Question

What is electric susceptibility in physics?

Answer 1

**Electric susceptibility** is a property of materials that measures how much they become polarized in response to an applied electric field. In other words, it quantifies how easily the electric dipoles within the material align with the external electric field.

Mathematically, it is defined as the ratio of the polarization \( \mathbf{P} \) (electric dipole moment per unit volume) to the applied electric field \( \mathbf{E} \):

\[
\mathbf{P} = \varepsilon_0 \chi_e \mathbf{E}
\]

Where:
- \( \mathbf{P} \) is the polarization of the material.
- \( \varepsilon_0 \) is the permittivity of free space (a constant).
- \( \chi_e \) is the electric susceptibility (dimensionless quantity).
- \( \mathbf{E} \) is the applied electric field.

### Key Points:
1. **Linear Relationship**: In many materials, the polarization is linearly related to the applied electric field, particularly for small fields. In such cases, \( \chi_e \) remains constant.
2. **Dielectric Constant**: The electric susceptibility is related to the dielectric constant (or relative permittivity \( \varepsilon_r \)) of the material by the relation:
   \[
   \varepsilon_r = 1 + \chi_e
   \]
3. **Types of Materials**:
   - **Diamagnetic and paramagnetic materials** have a small, often negative or weak positive susceptibility.
   - **Ferroelectric materials** can have very large susceptibilities, leading to strong polarization effects.

Electric susceptibility helps in understanding how materials interact with electric fields, particularly in the context of dielectrics and insulating materials.

Answer 2

Electric susceptibility, often denoted by the symbol \( \chi_e \), is a measure of how much a material becomes polarized in response to an applied electric field. It quantifies the extent to which a material can be polarized, which is essentially how easily the material's electric dipoles align with the electric field.

In more technical terms:

- **Electric Susceptibility (\( \chi_e \))**: This is a dimensionless quantity that relates the polarization \( \mathbf{P} \) of a material to the electric field \( \mathbf{E} \) applied to it. It is defined as \( \mathbf{P} = \epsilon_0 \chi_e \mathbf{E} \), where \( \epsilon_0 \) is the permittivity of free space.

- **Relation to Dielectric Constant**: The electric susceptibility is related to the dielectric constant \( \kappa \) (also known as the relative permittivity) by the equation \( \kappa = 1 + \chi_e \).

Materials with high electric susceptibility are easily polarized by an electric field, while those with low susceptibility are less responsive. This property is crucial in understanding how materials interact with electric fields and is fundamental in various applications, including capacitors, insulators, and sensors.