A container has a base of 50   cm × 5   cm and height 50   cm , as shown in the figure.…

A container has a base of $50 \mathrm{cm}\times 5 \mathrm{cm}$ and height $50 \mathrm{cm}$, as shown in the figure. It has two parallel electrically conducting walls each of area $50 \mathrm{cm}\times 50 \mathrm{cm}$. The remaining walls of the container are thin and non-conducting. The container is being filled with a liquid of dielectric constant $3$ at a uniform rate of $250 {\mathrm{cm}}^3 {\mathrm{s}}^{-1}$. What is the value of the capacitance of the container after $10$ seconds?

[Given: Permittivity of free space ${\epsilon }_0=9\times {10}^{-12} {\mathrm{C}}^2 {\mathrm{N}}^{-1} {\mathrm{m}}^{-2}$, the effects of the non-conducting walls on the capacitance are negligible]