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Question: Relative permittivity of water is \(81\). If \({{\varepsilon }_{w}}\)and \({{\varepsilon }_{0}}\)​ar...

Relative permittivity of water is 8181. If εw{{\varepsilon }_{w}}and ε0{{\varepsilon }_{0}}​are permittivities of water and vacuum respectively, then:
A.ε0=9εw B.ε0=81εw C.εw=9ε0 D.εw=81ε0 \begin{aligned} & A.{{\varepsilon }_{0}}=9{{\varepsilon }_{w}} \\\ & B.{{\varepsilon }_{0}}=81{{\varepsilon }_{w}} \\\ & C.{{\varepsilon }_{w}}=9{{\varepsilon }_{0}} \\\ & D.{{\varepsilon }_{w}}=81{{\varepsilon }_{0}} \\\ \end{aligned}

Explanation

Solution

Relative permittivity of a medium is described as the ratio of the electrostatic force between two charges kept in vacuum or air or free space to the electrostatic force between them placed at the same distance in the particular medium.

Complete step by step solution:
A relative permittivity is described as the ratio of the material permittivity to the permittivity of free space or vacuum,
The equation of relative permittivity is given as,
εr=εwε0{{\varepsilon }_{r}}=\dfrac{{{\varepsilon }_{w}}}{{{\varepsilon }_{0}}}
The unit for relative permittivity is Farad per metre.
Relative permittivity is determined using a metallic waveguide or a coaxial waveguide which is filled with the material to be measured. These methods need lots of time and cost in order to develop a material to fit in a waveguide without a gap between the metal walls and the dielectric material. Here in this question, the relative permittivity of water has been given,
And also we know that relative permittivity of a material is given by the formula,
εr=εwε0{{\varepsilon }_{r}}=\dfrac{{{\varepsilon }_{w}}}{{{\varepsilon }_{0}}}
Substituting the value of the relative permittivity,
εr=εwε0=81{{\varepsilon }_{r}}=\dfrac{{{\varepsilon }_{w}}}{{{\varepsilon }_{0}}}=81
Therefore by rearranging the terms, we get,
εw=81×ε0{{\varepsilon }_{w}}=81\times {{\varepsilon }_{0}}

So, the correct answer is “Option D”.

Note: The dielectric constant is the other name of the relative permittivity which indicates how readily a material can become polarized by imposition of an electric field on an insulator. Inside a conductor the electric field is null therefore its relative permittivity is infinite. Value of k gives us an idea of how it will isolate the charges. The Electric field abbreviated as E inside a conductor is generally zero under the static situation therefore the dielectric constant for the conductor is infinite.