Question

Dielectric constant of water is $80$ . What is its permittivity?

Answer 1

Hint Because of the induced charges, an extra electric field is produced inside the material. Let $\overrightarrow {{E_o}}$ be the applied field due to external sources and $\overrightarrow {{E_p}}$ be the field due to polarization. The resultant field is $\overrightarrow E = \overrightarrow {{E_o}} + \overrightarrow {{E_p}} .$ For homogeneous and isotropic dielectrics, the direction of $\overrightarrow {{E_p}}$ is opposite to the direction of $\overrightarrow {{E_o}}$ . The resultant field $\overrightarrow E$ is in the same direction as the applied field $\overrightarrow {{E_o}}$ but its magnitude is reduced. We can write,
$\overrightarrow E = \dfrac{{\overrightarrow {{E_o}} }}{K}$
Where, $K$ is a constant for a given dielectric and is called dielectric constant.

Complete Step by step solution
Given: $K = 80$
Now the dielectric constant is also called relative permittivity.
Mathematically, we can write
$K = \dfrac{\varepsilon }{{{\varepsilon _o}}}$
Where, $\varepsilon$ is permittivity of the material
${\varepsilon _o}$ is permittivity of free space
Now given $K = 80$ and
we know that the permittivity of free space is equal to
${\varepsilon _o} = 8.85419 \times {10^{ - 12}}{C^2}{N^{ - 1}}{m^{ - 2}}$
Therefore, we have
$\Rightarrow$ $\varepsilon = {\varepsilon _o}K \\\ \varepsilon = 80 \times 8.85419 \times {10^{ - 12}}{C^2}{N^{ - 1}}{m^{ - 2}} \\\ \varepsilon = 708.3352 \times {10^{ - 12}}{C^2}{N^{ - 1}}{m^{ - 2}} \\\ \varepsilon = 7.083 \times {10^{ - 10}}{C^2}{N^{ - 1}}{m^{ - 2}} \\\$
Hence the permittivity of water as calculated from above is $\varepsilon = 7.083 \times {10^{ - 10}}{C^2}{N^{ - 1}}{m^{ - 2}}$

Note Dielectric constant is always greater than 1. For vacuum there is no polarization and hence $\overrightarrow E = \overrightarrow {{E_o}}$ and $K = 1$ . if a very high electric field is created in dielectrics, the outer electron may get detached from their parent atom. The dielectrics then behave like a conductor. This phenomenon is known as dielectric breakdown. The minimum field at which the breakdown occurs is called dielectric strength.