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Q. In a parallel plate capacitor the separation between the plates is $3\, mm$ with air between them. Now, a dielectric of dielectric constant $2$ is introduced between the plates due to which the capacity increases. In order to bring its capacity of the original value the separation between the plates must be made

Electrostatic Potential and Capacitance

Solution:

Given, initial separation $d=3\, mm$
Let new separation between the plates is $d^{\prime}$.
$\therefore \frac{C^{\prime} d^{\prime}}{k}=C d$
Given, $ C^{\prime}=C$
$\Rightarrow d^{\prime}=k d$
$\Rightarrow d^{\prime}=(2)(3)=6\, mm$