Question

The dielectric constant of water is 80, what is its permittivity?

Answer 1

Hint We know that dielectric constant is given by the ratio of electric permeability of the material to the electric permeability of free space,that is , $K=\dfrac{\text{ }\\!\\!\varepsilon\\!\\!\text{ }medium}{{{\text{ }\\!\\!\varepsilon\\!\\!\text{ }}_{\circ }}}$ and calculated $\varepsilon$ medium. As value of K and electric permeability of free space is known, hence we can calculate the permeability of medium

Formula Used $K=\dfrac{\varepsilon \text{ }medium}{{{\varepsilon }_{\circ }}}$

Complete step by step solution
$K=80$, given
We know that

& K=\dfrac{\text{permitivity of medium}}{\text{permitivity of air }} \\\ & \text{ =}\dfrac{\varepsilon \text{ medium }}{\varepsilon \text{ air }\left( {{\varepsilon }_{\circ }} \right)} \\\ \end{aligned}$$ As, $K=80\to given$ Therefore, $$\begin{aligned} & 80=\dfrac{\varepsilon \text{ medium}}{{{\varepsilon }_{\circ }}} \\\ & \varepsilon \text{ medium = 80}{{\varepsilon }_{\circ }} \\\ & \text{ = 80}\times \text{8}\text{.85}\times \text{1}{{\text{0}}^{-12}} \\\ & \text{ =708}\times \text{1}{{\text{0}}^{-12}} \\\ & \end{aligned}$$ **Note** Permittivity of free space ${{\varepsilon }_{\circ }}$ is a physical constant it represent the capability of a vacuum to permit electric fields .it is also related to the energy stored within an electric field and capacitance . Dielectric constant is also called relative permittivity. it is an expression of the constant to which a material concentrates electric flux and is the electrical equivalent of relative magnetic permeability