The plates of parallel plate capacitor with air as medium are separated by a distance of 8 mm . A me

Question

The plates of parallel plate capacitor with air as medium are separated by a distance of 8 mm . A medium of dielectric constant 2 and thickness 4 mm having the same area is introduced between the plates. For the capacitance of remain the same, the distance between the plates is\

Professor PC Thomas Classes · Answer

With air, $\mathrm{C}=\frac{\varepsilon_{0} 4}{\mathrm{~d}}=\frac{\varepsilon_{0} \mathrm{~A}}{8 	imes 10^{-3}}=\frac{\varepsilon_{0} \mathrm{~A} 	imes 10^{3}}{8}$ Let the new distance $=\mathrm{d} \mathrm{mm}$\ Thickness of dielectric medium $=4 \mathrm{~mm}$\ Thickness of air layer $=\left(\mathrm{d}^{\prime}-4ight) \mathrm{mm}$\ $	herefore$ Capacity $\mathrm{C}^{\prime}=\frac{\varepsilon_{0} \mathrm{~A} 	imes 10^{3}}{\frac{4}{2}+\frac{\mathrm{d}^{\prime}-4}{1}}=\frac{\varepsilon_{0} \mathrm{~A} 	imes 10^{3}}{\mathrm{~d}^{\prime}-2}$\ $\because C=C^{\prime}, \frac{\varepsilon_{0} A 	imes 10^{3}}{8}=\frac{\varepsilon_{0} A 	imes 10^{3}}{\left(\mathrm{~d}^{\prime}-2ight)}$\