Otis Singleton
The electric constant, also known as vacuum permittivity, is the capability of a vacuum to permit electric field lines. It is denoted by ε0 and is used to determine charged particle interaction and force. It is included in the formulation of Coulomb's Law, which gives the expression for the force acting between two electric charges. The electric constant is a fundamental concept in physics, relating the electric charge with mechanical units such as force and distance.
| Characteristics | Values |
|---|---|
| Other Names | Vacuum permittivity, permittivity of free space, distributed capacitance of the vacuum, dielectric constant of vacuum |
| Symbol | ε0 ("epsilon nought" or "epsilon zero") |
| Definition | The capability of the vacuum to permit electric field lines |
| Calculation | ε0 = 1/μ0c^2, where c is the defined value for the speed of light in classical vacuum in SI units, and μ0 is the magnetic constant |
| SI Value | 8.854 x 10^-12 F/m |
| Coulomb's Law | F_C = (1/4π ε0) x (q1q2/r^2) |
| Use Cases | Determining charged particle interaction and force, formulation of Coulomb's Law, expressing electric displacement field D |
| Related Concepts | Dielectric constant, relative permittivity, polarization density vector, electric susceptibility |
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What You'll Learn
- The electric constant is also known as vacuum permittivity
- It measures a vacuum's ability to permit electric field lines
- It is used to determine charged particle interaction and force
- It is included in the formulation of Coulomb's Law
- It is a constant factor in the centimetre–gram–second electrostatic system of units
The electric constant is also known as vacuum permittivity
The electric constant, also known as vacuum permittivity, is denoted by ε0 (pronounced "epsilon nought" or "epsilon zero"). It is the value of the absolute dielectric permittivity of classical vacuum. It is an ideal (baseline) physical constant.
Vacuum permittivity is defined as the vacuum's ability to permit an electric field or the capacity of the electric field to travel through a vacuum. It is a measure of how dense an electric field is "permitted" to form in response to electric charges. It relates the units for electric charge to mechanical quantities such as length and force. For example, the force between two separated electric charges with spherical symmetry (in the vacuum of classical electromagnetism) is given by Coulomb's law.
The electric constant is also referred to as the permittivity of free space or the distributed capacitance of the vacuum. It is used as a unit in electrical engineering to quantify the permittivity of various dielectric materials.
Historically, the electric constant has been known by many different names. The terms vacuum permittivity or its variants, such as permittivity in/of vacuum, permittivity of empty space, or permittivity of free space are widespread. The term dielectric constant of vacuum for the electric constant ε0 is considered obsolete by most modern authors, although occasional examples of continuing usage can be found.
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It measures a vacuum's ability to permit electric field lines
The electric constant, also known as vacuum permittivity, is a measurement of a vacuum's ability to permit electric field lines. It is denoted by the symbol ε0 (pronounced "epsilon nought" or "epsilon zero") and is considered an ideal (baseline) physical constant. It is a measure of how dense an electric field is "permitted" to form in response to electric charges. In other words, it describes the capacity of an electric field to travel through a vacuum.
Vacuum permittivity tells us about the capacitance of a capacitor. A vacuum is defined as a space that is free from matter. Permittivity, in this context, refers to the material's ability to store electrical potential energy under the influence of an electric field. Therefore, vacuum permittivity specifically pertains to the vacuum's ability to permit an electric field.
The electric constant is used in equations that define electromagnetic quantities, such as Maxwell's equations, which describe the properties of electric and magnetic fields, electromagnetic radiation, and their sources. It also appears in the relationship that defines the electric displacement field (D) in terms of the electric field (E) and the classical electrical polarization density (P) of the medium.
The value of ε0 is determined by the values of c0 (the speed of light in a vacuum) and μ0 (the magnetic constant or vacuum permeability). The formula for the electric constant is given as ε0 = 1/µ0c0. The numerical value of ε0 is approximately 9 x 10^9 N⋅m2⋅C^-2.
The electric constant is also related to the concept of the dielectric constant, which is the ratio of the absolute permittivity of a medium to the absolute permittivity of a vacuum. The dielectric constant measures the ability of a dielectric material to store energy in an electric field. It is used in capacitor design to increase capacitance in a circuit.
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It is used to determine charged particle interaction and force
The electric constant, also known as vacuum permittivity, is a measure of how dense an electric field is allowed to form in response to electric charges. It is denoted by ε0 ("epsilon nought" or "epsilon zero") and is an ideal physical constant.
