Permittivity|What is Permittivity or Dielectric constant ?|relative permittivity

Permittivity or Dielectric constant : When two charges are placed in any medium other than air, the force between them is greatly affected.

Permittivity is o property of the medium which determines the electric force between two charges situated in that medium.

For example. the force between two charges located some distance apart in water is about 1/80th of the force between them when they are separated by same distance in air.

This is because the absolute permittivity of water is about 80 times greater than the absolute permittivity of air or free space.

Dielectric constant or relative permittivity

According to Coulomb’s law, the force between two point charges q, and q,, placed in vacuum at distance r from each other, is given by

$\displaystyle F_{vacuum}=\frac{1}{4\pi \epsilon _{0}}\cdot \frac{q_{1}q_{2}}{r^{2}}\ ...(1)$

9192 .(1) %3D

When the same two charges are placed same distance apart in any medium other than vacuum, the force between them becomes

$\displaystyle F_{medium}=\frac{1}{4\pi \epsilon }\cdot \frac{q_{1}q_{2}}{r^{2}}\ ...(2)$

The quantity & is called absolute permittivity or just permittivity of the intervening medium. Dividing equation (1) by equation (2), we get,

$\displaystyle \frac{F_{vacuum}}{F_{medium}}=\frac{\frac{1}{4\pi \epsilon _{0}}\cdot \frac{q_{1}q_{2}}{r^{2}}}{\frac{1}{4\pi \epsilon }\cdot \frac{q_{1}q_{2}}{r^{2}}}=\frac{\epsilon }{\epsilon _{0}}$

The ratio ( $\displaystyle \frac{\epsilon }{\epsilon _{0}}$

) of the permittivity( $\displaystyle \epsilon$

)of the medium to the permittivity ( $\displaystyle \epsilon _{0}$

) of free space is called relative permittivity ( $\displaystyle \epsilon _{r}$

) or dielectric constant (k) of the given medium. Thus

$\displaystyle \epsilon _{r}$

, or $\displaystyle k=\frac{\epsilon }{\epsilon _{0}}=\frac{F_{vacuum}}{F_{medium}}$

So one can define dielectric constant in terms of forces between charges as follows :

The dielectric constant of a medium may be defined as the ratio of the force between two charges placed some distance apart in free space to the force between the same two charges when they are placed the same distance apart in the given medium.

Clearly, when a material medium of dielectric constant K is placed between the charges, the force between them becomes 1/k times the original force in vacuum. That is,

$\displaystyle F_{medium}=\frac{F_{vacuum}}{k}$

Hence the Coulomb’s law for any material medium may be written as

$\displaystyle F_{medium}=\frac{1}{4\pi \epsilon_{0}k }\cdot \frac{q_{1}q_{2}}{r^{2}}$

k(vacuum)=1

k(air)=1.00054

k(water)=80

Dielectric constant or relative permittivity

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