Question

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

Answer 1

Hint: We know that the dielectric constant of a substance is the ratio of the permittivity of the substance to the permittivity of the free space. Where permittivity is the opposition offered by the substance and an ability of the substance to store the electrical potential \[81\] energy under the influence of an electric field. It is denoted by \[\varepsilon \].

Complete answer:
The dielectric constant is mathematically expressed as
\[k = \dfrac{\varepsilon }{{{\varepsilon _0}}}\]----(1)
Where, \[k\] is the dielectric constant, \[\varepsilon \] is the permittivity of the substance and \[{\varepsilon _0}\] is the permittivity of the free space.
 Given dielectric constant of water \[k = 81\], Also we know that \[{\varepsilon _0} = 8.854 \times {10^{ - 12}}\]\[F/m\]
Then the equation (1) becomes
\[81 = \dfrac{\varepsilon }{{8.854 \times {{10}^{ - 12}}}}\]
\[ \Rightarrow \varepsilon = 81 \times 8.854 \times {10^{ - 12}}\]
\[ \Rightarrow \varepsilon = 717.174 \times {10^{ - 12}}\]\[F/m\]
 Hence, when the dielectric constant of water is \[81\], then its permittivity will be \[717.174 \times {10^{ - 12}}\]\[F/m\].

Note:
Note that the dielectric constant of a substance determines the amount of energy that a capacitor can store when voltage is applied. It also expresses the extent to which a material can hold electric flux in it. The value of a dielectric constant is always greater than one.