The electric constant is used to determine charged particle interaction and force. It can be used in place of Coulomb's constant for this purpose. Coulomb's law states that the magnitude of the attractive or repulsive electrostatic force between two point charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. Coulomb's law was discovered by French physicist Charles-Augustin de Coulomb and was essential to the development of the theory of electromagnetism.
The electric constant is the inverse of 4πke (Coulomb constant). The value of ke may be chosen arbitrarily if there are no constraints. The formula for the force between two separated electric charges with spherical symmetry in a vacuum is:
> {\displaystyle F_{\text{C}}={\frac {1}{4\pi \varepsilon _{0}}}{\frac {q_{1}q_{2}}{r^{2}}}}
Here, q1 and q2 are the charges, r is the distance between their centres, and the value of the constant fraction 1/(4πε0) is approximately 9×109 N⋅m2⋅C−2.
The electric constant is also related to Maxwell's equations, which describe the properties of electric and magnetic fields, electromagnetic radiation, and their sources. In these equations, ε0 appears alongside the magnetic constant (also known as the permeability of free space) and the speed of light in a vacuum.
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It is included in the formulation of Coulomb's Law
The electric constant, also known as vacuum permittivity, is the capability of a vacuum to permit electric field lines. It is denoted by ε0 (epsilon naught or epsilon zero) and is an ideal physical constant. The electric constant is a measurement-system constant that appears in Maxwell's equations, which describe the properties of electric and magnetic fields, electromagnetic radiation, and their sources.
Coulomb's law, or Coulomb's inverse-square law, is an experimental law of physics that calculates the amount of force between two electrically charged particles at rest. It was first published in 1785 by French physicist Charles-Augustin de Coulomb. The law states that the magnitude or absolute value of the attractive or repulsive electrostatic force between two point charges is directly proportional to the product of their charge magnitudes and inversely proportional to the square of the distance between them.
The electric constant is included in the formulation of Coulomb's law. Coulomb's law can be written as:
> {\\displaystyle F\_{\\text{C}}=\\frac{1}{4\\pi \
\\varepsilon \_0}\\frac{q\_1q\_2}{r^{2}}}
In this equation, FC represents the electrostatic force, ε0 is the electric constant, q1 and q2 are the charges, and r is the distance between their centres. The value of the constant fraction 1/(4πε0) is approximately 9×109 N⋅m2⋅C−2.
Coulomb's law is an inverse-square law, similar to Newton's law of universal gravitation. However, they differ in that gravity is always attractive, while electrostatic forces can be attractive or repulsive, depending on the charges. Coulomb's law is essential to the development of the theory of electromagnetism and provides insights into the form of the magnetic field generated by moving charges.
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It is a constant factor in the centimetre–gram–second electrostatic system of units
The electric constant, also known as vacuum permittivity, is the capability of a vacuum to permit electric field lines. It is denoted by ε0 (epsilon naught or epsilon zero) and is a measurement-system constant. It is an ideal (baseline) physical constant and is used to determine charged particle interaction and force.
The electric constant is a factor in the centimetre–gram–second electrostatic system of units (the cgs esu system). This system was developed in the 1860s and formalised in 1874 by James Clerk Maxwell, William Thomson (later Lord Kelvin), and others. It is based on the concept of a coherent system of units, where base units combine to define derived units without extra factors.
In the cgs esu system, the constant ke is taken to be equal to 1, and a quantity known as "Gaussian electric charge" is defined by the resulting equation. The unit of Gaussian charge, the statcoulomb, is such that two units, one centimetre apart, repel each other with a force equal to the cgs unit of force, the dyne. The ESU unit of charge, franklin (Fr), is defined as follows: two equal point charges spaced one centimetre apart are said to have one franklin each if the electrostatic force between them is one dyne.
The electric constant is also related to Coulomb's law, which describes the force between two charged bodies. In the cgs system, Coulomb's law takes a specific form without a multiplying constant, and the unit of charge is defined in terms of the electrostatic unit of charge, or the statcoulomb. The electric constant, ε0, is equal to the permittivity of a vacuum, ε, which is also equal to 1 in this system.
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Frequently asked questions
The electric constant, also known as vacuum permittivity, is the capability of a vacuum to permit electric field lines. It is used to determine charged particle interaction and force.
The electric constant is a constant factor in Coulomb's Law, relating electric charge with mechanical units such as force and distance.
The value of the electric constant is approximately 8.85 x 10^-12 F/m. It is often denoted as ε0 (epsilon zero) and is equal to the permittivity of free space.
