Permittivity and Permeability

Permittivity and Permeability are two fundamental properties of materials that play a crucial role in the behavior of electromagnetic waves and related fields. Permittivity, represented by the symbol ε (epsilon), describes a material’s ability to permit the electric field to pass through it. Permittivity is a measure of how easily electric charges can be separated within the material in response to an applied electric field. On the other hand, Permeability, denoted as μ (mu), characterizes a material’s ability to allow magnetic fields to pass through it. Permeability represents how readily magnetic flux can propagate within the material when subjected to a magnetic field.

Together, Permittivity and Permeability determine the speed at which electromagnetic waves, such as light and radio waves, travel through a given medium. This article provides a brief description of both Permittivity and Permeability, other than that we will also discuss the key differences between Permittivity and Permeability.

What is Permittivity?

Permittivity as the name suggests, must be something related to giving permission. Permittivity is the property of a matter or a medium to permit its own field to decrease the electrostatic force/electronic interaction between two charges. Permittivity can also be defined as the measure of electric polarizability of a dielectric, polarization of material causes induction of charges which in turn creates electric fields within the material, thus opposing the electricity between the original charged particles and also storing energy at the same time.

Definition of Permittivity

Permittivity is the property of the material or medium which measure the material’s ability to resist the formation of an electric field within it or to permit the passage of electric flux.

Permittivity Symbol: Electric Permittivity is denoted by the Greek symbol ε, pronounced as epsilon.

Unit of Permittivity: The SI unit of permittivity is Farad/meter (F/m).

Dimensional Formula of Permittivity: The dimensional formula of permittivity is [M¹ L^-3 T⁴ A²].

Types of Permittivity

There are two types of permittivity:

• Permittivity of Free Space
• Relative Permittivity

Let’s dicuss these types as below:

Permittivity of Free Space (ε_₀)

The resistivity offered by the free space is the lowest and is the fundamental constant, it is referred as permittivity of free space and is denoted by ε₀. It has a value of 8.85✕ 10-12 Farad/meter.

Relative Permittivity (ε_r)

Dielectric material also shows permittivity, it is represented as the ratio of absolute permittivity of the medium or material and the permittivity of free space, known as relative permittivity. Thus relative permittivity is a dimensionless quantity, represented as ε_r.

Formula for Relative Permittivity (ε_r) is given as:

ε_r = ε/ε_₀

Where,

• ε_r is the relative permittivity of the material,
• ε is the absolute permittivity of the material, and
• ε_₀ is the permittivity of the free space.

What is Permeability?

Permeability as the name suggests refers to easy of passing through. Permeability is the property of the matter which measure how easily it is allowing external magnetic field to pass through it or how much it gets magnetized when place in an external magnetic field. When an object in placed in an external magnetic field or when magnetic lines of forces are passed through a medium the dipoles in the medium get oriented in the material so as to facilitate the passage of the magnetic flux, this is called permeability. The high the permeability of the material the more magnetization it will show in presence of external magnetic field.

Definition of Permeability

Permeability is a property of matter to get magnetized when placed in an external magnetic field. It is the property of a material or the medium which reflects the easiness offered my the material or medium to pass magnetic flux through it when placed in an external electric field.

• Permeability Symbol: Permeability is denoted by the Greek letter μ, pronounced as mu.
• Unit of Permeability: The SI unit of permeability is Henry / meter (H/m).
• Dimensional Formula of Permeability: The dimensional formula of permeability is [M¹L¹T^-2A^-2].

Types of Permeability

Permeability can be categorised as:

• Permeability of Free Space or Vacuum Permeability
• Relative Permeability

Let’s discuss these in detail.

Vacuum Permeability (μ_₀)

Just like permittivity of vacuum, permeability of vacuum is considered to be a fundamental constant. Its value is approximately 4π x 10⁻⁷ H/m. It is also referred as the permeability of the free space.

Relative Permeability (μ_r)

Relative permeability the ratio of the permeability of the material to the permeability of vacuum (μr = μ/μ₀). It is a dimensionless number that shows how much a given material can be magnetized when placed in an external electric field.

