Solution:

The dielectric constant (also called the relative permittivity,

$\varepsilon_r$

) is a dimensionless quantity because it is defined as the ratio:

$$\varepsilon_r = \frac{\varepsilon}{\varepsilon_0}$$

Where:

• 
  $\varepsilon$ 

  = permittivity of the medium (units: $\text{F/m}$ 

  , farads per meter)

• 
  $\varepsilon_0$ 

  = permittivity of free space ( $\text{F/m}$ 

  , farads per meter)

Since it is a ratio of two quantities with the same unit, the dielectric constant has no unit (it is dimensionless).