What is electric polarization and displacement vector?
2 Answers
Electric polarization and the electric displacement vector are important concepts in electromagnetism, particularly in the study of dielectric materials and their response to electric fields. Here's a detailed explanation of each:
### Electric Polarization
**Definition:**
Electric polarization (\(\mathbf{P}\)) is a measure of the extent to which a material becomes polarized when subjected to an electric field. It represents the alignment of electric dipoles within a dielectric material under the influence of an external electric field.
**Physical Concept:**
In a dielectric material (an insulating material that can be polarized), when an electric field is applied, the positive and negative charges within the material shift slightly. This shift creates dipole moments, which contribute to the overall polarization of the material.
**Mathematical Representation:**
The polarization \(\mathbf{P}\) is defined as the dipole moment per unit volume. Mathematically, it's given by:
\[ \mathbf{P} = \frac{\mathbf{p}}{V} \]
where \(\mathbf{p}\) is the dipole moment of a single dipole and \(V\) is the volume.
**Relation to Electric Field:**
The polarization \(\mathbf{P}\) is related to the electric field \(\mathbf{E}\) through the material's susceptibility \(\chi_e\):
\[ \mathbf{P} = \epsilon_0 \chi_e \mathbf{E} \]
where \(\epsilon_0\) is the permittivity of free space, and \(\chi_e\) is the electric susceptibility of the material.
### Electric Displacement Vector
**Definition:**
The electric displacement vector (\(\mathbf{D}\)) is a vector field used to describe the electric field in a medium that includes the effects of free and bound charges. It accounts for the polarization of the material and is useful in simplifying Maxwell's equations in the presence of dielectric materials.
**Physical Concept:**
\(\mathbf{D}\) combines the effects of the external electric field and the polarization of the material. It helps in understanding how the electric field interacts with dielectric materials and free charges.
**Mathematical Representation:**
The electric displacement vector is defined as:
\[ \mathbf{D} = \epsilon_0 \mathbf{E} + \mathbf{P} \]
where \(\mathbf{E}\) is the electric field, and \(\mathbf{P}\) is the polarization.
**Relation to Electric Field:**
In a linear isotropic dielectric material, where the relationship between polarization and electric field is linear, \(\mathbf{D}\) can also be expressed as:
\[ \mathbf{D} = \epsilon \mathbf{E} \]
where \(\epsilon\) is the permittivity of the material, which is related to the permittivity of free space and the relative permittivity (\(\epsilon_r\)) of the material:
\[ \epsilon = \epsilon_0 \epsilon_r \]
### Summary
- **Electric Polarization (\(\mathbf{P}\))**: Describes the alignment of dipoles in a material due to an electric field. It's a measure of how a dielectric material responds internally to the external electric field.
- **Electric Displacement Vector (\(\mathbf{D}\))**: Accounts for both the applied electric field and the polarization effects. It simplifies the analysis of electric fields in materials by combining the effects of free charges and bound charges.
Understanding these concepts is crucial in the study of electromagnetism, especially when dealing with dielectric materials and their interactions with electric fields.
### Electric Polarization
**Definition:**
Electric polarization (\(\mathbf{P}\)) is a measure of the extent to which a material becomes polarized when subjected to an electric field. It represents the alignment of electric dipoles within a dielectric material under the influence of an external electric field.
**Physical Concept:**
In a dielectric material (an insulating material that can be polarized), when an electric field is applied, the positive and negative charges within the material shift slightly. This shift creates dipole moments, which contribute to the overall polarization of the material.
**Mathematical Representation:**
The polarization \(\mathbf{P}\) is defined as the dipole moment per unit volume. Mathematically, it's given by:
\[ \mathbf{P} = \frac{\mathbf{p}}{V} \]
where \(\mathbf{p}\) is the dipole moment of a single dipole and \(V\) is the volume.
**Relation to Electric Field:**
The polarization \(\mathbf{P}\) is related to the electric field \(\mathbf{E}\) through the material's susceptibility \(\chi_e\):
\[ \mathbf{P} = \epsilon_0 \chi_e \mathbf{E} \]
where \(\epsilon_0\) is the permittivity of free space, and \(\chi_e\) is the electric susceptibility of the material.
### Electric Displacement Vector
**Definition:**
The electric displacement vector (\(\mathbf{D}\)) is a vector field used to describe the electric field in a medium that includes the effects of free and bound charges. It accounts for the polarization of the material and is useful in simplifying Maxwell's equations in the presence of dielectric materials.
**Physical Concept:**
\(\mathbf{D}\) combines the effects of the external electric field and the polarization of the material. It helps in understanding how the electric field interacts with dielectric materials and free charges.
**Mathematical Representation:**
The electric displacement vector is defined as:
\[ \mathbf{D} = \epsilon_0 \mathbf{E} + \mathbf{P} \]
where \(\mathbf{E}\) is the electric field, and \(\mathbf{P}\) is the polarization.
**Relation to Electric Field:**
In a linear isotropic dielectric material, where the relationship between polarization and electric field is linear, \(\mathbf{D}\) can also be expressed as:
\[ \mathbf{D} = \epsilon \mathbf{E} \]
where \(\epsilon\) is the permittivity of the material, which is related to the permittivity of free space and the relative permittivity (\(\epsilon_r\)) of the material:
\[ \epsilon = \epsilon_0 \epsilon_r \]
### Summary
- **Electric Polarization (\(\mathbf{P}\))**: Describes the alignment of dipoles in a material due to an electric field. It's a measure of how a dielectric material responds internally to the external electric field.
- **Electric Displacement Vector (\(\mathbf{D}\))**: Accounts for both the applied electric field and the polarization effects. It simplifies the analysis of electric fields in materials by combining the effects of free charges and bound charges.
Understanding these concepts is crucial in the study of electromagnetism, especially when dealing with dielectric materials and their interactions with electric fields.