

The absolute permeability for other materials can be expressed relative to the permeability of free space as:

μ = μ0μr

Where μis the relative permeability which is a dimensionless quantity.

Relative Permeability

Relative permeability for a magnetic material is defined as the ratio of absolute permeability to absolute permeability of air.

Permeability and Relative Permeability of Materials

Material Permeability (μ) (H.m-1) Relative Permeability (μr)
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

Permittivity Vs Permeability

Parameters for comparison Permittivity Permeability
Definition A measure of the opposition offered by any material for against the formation of an electric field It is the measure of the extent to which magnetic field lines can enter substance.
Formula \(Permittivity=\frac{Electric\;displacement}{Electric\;field\;intensity}\) \(Permeability=\frac{Magnitude\;of\;magnetic\;induction(B)}{Intensity\;of\;magnetic\;field(H)}\)
Represented by ϵ μ
SI Unit Farady/meter or F/m Henries/meter or H/m
The value in free space The permittivity of Free Space ϵ0= 8.85✕ 10-12 Faraday/meter The permeability of free space μ0 = 4𝝅×10-7 H/m
Field Electric field Magnetic field
Principle involved Polarisation of electric charges Magnetization
Application Capacitors Transformer core and Inductors

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