A group of students designs an experiment to determine the dielectric constant \(\kappa\) of an unknown liquid. They use a parallel-plate capacitor with large rectangular plates of width \(W = 0.50 \text{ m}\) and height \(H = 0.30 \text{ m}\), separated by a small gap of \(d = 2.0 \times 10^{-3} \text{ m}\). The capacitor is placed upright in an empty container, as shown in Figure 1, and connected to a meter that measures capacitance \(C\). The students slowly pour the liquid into the container, measuring the capacitance \(C\) as a function of the depth \(x\) of the liquid.