What is the formula for electric susceptibility in terms of dielectric constant?
2 Answers
Electric susceptibility (\(\chi_e\)) is a measure of how easily a material can be polarized by an electric field. It relates to the dielectric constant (also known as the relative permittivity, \(\varepsilon_r\)) of a material. The dielectric constant is a measure of a material's ability to store electrical energy in an electric field.
The relationship between electric susceptibility (\(\chi_e\)) and dielectric constant (\(\varepsilon_r\)) is given by the following formula:
\[
\chi_e = \varepsilon_r - 1
\]
### Where:
- \(\chi_e\) is the **electric susceptibility**.
- \(\varepsilon_r\) is the **relative permittivity** (dielectric constant).
- The value \(1\) represents the dielectric constant of a vacuum (or free space).
### Explanation:
- **Relative permittivity (\(\varepsilon_r\))**: This is the ratio of the permittivity of a material to the permittivity of free space. It tells us how much more or less the material can store electric energy compared to a vacuum.
\[
\varepsilon_r = \frac{\varepsilon}{\varepsilon_0}
\]
Where \(\varepsilon\) is the permittivity of the material, and \(\varepsilon_0\) is the permittivity of free space (also called the vacuum permittivity).
- **Electric susceptibility (\(\chi_e\))**: It quantifies the extent of the polarization of a material in response to an electric field. Higher \(\chi_e\) means the material is more easily polarized.
Thus, the electric susceptibility is directly linked to how much more or less a material can polarize in an electric field relative to a vacuum, as captured by the dielectric constant.
The relationship between electric susceptibility (\(\chi_e\)) and dielectric constant (\(\varepsilon_r\)) is given by the following formula:
\[
\chi_e = \varepsilon_r - 1
\]
### Where:
- \(\chi_e\) is the **electric susceptibility**.
- \(\varepsilon_r\) is the **relative permittivity** (dielectric constant).
- The value \(1\) represents the dielectric constant of a vacuum (or free space).
### Explanation:
- **Relative permittivity (\(\varepsilon_r\))**: This is the ratio of the permittivity of a material to the permittivity of free space. It tells us how much more or less the material can store electric energy compared to a vacuum.
\[
\varepsilon_r = \frac{\varepsilon}{\varepsilon_0}
\]
Where \(\varepsilon\) is the permittivity of the material, and \(\varepsilon_0\) is the permittivity of free space (also called the vacuum permittivity).
- **Electric susceptibility (\(\chi_e\))**: It quantifies the extent of the polarization of a material in response to an electric field. Higher \(\chi_e\) means the material is more easily polarized.
Thus, the electric susceptibility is directly linked to how much more or less a material can polarize in an electric field relative to a vacuum, as captured by the dielectric constant.
The electric susceptibility (\(\chi_e\)) of a material is related to its dielectric constant (\(\kappa\)) by the formula:
\[ \chi_e = \kappa - 1 \]
Here, \(\kappa\) (also known as the relative permittivity) represents how much the dielectric constant of the material increases compared to the vacuum, and \(\chi_e\) measures how easily the material becomes polarized in response to an electric field.
\[ \chi_e = \kappa - 1 \]
Here, \(\kappa\) (also known as the relative permittivity) represents how much the dielectric constant of the material increases compared to the vacuum, and \(\chi_e\) measures how easily the material becomes polarized in response to an electric field.