(Solved): Problem 3 - Parallel Plate Capacitor The parallel plate capacitor shown below is filled with a fun ...

Problem 3 - Parallel Plate Capacitor The parallel plate capacitor shown below is filled with a functionally-graded dielectric where the dielectric constant changes in the \( x \) direction. The permittivity gradient is characterized by \( \varepsilon_{\mathrm{r}}(x)=\varepsilon_{\mathrm{r} 0}+\Delta \varepsilon_{\mathrm{r}} x^{2} \), where \( \varepsilon_{\mathrm{r} 0}=2.1 \) and \( \Delta \varepsilon_{\mathrm{r}}=1.2 \times 10^{5} 1 / \mathrm{m}^{2} \). This device has width \( w= \) \( 2.0 \mathrm{~cm} \) and a plate separation of \( h=0.5 \mathrm{~mm} \). Calculate the overall capacitance \( C \) of this device.