Question

What is the difference between dielectric constant and electric susceptibility?

Answer 1

The dielectric constant and electric susceptibility are related concepts in electromagnetism, but they describe different properties of materials in response to an electric field. Here's the difference between them:

1. Dielectric Constant (Relative Permittivity)

1. The dielectric constant (also called relative permittivity, symbol \( \varepsilon_r \)) of a material describes how much the material can polarize in response to an applied electric field. It’s a measure of the material’s ability to store electrical energy in an electric field.
   

1. Mathematically, it's the ratio of the permittivity of the material (\( \varepsilon \)) to the permittivity of free space (\( \varepsilon_0 \)):
   

  \[
  \varepsilon_r = \frac{\varepsilon}{\varepsilon_0}
  \]

1. It gives an indication of how much a material can reduce the effective electric field within it. Materials with a higher dielectric constant can store more electrical energy.
   

  

2. Electric Susceptibility

1. Electric susceptibility (\( \chi_e \)) is a measure of how easily a material becomes polarized in response to an electric field. It tells you how much the material’s electric polarization increases when the electric field is applied.
   

1. The susceptibility is related to the dielectric constant by the following equation:
   

  \[
  \varepsilon_r = 1 + \chi_e
  \]

1. A material with high susceptibility is more easily polarized, and hence has a higher dielectric constant.
   

Key Differences

1. Physical meaning:  
   

  - Dielectric constant refers to the material's ability to store electrical energy in an electric field. It’s more of a macroscopic property.
  - Electric susceptibility measures the degree of polarization within the material when an electric field is applied. It's a microscopic property.

1. Mathematical relationship:  
   

  The dielectric constant is related to susceptibility through the equation \( \varepsilon_r = 1 + \chi_e \).

1. Unit:  
   

  - The dielectric constant is dimensionless (it has no units).
  - Electric susceptibility has no units, but it’s typically measured in the same way as the dielectric constant, since they are directly related.

Example to relate both:

In a material with a dielectric constant of 3, the electric susceptibility would be:
\[
\chi_e = \varepsilon_r - 1 = 3 - 1 = 2
\]

In simple terms:

1. Dielectric constant is about how much a material "stores" energy from an electric field.
   

1. Electric susceptibility is about how much the material "responds" to the electric field by polarizing.