What is the relation between electric flux density and field intensity?
2 Answers
Electric flux density (\( \mathbf{D} \)) and electric field intensity (\( \mathbf{E} \)) are related through the permittivity of the material. The relationship is given by:
\[ \mathbf{D} = \epsilon \mathbf{E} \]
where \( \epsilon \) is the permittivity of the medium. In free space, \( \epsilon \) is the permittivity of free space (\( \epsilon_0 \)), while in other materials, it is the product of \( \epsilon_0 \) and the relative permittivity (\( \epsilon_r \)). This equation shows how electric flux density is the product of the electric field intensity and the material's ability to permit electric field lines.
\[ \mathbf{D} = \epsilon \mathbf{E} \]
where \( \epsilon \) is the permittivity of the medium. In free space, \( \epsilon \) is the permittivity of free space (\( \epsilon_0 \)), while in other materials, it is the product of \( \epsilon_0 \) and the relative permittivity (\( \epsilon_r \)). This equation shows how electric flux density is the product of the electric field intensity and the material's ability to permit electric field lines.
Electric flux density (also known as electric displacement field) and electric field intensity are related concepts in electromagnetism. Here’s a detailed explanation of their relationship:
### Electric Field Intensity (E)
Electric field intensity, often represented by the symbol **E**, is a measure of the force experienced by a unit positive charge placed in an electric field. It is a vector quantity that describes the strength and direction of the electric field. The electric field intensity at a point in space is given by:
\[ \mathbf{E} = \frac{\mathbf{F}}{q} \]
where **F** is the force experienced by a small positive test charge **q** placed at that point.
### Electric Flux Density (D)
Electric flux density, also known as the electric displacement field, is represented by the symbol **D**. It accounts for the effects of both free charges and bound charges (such as those in dielectric materials) within a medium. The electric flux density **D** is given by:
\[ \mathbf{D} = \varepsilon \mathbf{E} \]
where **ε** is the permittivity of the medium. In free space or a vacuum, **ε** is denoted as **ε₀** (the permittivity of free space), and in a material, it is often represented as **ε** (which can be expressed as **ε = ε₀ εᵣ**, where **εᵣ** is the relative permittivity of the material).
### Relationship Between Electric Flux Density and Electric Field Intensity
The relationship between **D** and **E** is influenced by the material through which the electric field is passing. In different media, the permittivity ε can change, thus affecting **D**.
- **In a Vacuum or Air:** Here, **ε** is equal to **ε₀**, the permittivity of free space. The relationship simplifies to:
\[ \mathbf{D} = \varepsilon_0 \mathbf{E} \]
- **In a Dielectric Medium:** For materials with permittivity **ε**, the relationship becomes:
\[ \mathbf{D} = \varepsilon \mathbf{E} \]
where **ε = ε₀ εᵣ**.
### Physical Interpretation
- **Electric Field Intensity (E):** Represents the force per unit charge and is fundamental in understanding the force experienced by charges in an electric field.
- **Electric Flux Density (D):** Incorporates the effect of the medium’s polarization, which includes both free and bound charge effects. It is useful in understanding the distribution of electric flux within materials, especially those with dielectric properties.
In summary, **D** and **E** are related through the permittivity of the material. While **E** describes the electric field in terms of force per unit charge, **D** describes how the electric field affects the distribution of electric flux, considering the material’s dielectric properties.
### Electric Field Intensity (E)
Electric field intensity, often represented by the symbol **E**, is a measure of the force experienced by a unit positive charge placed in an electric field. It is a vector quantity that describes the strength and direction of the electric field. The electric field intensity at a point in space is given by:
\[ \mathbf{E} = \frac{\mathbf{F}}{q} \]
where **F** is the force experienced by a small positive test charge **q** placed at that point.
### Electric Flux Density (D)
Electric flux density, also known as the electric displacement field, is represented by the symbol **D**. It accounts for the effects of both free charges and bound charges (such as those in dielectric materials) within a medium. The electric flux density **D** is given by:
\[ \mathbf{D} = \varepsilon \mathbf{E} \]
where **ε** is the permittivity of the medium. In free space or a vacuum, **ε** is denoted as **ε₀** (the permittivity of free space), and in a material, it is often represented as **ε** (which can be expressed as **ε = ε₀ εᵣ**, where **εᵣ** is the relative permittivity of the material).
### Relationship Between Electric Flux Density and Electric Field Intensity
The relationship between **D** and **E** is influenced by the material through which the electric field is passing. In different media, the permittivity ε can change, thus affecting **D**.
- **In a Vacuum or Air:** Here, **ε** is equal to **ε₀**, the permittivity of free space. The relationship simplifies to:
\[ \mathbf{D} = \varepsilon_0 \mathbf{E} \]
- **In a Dielectric Medium:** For materials with permittivity **ε**, the relationship becomes:
\[ \mathbf{D} = \varepsilon \mathbf{E} \]
where **ε = ε₀ εᵣ**.
### Physical Interpretation
- **Electric Field Intensity (E):** Represents the force per unit charge and is fundamental in understanding the force experienced by charges in an electric field.
- **Electric Flux Density (D):** Incorporates the effect of the medium’s polarization, which includes both free and bound charge effects. It is useful in understanding the distribution of electric flux within materials, especially those with dielectric properties.
In summary, **D** and **E** are related through the permittivity of the material. While **E** describes the electric field in terms of force per unit charge, **D** describes how the electric field affects the distribution of electric flux, considering the material’s dielectric properties.