What are Permittivity and Permeability?
In electromagnetic theory, there are two concepts known as permittivity and permeability. The concept related to the formation of an electric field is known as permittivity, and the one related to the magnetic field is known as permeability.
Definition of Permittivity
Permittivity can be explained as the ratio of electric displacement to the electric field intensity. It is the property of a material to measure the opposition generated by the material during the electric current development.
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The permittivity of a material is represented by the symbol ε. The SI unit of permittivity is Farad per metre. The approximate value for permittivity is 8.85 X 10-12 Faraday/metre, which is found in a vacuum medium. The permittivity measures the number of charges needed for generating a unit of electric flux in a specific channel.
Permittivity is expressed in relative terms in engineering applications instead of absolute terms. The permittivity of free space (that is, 8.85 x 10-12 F/m) is represented by eo and the permittivity of substance in question (also represented in farads per metre) is represented by e. Here, the relative permittivity dielectric constant er, is given by:
\[e_r = \frac{e}{e_o} \]
= e (1.13 x 1011)
Definition of Permeability
The property of the material which supports the formation of magnetic flux when passed through a magnetic field is known as permeability. It is affected by the field frequency, temperature, field strength, and humidity. It is represented by μ.
The permeability of the material is defined as the ratio of flux density to the field strength of a material. It is also directly proportional to the conduction of magnetic lines of force. The permeability of free space is also known as the permeability constant and is represented by μ0, which is approximately equal to 4Π X 10-7Henry/metre.
The symbol for permeability is μ. It is also defined as the ratio of the intensity of magnetic field (simple magnetic field) to the magnetic field (i.e., the limit to which the magnetic field can magnetize a material).
\[\mu = \frac{\text{Intensity of Magnetic Field (B)}}{\text{Intensity of Magnetizing Field (H)}}\]
or, \[\mu = \frac{B}{H}\]
Unit of Permeability
The unit of measurement for the intensity of the magnetic field is Tesla (T) or Newton per Ampere metre (N/Am).
Ampere per metre (A/m) is the unit of a magnetizing field.
Magnetic reluctivity is the reciprocal of magnetic permeability. The SI unit of permeability is given as Henries-per-metre (H/m). It is measured in Newtons-per Ampere squared (N/A2)
So as per the above permeability formula, it becomes unit Newton per Ampere square.
\[\mu = \frac{Newton}{\text{ Ampere Square}}\]
Or \[\mu = \frac{N}{A^2} \]
By calculating their equations and units, we will find the dimension of permeability to be
[M1L1T-2I-2].
Difference Between Permittivity and Permeability
The main differences between permittivity and permeability are explained below.
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From the above text, we understand that during the formation of electric fields, the obstruction produced by the material is measured by the permittivity. In contrast, the ability of the material to allow magnetic lines to conduct through it is known as permeability.
FAQs on Permittivity and Permeability
1. What is the fundamental difference between permittivity (ε) and permeability (μ)?
Permittivity and permeability describe how electric and magnetic fields behave in a material. Permittivity (ε) relates to the electric field, measuring a material's ability to store electrical energy when an electric field is applied. It essentially quantifies the resistance to the formation of an electric field. In contrast, permeability (μ) relates to the magnetic field, measuring a material's ability to support the formation of a magnetic field within itself. In simple terms, permittivity is for electricity, and permeability is for magnetism.
2. What are the defined values and SI units for the permittivity and permeability of free space?
In free space (a vacuum), these constants have defined values that are crucial in physics.
- The permittivity of free space (ε₀) is approximately 8.854 x 10⁻¹² Farads per meter (F/m).
- The permeability of free space (μ₀) is defined as exactly 4π x 10⁻⁷ Tesla meters per Ampere (T·m/A), which is also expressed as Henry per meter (H/m).
3. How do permittivity and permeability determine the speed of light in any medium?
The speed of an electromagnetic wave, such as light, in any medium is determined by the medium's permittivity (ε) and permeability (μ). The relationship is given by the formula: c = 1 / √(εμ). In a vacuum, the speed of light 'c' is constant because it is calculated using the constants ε₀ and μ₀. When light enters a material medium like glass or water, the values of ε and μ are different from those in a vacuum, which causes the speed of light to decrease within that medium.
4. What is the physical meaning of relative permittivity, often called the dielectric constant?
Relative permittivity (εᵣ), also known as the dielectric constant (K), is a dimensionless factor that shows how much a material can reduce the electric field strength inside it. It is the ratio of the permittivity of a substance (ε) to the permittivity of free space (ε₀). For example, water has a relative permittivity of about 80. This means water can reduce the electrostatic force between two charges to 1/80th of its value in a vacuum, which explains its effectiveness as a solvent for ionic compounds.
5. Why do different materials exhibit unique permittivity and permeability values?
Different materials have unique permittivity and permeability values due to their atomic and molecular structure.
- Permittivity is determined by how easily the molecules or atoms in a material can be polarised by an external electric field. Materials with easily polarisable molecules (like water) have high permittivity.
- Permeability depends on how the electron orbits and spins within a material's atoms align with an external magnetic field. In materials like iron (ferromagnetic), atomic magnetic moments align easily, resulting in very high permeability.
6. How does the permittivity of a dielectric material affect the capacitance of a capacitor?
The permittivity of a dielectric material directly increases the capacitance of a capacitor. When a dielectric is inserted between a capacitor's plates, its molecules polarise, creating an internal electric field that opposes the external field. This reduces the potential difference across the plates for the same amount of charge, allowing more charge to be stored. The capacitance (C) of a parallel-plate capacitor with a dielectric is given by C = K * C₀, where C₀ is the capacitance in a vacuum and K is the dielectric constant (relative permittivity) of the material.
7. In what practical devices are the properties of permittivity and permeability critically important?
These properties are crucial in the design and function of many technologies:
- Permittivity is vital for designing capacitors, where high-permittivity materials (dielectrics) are used to increase charge storage. It's also important in high-frequency circuits and manufacturing semiconductor devices.
- Permeability is essential for devices involving magnetism, such as transformers, inductors, and electromagnets. Materials with high permeability (like soft iron) are used as cores to concentrate magnetic fields, making these devices more efficient.
