Capacitor

A parallel plate capacitor with plate area \(\mathrm{A}\) and plate separation \(\mathrm{d}\) is filled with a dielectric material of dielectric constant \(K=4\). The thickness of the dielectric material is \(x\), where \(x < d\).

Let \(\mathrm{C}_{1}\) and \(\mathrm{C}_{2}\) be the capacitance of the system for \(\chi=\frac{1}{3} d\) and \(\mathcal{X}=\frac{2 d}{3}\), respectively. If \(\mathrm{C}_{1}=2 \mu \mathrm{F}\) the value of \(\mathrm{C}_{2}\) is __________ \(\mu \mathrm{F}\)