A frequently used model for a capacitor is shown in Fig. P5.1.5, where two plane parallel…
A frequently used model for a capacitor is shown in Fig. P5.1.5, where two plane parallel electrodes have a spacing that is small compared to either of their planar dimensions. The potential difference between the electrodes is v, and so over most of the region between the electrodes, the electric field is uniform.
(a) Show that in the region well removed from the edges of the electrodes, the field 
z satisfies Laplace’s equation and the boundary conditions on the electrode surfaces.
(b) Show that the surface charge density on the lower surface of the upper electrode is 
s
o
(c) For a single pair of electrodes, the capacitance C is defined such that 
(13). Show that for the plane parallel capacitor of Fig. P5.1.5, 
o
, where A is the area of one of the electrodes.
(d) Use the integral form of charge conservation, (1.5.2), to show that 
Fig. P5.1.5