Permeability of Materials

Permeability of some of the most common Materials are given in the following table:

Material	Permeability (H/m)	Relative Permeability (μr)
Air	1.25 x 10-6	1.0000004
Water	1.26 x 10-6	1.0000004
Wood	1.26 x 10-6	1.0000004
Copper	1.257 x 10-6	0.9999
Iron	5.3 x 10-3	4000

Difference between Permittivity and Permeability

The Key differences between Permittivity and Permeability are listed in the following table:

Parameters	Permittivity	Permeability
Definition	Permittivity is the property of a medium or material to oppose the formation of external electric field.	Permeability is the property of a material or the medium which reflects the ease to pass the amgnetic flux when placed in an external magnetic field.
Relation	Permittivity is related to the electric fields.	Permeability is related to magnetic fields.
Representation	Permittivity is denoted by ε (epsilon)	Permeability is denoted by the μ (mu).
Unit	F/m ( Farad/meter)	H/m (Henry / meter)
Value in Vacuum	8.85✕ 10-12 Farad/meter	4π x 10⁻⁷ H/m.
Principle Concept	Polarization of charges	Magnetization
Application	Capacitors storing energy.	Inductors (paramagnetic and diamagnetic).

Read More,

• Electric Field Lines
• Magnetic Field
• Electric Charge and Electric Field

Sample Questions on Permittivity and Permeability

Question 1: Establish a relation between electrostatic force between two charge particle in free space to that of electrostatic force between two charge particles in a medium with relative permittivity given to be εᵣ.

Answer:

F_medium = q₁ × q₂ / 4 πε × r²

⇒ F_medium = q₁ × q₂ / 4 πε_rε_₀ × r² [As ε_r = ε/ε_₀]

⇒ F_medium = F_air/ε_r

⇒ ε_r = F_air/F_medium

Question 2: What is the relationship between relative permittivity and relative permeability?

Answer:

Both relative permittivity (εr) and relative permeability (μr) are dimensionless constants that describe how a material responds to electric and magnetic fields with respect to their behaviour in free space.

Question 3: How will the electrostatic force between two charge particle changes when placed in a material of relative permittivity of 2.0?

Answer:

Since the relative permittivity of the medium is 2.0 the electrostatic force between two charge particle changes will reduce to half in medium as compared to that in free space.

Practice Problems on Permittivity and Permeability

Problem 1: Calculate the relative permittivity of a material with a permittivity of 6.4 x 10⁻¹² C²/N·m².

Problem 2: Determine the relative permeability of a substance with a permeability of 2.8 x 10⁻⁷ N/A².

Problem 3: Explain the role of permittivity in dielectric materials.

Problem 4: Discuss how permeability affects the propagation of electromagnetic waves.

Permittivity and Permeability: FAQs

1. Define Permittivity.

The ability of the material to resist the formation of an electric field when exposed to an electric field is called permittivity.

2. What is the unit of Permittivity?

Unit of Permittivity is farad per meter (F/m).

3. How does Permeability of Free Space Differs from Permeability of Materials?

Permeability of free space is a constant denoted as μ₀, where as materials have their own relative permeability (μᵣ), which is the ratio of a material’s absolute permeability to that of permeability of free space.

4. Can Materials have both High Permittivity and Permeability?

Yes, materials like ferromagnetic substances can have high values of both relative permittivity as well as relative permeability.

5. How does Permittivity Affect Capacitance?

Capacitance is directly proportional to the permittivity of the material between the plates of a capacitor. Increasing the permittivity of the dielectric material between the plates increases the capacitance of the capacitor.

6. Define Permeability.

Permeability, represented by the symbol μ (mu), is a measure of a material’s ability to permit the magnetic field to pass through it. It quantifies how much a magnetic field is weakened or distorted when passing through a particular medium.

7. What is Relative Permeability?

Relative permeability is a dimensionless quantity that represents the ratio of a material’s permeability to the permeability of free space (μ₀). It is denoted by μ_r. Relative permeability quantifies how much a material’s permeability differs from that of free space.