Question

What is the difference between permittivity and susceptibility?

Answer 1

Permittivity and susceptibility both describe how materials interact with electric fields, but they refer to different aspects of this interaction.

### Permittivity:
- **Definition**: Permittivity (denoted as **ε**) measures how much a material resists the formation of an electric field within it. In simpler terms, it indicates how easily a material can be polarized when placed in an electric field.
- **Formula**: It’s related to the electric field and the induced electric displacement (D) through the relationship:  
  \[
  D = \epsilon E
  \]
  where \( D \) is the electric displacement field, \( \epsilon \) is the permittivity, and \( E \) is the electric field.
- **Impact**: Materials with high permittivity can store more electric charge in the presence of an electric field, which is why they are used as dielectric materials in capacitors.
- **Relative permittivity** (also called the **dielectric constant**), is the permittivity of a material relative to the permittivity of free space (vacuum).  
  \[
  \epsilon_r = \frac{\epsilon}{\epsilon_0}
  \]
  where \( \epsilon_0 \) is the permittivity of free space.

### Susceptibility:
- **Definition**: Susceptibility (denoted as **χ**) measures how much a material becomes polarized in response to an applied electric field. It’s a measure of the material's ability to be polarized by the electric field.
- **Formula**: The relationship between electric polarization (P) and electric field (E) is:  
  \[
  P = \epsilon_0 \chi E
  \]
  where \( P \) is the polarization, \( \epsilon_0 \) is the permittivity of free space, and \( \chi \) is the electric susceptibility.
- **Impact**: Materials with high susceptibility will polarize more easily when an electric field is applied, contributing to a stronger overall polarization in the material.

### Key Differences:
1. **Permittivity** is a property of the material that tells you how much the material resists the electric field and how much it can store energy in the field. It’s a more fundamental property than susceptibility.
2. **Susceptibility** is a measure of how easily the material polarizes in response to an electric field, and it’s related to the permittivity, but it focuses on the material’s polarization behavior rather than energy storage.

To summarize:
- **Permittivity** tells you how well a material responds to and stores an electric field.
- **Susceptibility** tells you how easily a material gets polarized when exposed to an electric field.

Mathematically, you can relate them through:
\[
\epsilon = \epsilon_0 (1 + \chi)
\]