Question

Define permittivity of vacuum ${\varepsilon _0}$.

Answer 1

The absolute permittivity is also, called permittivity, is the measure of the electric polarizability of a dielectric.

Complete step-by-step answer:
The dielectric is defined as the electric insulator that can be polarised by applying an electric field. That means that whenever a dielectric medium is placed in an external electric field, the electric charges do not flow through the material like it happens in a normal electric conductor, but the charge carries a slight shift from their equilibrium positions. This results in dielectric polarization. In other words, the positive and negative charges re-align themselves along the direction of the electric field.
The permittivity is a measure of this particular property.
This means that the materials which have a higher permittivity polarizes to a greater extent in the presence of an external electric field compared to a material with lower permittivity.
The field created due to the polarisation –
$D = \varepsilon E$
The permittivity of free space, also called vacuum permittivity, is the ratio of $\dfrac{D}{E}$in space.
The value is calculated by –
${\varepsilon _0} = \dfrac{1}{{{c_0}^2{\mu _0}}} = \dfrac{1}{{\left( {3 \times {{10}^8}} \right) \times 4\pi \times {{10}^{ - 7}}}} = 8.854 \times {10^{ - 12}}F/m$
where ${\mu _0}$is called absolute permeability of free space (related to magnetism). The units of permittivity is farad per meter $F/m$.
However, for other homogenous materials, their permittivity is always relative to that of the absolute permittivity. This is called relative permittivity ${\varepsilon _r}$.
The total permittivity is
$\varepsilon = {\varepsilon _r}{\varepsilon _0}$=$\left( {1 + \chi } \right){\varepsilon _0}$
where $\chi$is called electric susceptibility, which means the dimensionless proportionality constant that indicates the degree of polarisation of a dielectric medium in response to the external electric field.

Note: This concept is applicable in the theory of capacitance.Capacitor is an electronic device that is used to store charges. It consists of two plates separated by a dielectric medium like air, paper, ceramic etc.
In such cases, the capacitance depends on the total permittivity of the dielectric medium.
Capacitance,
$C = {\varepsilon _0}\dfrac{A}{d}$