What is the difference between relative permittivity and permittivity of free space?
2 Answers
The permittivity of free space, often denoted as \( \varepsilon_0 \), is a constant that describes how electric fields interact with a vacuum. It has a value of approximately \( 8.854 \times 10^{-12} \, \text{F/m} \) (farads per meter). On the other hand, relative permittivity, also known as the dielectric constant and denoted as \( \varepsilon_r \), is a dimensionless number that describes how a material affects the electric field relative to how a vacuum does.
In essence, relative permittivity compares a material's ability to store electrical energy in an electric field to that of a vacuum. The absolute permittivity \( \varepsilon \) of a material is the product of \( \varepsilon_0 \) and \( \varepsilon_r \), expressed as \( \varepsilon = \varepsilon_0 \cdot \varepsilon_r \).
In essence, relative permittivity compares a material's ability to store electrical energy in an electric field to that of a vacuum. The absolute permittivity \( \varepsilon \) of a material is the product of \( \varepsilon_0 \) and \( \varepsilon_r \), expressed as \( \varepsilon = \varepsilon_0 \cdot \varepsilon_r \).
Permittivity is a measure of how a material affects the electric field within it. Here's the distinction between relative permittivity and permittivity of free space:
1. **Permittivity of Free Space (\(\varepsilon_0\))**:
- This is a constant that describes how electric fields propagate in a vacuum.
- It has a fixed value of approximately \(8.854 \times 10^{-12} \, \text{F/m}\) (farads per meter).
2. **Relative Permittivity (\(\varepsilon_r\))**:
- Also known as the dielectric constant, this is a dimensionless quantity that measures how much a material can increase the capacitance of a capacitor compared to a vacuum.
- It is the ratio of the permittivity of the material (\(\varepsilon\)) to the permittivity of free space (\(\varepsilon_0\)): \[\varepsilon_r = \frac{\varepsilon}{\varepsilon_0}\]
- For example, a material with a relative permittivity of 10 would mean it is 10 times more effective at storing electric charge than a vacuum.
So, the permittivity of free space is a fundamental constant, while relative permittivity is a property of materials that indicates how much more or less effective they are in storing electric charge compared to a vacuum.
1. **Permittivity of Free Space (\(\varepsilon_0\))**:
- This is a constant that describes how electric fields propagate in a vacuum.
- It has a fixed value of approximately \(8.854 \times 10^{-12} \, \text{F/m}\) (farads per meter).
2. **Relative Permittivity (\(\varepsilon_r\))**:
- Also known as the dielectric constant, this is a dimensionless quantity that measures how much a material can increase the capacitance of a capacitor compared to a vacuum.
- It is the ratio of the permittivity of the material (\(\varepsilon\)) to the permittivity of free space (\(\varepsilon_0\)): \[\varepsilon_r = \frac{\varepsilon}{\varepsilon_0}\]
- For example, a material with a relative permittivity of 10 would mean it is 10 times more effective at storing electric charge than a vacuum.
So, the permittivity of free space is a fundamental constant, while relative permittivity is a property of materials that indicates how much more or less effective they are in storing electric charge compared to a vacuum.