What is electric polarization directly proportional to?
2 Answers
Electric polarization (\(\mathbf{P}\)) is directly proportional to the applied electric field (\(\mathbf{E}\)). This relationship is expressed in materials as:
\[
\mathbf{P} = \varepsilon_0 \chi_e \mathbf{E}
\]
Here’s a detailed breakdown of the terms:
1. **\(\mathbf{P}\)**: Electric polarization, which is the dipole moment per unit volume of a material.
2. **\(\mathbf{E}\)**: Applied electric field.
3. **\(\varepsilon_0\)**: The permittivity of free space, a constant value (\(8.854 \times 10^{-12} \, \text{F/m}\)).
4. **\(\chi_e\)**: The electric susceptibility of the material, which is a measure of how easily the material becomes polarized in response to the electric field.
### Explanation:
When an electric field is applied to a dielectric (non-conductive) material, it induces dipoles within the material. These dipoles align with the applied electric field, creating a net electric polarization. The degree of polarization depends on the strength of the electric field and the material’s ability to become polarized, characterized by its electric susceptibility.
Thus, **electric polarization is directly proportional to**:
1. **The applied electric field (\(\mathbf{E}\))**: A stronger electric field creates more dipole moments, leading to greater polarization.
2. **The electric susceptibility (\(\chi_e\))**: Materials with higher susceptibility polarize more easily for the same electric field.
In summary, electric polarization is proportional to the applied electric field, modified by the material's susceptibility.
\[
\mathbf{P} = \varepsilon_0 \chi_e \mathbf{E}
\]
Here’s a detailed breakdown of the terms:
1. **\(\mathbf{P}\)**: Electric polarization, which is the dipole moment per unit volume of a material.
2. **\(\mathbf{E}\)**: Applied electric field.
3. **\(\varepsilon_0\)**: The permittivity of free space, a constant value (\(8.854 \times 10^{-12} \, \text{F/m}\)).
4. **\(\chi_e\)**: The electric susceptibility of the material, which is a measure of how easily the material becomes polarized in response to the electric field.
### Explanation:
When an electric field is applied to a dielectric (non-conductive) material, it induces dipoles within the material. These dipoles align with the applied electric field, creating a net electric polarization. The degree of polarization depends on the strength of the electric field and the material’s ability to become polarized, characterized by its electric susceptibility.
Thus, **electric polarization is directly proportional to**:
1. **The applied electric field (\(\mathbf{E}\))**: A stronger electric field creates more dipole moments, leading to greater polarization.
2. **The electric susceptibility (\(\chi_e\))**: Materials with higher susceptibility polarize more easily for the same electric field.
In summary, electric polarization is proportional to the applied electric field, modified by the material's susceptibility.
Electric polarization is directly proportional to the applied electric field.
In more detail, when an electric field is applied to a material, the charges within the material shift slightly, creating an induced dipole moment. This process of shifting charges and creating dipoles is known as electric polarization.
Mathematically, this relationship can be expressed as:
\[ \mathbf{P} = \epsilon_0 \chi_e \mathbf{E} \]
where:
- \( \mathbf{P} \) is the polarization vector,
- \( \epsilon_0 \) is the permittivity of free space,
- \( \chi_e \) is the electric susceptibility of the material,
- \( \mathbf{E} \) is the applied electric field.
The electric susceptibility \( \chi_e \) is a measure of how easily a material can be polarized. In linear dielectric materials, the polarization \( \mathbf{P} \) increases linearly with the applied electric field \( \mathbf{E} \), meaning \( \mathbf{P} \) is directly proportional to \( \mathbf{E} \).
In more detail, when an electric field is applied to a material, the charges within the material shift slightly, creating an induced dipole moment. This process of shifting charges and creating dipoles is known as electric polarization.
Mathematically, this relationship can be expressed as:
\[ \mathbf{P} = \epsilon_0 \chi_e \mathbf{E} \]
where:
- \( \mathbf{P} \) is the polarization vector,
- \( \epsilon_0 \) is the permittivity of free space,
- \( \chi_e \) is the electric susceptibility of the material,
- \( \mathbf{E} \) is the applied electric field.
The electric susceptibility \( \chi_e \) is a measure of how easily a material can be polarized. In linear dielectric materials, the polarization \( \mathbf{P} \) increases linearly with the applied electric field \( \mathbf{E} \), meaning \( \mathbf{P} \) is directly proportional to \( \mathbf{E} \).