It is defined as the Ratio of the force b/w two charges placed at certain distance apart in free space or vaccum to the force b/w same two charges placed at same distance apart in medium.
Therefore, Dielectric constant or relative permittivity is the ratio of the absolute permittivity of the medium to the absolute permittivity of free space.
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Dielectric constant or relative permittivity:
It is defined as the Ratio of the force b/w two charges placed at certain distance apart in free space or vaccum to the force b/w same two charges placed at same distance apart in medium.
[tex] \dashrightarrow \: \sf \epsilon_r = \: K = \dfrac{F_{vac}}{F_{med}} [/tex]
It is denoted by [tex]\sf \epsilon_r [/tex](relative permittivity) or K (dielectric constant)
[tex] \dashrightarrow \sf \: F_{vac} = \dfrac{1}{4 \pi\epsilon_o } \dfrac{q_1q_2}{ {r}^{2}}[/tex]
[tex]\dashrightarrow \sf \: F_{med} = \dfrac{1}{4 \pi\epsilon } \dfrac{q_1q_2}{ {r}^{2}}[/tex]
Where,
Substituting the values,
[tex] \dashrightarrow \: \sf \epsilon_r \:( or \: K) = \dfrac{ \dfrac{1}{4 \pi\epsilon_o } \dfrac{q_1q_2}{ {r}^{2} } }{{ \dfrac{1}{4 \pi\epsilon } \dfrac{q_1q_2}{ {r}^{2} }}} [/tex]
[tex] \dashrightarrow \: \sf \epsilon_r \:( or \: K) = \dfrac{\epsilon}{\epsilon_o} [/tex]
Therefore, Dielectric constant or relative permittivity is the ratio of the absolute permittivity of the medium to the absolute permittivity of free space.