Question

In a parallel plate capacitor set up, the plate area of capacitor is $2\,m^{2}$ and the plates are separated by $1\,m$. If the space between the plates are filled with a dielectric material of thickness $0.5\, m$ and area $2\,m^2$ (see fig.) the capacitance of the set-up will be ____ $\varepsilon_{0}$.
(Dielectric constant of the material $= 3.2$)
(Round off to the Nearest Integer)

Answer 1

$C =\frac{\varepsilon_{0} A}{\frac{d}{2 K}+\frac{d}{2}}=\frac{2 \varepsilon_{0} A}{\frac{d}{K}+d} $
$=\frac{2 \times 2 \varepsilon_{0}}{\frac{1}{3.2}+1}=\frac{4 \times 3.2}{4.2} \varepsilon_{0}$
$=3.04\, \varepsilon_{0} $