Question

What is the relation between electric permittivity of a medium and its dielectric constant?

Answer 1

The electric permittivity of a medium and its dielectric constant are closely related concepts, and understanding their connection helps in studying how materials respond to electric fields.

1. Electric Permittivity (\(\varepsilon\)):
   

   - It is a property of a material that describes how much the material resists or permits the formation of an electric field within it.
   - The electric permittivity of free space (vacuum) is denoted as \(\varepsilon_0\), and it has a fixed value of \(8.85 \times 10^{-12} \, \text{F/m}\) (farads per meter).
   - The electric permittivity of a material is typically written as \(\varepsilon\), and it can be expressed as:

     \[
     \varepsilon = \varepsilon_0 \cdot \varepsilon_r
     \]

     where:
     - \(\varepsilon_0\) is the permittivity of free space.
     - \(\varepsilon_r\) is the relative permittivity or dielectric constant of the material.

1. Dielectric Constant (\(\varepsilon_r\)):
   

   - It is a dimensionless number that describes how much a material can "store" electric energy compared to vacuum.
   - The dielectric constant is the ratio of the permittivity of the material to the permittivity of free space (\(\varepsilon_0\)).
   - Mathematically:

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

Summary:

1. The dielectric constant (\(\varepsilon_r\)) is a ratio of the material's electric permittivity to the permittivity of free space.
   

1. The relationship between them is:  
   

  \[
  \varepsilon = \varepsilon_0 \cdot \varepsilon_r
  \]

In other words, the electric permittivity of a medium is the product of the permittivity of free space and the dielectric constant of the medium.