What is the relative permittivity and permeability of free space?
2 Answers
In physics, the terms **relative permittivity** and **relative permeability** of free space (also called vacuum) are fundamental concepts in electromagnetism. Let's break them down clearly:
### 1. **Relative Permittivity of Free Space**:
The **relative permittivity** (\(\varepsilon_r\)) describes how much a material can "permit" or allow an electric field to pass through it compared to vacuum.
- For **free space (vacuum)**, the relative permittivity is exactly **1**. This is because vacuum is the reference material, and by definition, no material can permit an electric field better than vacuum.
\[
\varepsilon_r = 1
\]
- The absolute permittivity of free space (or vacuum permittivity), often denoted by \(\varepsilon_0\), is a fundamental constant with a value of:
\[
\varepsilon_0 \approx 8.854 \times 10^{-12} \, \text{F/m (farads per meter)}
\]
This constant appears in many electromagnetic equations, including Coulomb's law and Maxwell's equations.
### 2. **Relative Permeability of Free Space**:
The **relative permeability** (\(\mu_r\)) refers to how easily a material can support the formation of a magnetic field within it, compared to vacuum.
- For **free space (vacuum)**, the relative permeability is also exactly **1**. This means that vacuum is the baseline reference for the permeability of any material.
\[
\mu_r = 1
\]
- The absolute permeability of free space (or vacuum permeability), denoted by \(\mu_0\), is also a fundamental constant with a value of:
\[
\mu_0 = 4\pi \times 10^{-7} \, \text{H/m (henries per meter)}
\]
This constant is used in formulas involving magnetic fields, such as the Biot-Savart law and Ampère's law.
### Summary:
- **Relative Permittivity of Free Space** (\(\varepsilon_r\)) = 1
- **Relative Permeability of Free Space** (\(\mu_r\)) = 1
Both of these are dimensionless quantities, meaning they are ratios that have no units, and they are set to 1 because vacuum is the reference material for both electric and magnetic properties.
### 1. **Relative Permittivity of Free Space**:
The **relative permittivity** (\(\varepsilon_r\)) describes how much a material can "permit" or allow an electric field to pass through it compared to vacuum.
- For **free space (vacuum)**, the relative permittivity is exactly **1**. This is because vacuum is the reference material, and by definition, no material can permit an electric field better than vacuum.
\[
\varepsilon_r = 1
\]
- The absolute permittivity of free space (or vacuum permittivity), often denoted by \(\varepsilon_0\), is a fundamental constant with a value of:
\[
\varepsilon_0 \approx 8.854 \times 10^{-12} \, \text{F/m (farads per meter)}
\]
This constant appears in many electromagnetic equations, including Coulomb's law and Maxwell's equations.
### 2. **Relative Permeability of Free Space**:
The **relative permeability** (\(\mu_r\)) refers to how easily a material can support the formation of a magnetic field within it, compared to vacuum.
- For **free space (vacuum)**, the relative permeability is also exactly **1**. This means that vacuum is the baseline reference for the permeability of any material.
\[
\mu_r = 1
\]
- The absolute permeability of free space (or vacuum permeability), denoted by \(\mu_0\), is also a fundamental constant with a value of:
\[
\mu_0 = 4\pi \times 10^{-7} \, \text{H/m (henries per meter)}
\]
This constant is used in formulas involving magnetic fields, such as the Biot-Savart law and Ampère's law.
### Summary:
- **Relative Permittivity of Free Space** (\(\varepsilon_r\)) = 1
- **Relative Permeability of Free Space** (\(\mu_r\)) = 1
Both of these are dimensionless quantities, meaning they are ratios that have no units, and they are set to 1 because vacuum is the reference material for both electric and magnetic properties.
The relative permittivity and permeability of free space are fundamental constants in electromagnetism that characterize how electric and magnetic fields behave in a vacuum.
### Relative Permittivity (ε_r) of Free Space
**Relative Permittivity (ε_r)**, also known as the **dielectric constant**, describes how an electric field affects and is affected by a medium. For free space (or a vacuum), the relative permittivity is:
- **ε_r = 1**
This value indicates that free space does not have any dielectric effect that affects the electric field. The absolute permittivity of free space (ε₀) is:
- **ε₀ ≈ 8.854 x 10⁻¹² F/m (farads per meter)**
### Relative Permeability (μ_r) of Free Space
**Relative Permeability (μ_r)** describes how a magnetic field affects and is affected by a medium. For free space, the relative permeability is:
- **μ_r = 1**
This means that free space does not have any magnetic effect that influences the magnetic field. The absolute permeability of free space (μ₀) is:
- **μ₀ ≈ 4π x 10⁻⁷ H/m (henrys per meter)**
### Summary
In summary:
- **Relative Permittivity (ε_r) of free space = 1**
- **Relative Permeability (μ_r) of free space = 1**
These values serve as reference standards for comparing the properties of other materials. In materials other than free space, the relative permittivity and permeability will generally differ from these values, affecting how electric and magnetic fields propagate through those materials.
### Relative Permittivity (ε_r) of Free Space
**Relative Permittivity (ε_r)**, also known as the **dielectric constant**, describes how an electric field affects and is affected by a medium. For free space (or a vacuum), the relative permittivity is:
- **ε_r = 1**
This value indicates that free space does not have any dielectric effect that affects the electric field. The absolute permittivity of free space (ε₀) is:
- **ε₀ ≈ 8.854 x 10⁻¹² F/m (farads per meter)**
### Relative Permeability (μ_r) of Free Space
**Relative Permeability (μ_r)** describes how a magnetic field affects and is affected by a medium. For free space, the relative permeability is:
- **μ_r = 1**
This means that free space does not have any magnetic effect that influences the magnetic field. The absolute permeability of free space (μ₀) is:
- **μ₀ ≈ 4π x 10⁻⁷ H/m (henrys per meter)**
### Summary
In summary:
- **Relative Permittivity (ε_r) of free space = 1**
- **Relative Permeability (μ_r) of free space = 1**
These values serve as reference standards for comparing the properties of other materials. In materials other than free space, the relative permittivity and permeability will generally differ from these values, affecting how electric and magnetic fields propagate through those materials.