Question

The value of relative permittivity of air is
A. \[8.854\times {{10}^{-12}}{{C}^{2}}{{N}^{-1}}{{m}^{-2}}\]
B. \[9\times {{10}^{9}}{{C}^{2}}{{N}^{-1}}{{m}^{-2}}\]
C. 1
D. $8.854\times {{10}^{12}}$

Answer 1

Hint: Electric Permittivity in electromagnetism is the measure of the ability of a material to be electrically polarized when kept in an electric field. Relative permittivity is the ratio of permittivity of the material and the permittivity of free space i.e. vacuum.

Complete solution answer:
When some material is kept inside an electric field, free charges inside the material move to the edges of the material and the material gets polarized. The ability of the material to do this is known as electric permittivity. Electric permittivity is also defined as the ability of a material to store electrical potential energy when an electric field is applied across it. This electric field causes the polarization of free charges inside the material and due to that polarization potential energy gets stored in the charges on the two different ends. An easy way to find the relative permittivity is to find the ratio of capacitance of a capacitor with the material filled in between the plates and the capacitance of the same capacitor when there is no material filled inside it. Relative permittivity is also known as the dielectric constant of the material. As air is a gas with a very low number of molecules that will be in between the plates of the capacitor. The relative permittivity for air is 1.0006. This is very low and can be rounded off to 1 for all practical purposes.

Hence, the correct option is C, i.e. 1

Note:
Students must take care that we are asked the relative permittivity here and not the value of absolute permittivity of air. The value of absolute permittivity is \[8.854\times {{10}^{-12}}{{C}^{2}}{{N}^{-1}}{{m}^{-2}}\]. But as discussed earlier this is not the correct answer. And the relative permittivity which is 1 for air must be chosen.