Question

The dielectric constant of air is
     $A)\text{ }8.85\times {{10}^{-12}}{{C}^{2}}{{N}^{-1}}{{M}^{-2}}$
     B) 1
     C) infinite
     D) zero

Answer 1

Hint: This problem can be solved by using the direct formula for the dielectric constant of a medium in terms of its permittivity and the permittivity of free space. The permittivity of free space is essentially the permittivity of vacuum.
Formula used:
$K=\dfrac{\varepsilon }{{{\varepsilon }_{0}}}$

Complete step by step solution:
We will use the direct formula for the dielectric constant of a medium.
The dielectric constant $K$ of a medium which has a permittivity $\varepsilon $, is given by
$K=\dfrac{\varepsilon }{{{\varepsilon }_{0}}}$ --(1)
Where ${{\varepsilon }_{0}}\text{= }8.85\times {{10}^{-12}}{{m}^{-3}}k{{g}^{-1}}{{s}^{4}}{{A}^{2}}$ is the permittivity of free space or vacuum.
For dry air at room temperature, the permittivity is very close to the permittivity of free space. In fact the two differ by a factor of one-thousandth. Hence, using (1), we can say that the dielectric constant ${{K}_{air}}$ of air is
${{K}_{air}}\approx 1$
Hence, the dielectric constant of air is one.
Therefore, the correct option is B) 1.
Additional information:
The dielectric constant of a material is also known as its relative permittivity. It affects the ability of a material to store electric charges on it and affects the effects of the electric coulomb forces and electric fields in the medium. Usually dry air at room temperature has a dielectric constant close to one, however air filled with moisture has a greater dielectric constant.

Note: The dielectric constant of a medium can also be defined as the ratio of the capacitance of a capacitor whose space between the plates have been filled with a material of that medium, to the ratio of the capacitance of a capacitor which has air in between its plates. Hence, if the question is framed in such a way that these two capacitance values are given, then also the students can find out the dielectric constant of the material.