An aerospace engineering team is designing a parallel-plate capacitive sensor for a high-altitude research balloon. The sensor consists of two parallel metal plates of a fixed surface area, separated by a thin sheet of dielectric material.
The physical properties of four candidate dielectric substrates are detailed in the table below:
| Substrate | Relative permittivity εr\varepsilon_rεr | Thickness ddd / mm |
|---|---|---|
| Alumina | 9.0 | 0.45 |
| Mica | 6.0 | 0.25 |
| Quartz | 3.8 | 0.15 |
| Silicon Nitride | 7.5 | 0.35 |
Determine, with appropriate calculations, which dielectric substrate will produce the maximum capacitance.