In the three-electrode system of Fig. P5.1.6, the bottom electrode is taken as having the…
In the three-electrode system of Fig. P5.1.6, the bottom electrode is taken as having the reference potential. The upper and middle electrodes then have potentials 1 and 2, respectively. The spacings between electrodes, 2d and d, are small enough relative to the planar dimensions of the electrodes so that the fields between can be approximated as being uniform.
(a) Show that the fields denoted in the figure are then approximately
(b) Show that the net charges 1 and 2 on the top and middle electrodes, respectively, are related to the voltages by the capacitance matrix [in the form of (12)]