If ${q}_{{f}}$ is the free charge on the capacitor plates and ${q}_{{b}}$ is the bound charge on the dielectric slab of dielectric constant $k$ placed between the capacitor plates, then bound charge $q_{b}$ can be expressed as
${q}_{{b}}={q}_{{f}}\left(1-\frac{1}{{k}}\right)$
${q}_{{b}}={q}_{{f}}\left(1-\frac{1}{\sqrt{{k}}}\right)$
${q}_{{b}}={q}_{{f}}\left(1+\frac{1}{\sqrt{{k}}}\right)$
${q}_{{b}}={q}_{{f}}\left(1+\frac{1}{{k}}\right)$
Explain the effect of dielectric on capacitance of parallel plate capacitor and obtain the formula of dielectric constant.
A parallel plate capacitor is filled with $3$ dielectric materials of same thickness, as shown in the sketch. The dielectric constants are such that $k_3 > k_2 > k_1$. Let the magnitudes of the electric field in and potential drops across each dielectric be $E_3$, $E_2$,$ E_1$, $\Delta V_3$, $\Delta V_2$ and $\Delta V_1$, respectively. Which one of the following statement is true ?
A parallel plate capacitor with air between the plates has a capacitance of $8 \;pF \left(1 \;pF =10^{-12} \;F \right) .$ What will be the capacitance (in $pF$) if the distance between the plates is reduced by half, and the space between them is filled with a substance of dielectric constant $6 ?$
A parallel plate capacitor with air between plates has a capacitance of $8\,\mu F$ what will be capacitance if distance between plates is reduced by half, and the space between them is filled with a substance of dielectric constant $6$ ?.....$\mu F$
A parallel plate capacitor with plate area $'A'$ and distance of separation $'d'$ is filled with a dielectric. What is the capacity of the capacitor when permittivity of the dielectric varies as :
$\varepsilon(x)=\varepsilon_{0}+k x, \text { for }\left(0\,<\,x \leq \frac{d}{2}\right)$
$\varepsilon(x)=\varepsilon_{0}+k(d-x)$, for $\left(\frac{d}{2} \leq x \leq d\right)$