# Permittivity and Permeability

Permittivity and permeability are two different measures used in electromagnetism. Permittivity measures the ability of a material to store energy within the material. Permeability is a measure of the ability of a material to support the formation of a magnetic field within the material.

## What Is Permittivity?

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

 Mathematical expression $$\begin{array}{l}Permittivity=\frac{Electric\;displacement}{Electric\;field\;intensity}\end{array}$$ SI unit of permittivity Farad/metre

The vacuum characterises the least possible value of Permittivity. This is commonly referred to as the Permittivity of Free Space or electric constant, which is denoted by Ο΅0 and has the value 8.85β 10-12 Farad/metre. 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 the electric constant and is commonly called relative permittivity. It is a dimensionless quantity and is given as

 $$\begin{array}{l}\varepsilon_{r} =\frac{\varepsilon }{\varepsilon _{0}}\end{array}$$

Where,

• Ο΅0 is the electric constant
• Ο΅r is the relative permittivity
• Ο΅ 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(Ο΅r). By taking β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.β It is expressed as

 $$\begin{array}{l}\varepsilon_{r} =\frac{F_{a}}{F_{m}}\end{array}$$

Where,

• $$\begin{array}{l}F_{a}=\frac{1}{4\pi \varepsilon _{0}}\frac{q_{1}q_{2}}{r^{2}}\end{array}$$
• $$\begin{array}{l}F_{r}=\frac{1}{4\pi \varepsilon _{0}\varepsilon _{r}}\frac{q_{1}q_{2}}{r^{2}}\end{array}$$

## What Is Permeability?

In electrostatics, 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 of the ability of magnetisation that material possesses for the applied magnetic field. In simpler words, we can define magnetic permeability as βthe extent to which magnetic field lines can enter a substance.β or βThe power of conducting magnetic field lines by a substance.β It is denoted by the Greek alphabet ΞΌ. Following is the table with the mathematical representation of permeability, SI unit, and dimensional formula:

 Mathematical representation $$\begin{array}{l}Permeability=\frac{Magnitude\;of\;magnetic\;induction(B)}{Intensity\;of\;magnetic\;field(H)}\end{array}$$$$\begin{array}{l}\mu =\frac{B}{H}orB=\mu H\end{array}$$ 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 ΞΌ0 = 4πΓ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 magnetisation property of a material. The material is said to be diamagnetic if its magnetic permeability is less than ΞΌ0. Similarly, the material is said to be paramagnetic if its magnetic permeability is greater than ΞΌ0.

### Magnetic Permeability

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 metre.

### Magnetic Permeability Formula

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

 $$\begin{array}{l}\mu =\frac{B (Tesla)}{H (\frac{A-t}{m})}\end{array}$$

### Absolute Permeability

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

 ΞΌ0 = 4Ξ Β Γ 10-7 H.m-1

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

 ΞΌ =Β ΞΌ0ΞΌr

WhereΒ ΞΌrΒ is 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 (ΞΌ) (H.m-1) Relative Permeability (ΞΌr) Air 1.257Β Γ 10-6 1.000 Copper 1.257Β Γ 10-6 0.999 Vacuum 4ΟΒ Γ 10-7 1 Water 1.256Β Γ 10-6 0.999 Wood 1.257Β Γ 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 $$\begin{array}{l}Permittivity=\frac{Electric\;displacement}{Electric\;field\;intensity}\end{array}$$ $$\begin{array}{l}Permeability=\frac{Magnitude\;of\;magnetic\;induction(B)}{Intensity\;of\;magnetic\;field(H)}\end{array}$$ Represented by Ο΅ ΞΌ SI Unit Farad/metre or F/m Henries/metre or H/m The value in free space The permittivity of Free Space Ο΅0= 8.85β 10-12 Farad/metre The permeability of free space ΞΌ0 = 4πΓ10-7 H/m Field Electric field Magnetic field Principle involved Polarisation of electric charges Magnetization Application Capacitors Transformer core and Inductors

## Frequently Asked Questions β FAQs

Q1

Permittivity.

Q2

### What is the SI unit of permittivity?

SI unit of permittivity is Farad/metre.

Q3

### What is meant by the permittivity of free space?

It is a type of constant that shows the capacity of electrical fields to go through a vacuum.
Q4

### What is the SI unit of magnetic permeability?

The SI unit of magnetic permeability is Henry per metre.

Q5

### What is the relative permeability of vacuum?

The relative permeability of vacuum is 1.

Q6

### What is the permittivity of free space?

The Permittivity of Free Space

$$\begin{array}{l}\varepsilon _{0}= 8.85 * 10^{-12}\,\, Farad/metre.\end{array}$$