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A medium having dielectric constant $K>1$ fills the space between the plates of a parallel plate capacitor. The plates have large area, and the distance between them is $d$. The capacitor is connected to a battery of voltage $V$. as shown in Figure ($a$). Now, both the plates are moved by a distance of $\frac{d}{2}$ from their original positions, as shown in Figure ($b$).
In the process of going from the configuration depicted in Figure ($a$) to that in Figure ($b$), which of the following statement($s$) is(are) correct?
The electric field inside the dielectric material is reduced by a factor of $2 K$.
The capacitance is decreased by a factor of $\frac{1}{K+1}$.
The voltage between the capacitor plates is increased by a factor of $(K+1)$.
The work done in the process DOES NOT depend on the presence of the dielectric material.
Solution
For figure$(a)$
$E_0=\frac{V}{d} ; C=\frac{K \varepsilon_0 A}{d}$ For figure$(b)$
$C ^{\prime}=\frac{\varepsilon_0 A }{2 d – d + d / k } ;$
$C ^{\prime}=\frac{ K \varepsilon_0 A }{( K +1) d } ; C ^{\prime}=\frac{ C }{ K +1}$
