Question

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

Answer 1

Hint : To solve this question, we have to use the formula of the dielectric constant of a medium. Then, by putting the value of the dielectric constant in that formula which is given in the question, we will get the final answer.

Formula Used: In this solution we will be using the following formula,
$k = \dfrac{\varepsilon }{{{\varepsilon _0}}}$ where $k$ is the dielectric constant, $\varepsilon$ is the permittivity of any substance and ${\varepsilon _0}$ is the permittivity of water.

Complete step by step answer
The permittivity of a medium in electrostatics is defined with respect to its response to the electric field which is applied in the medium. The medium which gets more polarized, and therefore stores more electrical energy for a given electric field, is said to have higher permittivity.
The electric permittivities of all the mediums are expressed with the vacuum as a reference. So, instead of expressing their absolute permittivity values, their relative permittivity is expressed. The relative permittivity of a medium, also known as the dielectric constant, is defined as the ratio of the absolute permittivity of that medium to the permittivity of the vacuum. So, the dielectric constant is given as
$k = \dfrac{\varepsilon }{{{\varepsilon _0}}}$
Now, according to the question, the dielectric constant of water is $80$ . Let the permittivity of water be ${\varepsilon _w}$ . Substituting these above, we get
$80 = \dfrac{{{\varepsilon _w}}}{{{\varepsilon _0}}}$
Multiplying by ${\varepsilon _0}$ both the sides, we get
${\varepsilon _w} = 80{\varepsilon _0}$
Now, we know that the permittivity of free space is equal to $8.85 \times {10^{ - 12}}\dfrac{{{C^2}}}{{N{m^2}}}$ . So we have
${\varepsilon _w} = 80 \times 8.85 \times {10^{ - 12}}\dfrac{{{C^2}}}{{N{m^2}}}$
$\Rightarrow {\varepsilon _w} = 7.08 \times {10^{ - 12}}\dfrac{{{C^2}}}{{N{m^2}}}$
Hence, the permittivity of water is equal to $7.08 \times {10^{ - 12}}\dfrac{{{C^2}}}{{N{m^2}}}$ .

Note
The dielectric constant is used in many engineering applications. While designing a capacitor, its dielectric constant is taken into consideration. These are also used to measure environment factors such as temperature, humidity etc. Since the dielectric constant varies with these factors, so the sensors constructed to detect the change in the dielectric constant can be used for this purpose.