Question

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

Answer 1

Hint: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 –
$D=\epsilon E$
The permittivity of free space, also called vacuum permittivity, is the ratio of ${\displaystyle \frac{D}{E}}$in space.
The value is calculated by –
${\epsilon }_0={\displaystyle \frac{1}{{c_0}^2{\mu }_0}}={\displaystyle \frac{1}{\left(3\times {10}^8\right)\times 4\pi \times {10}^{-7}}}=8.854\times {10}^{-12}F/m$
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 ${\epsilon }_r$.
The total permittivity is
$\epsilon ={\epsilon }_r{\epsilon }_0$=$\left(1+\chi \right){\epsilon }_0$
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,
$C={\epsilon }_0{\displaystyle \frac{A}{d}}$