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 741e92d1 b30d 4a37 90dc bcd244fcb9d8z 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 be189c6e fc84 49fe 978a 6bde7114d109s7d5ff500 5370 4aeb 8ba6 3ba724c35858o200e7add 0d4c 42fa a908 a3c366f88f0c 

(c) For a single pair of electrodes, the capacitance C is defined such that 9a36c40e 2b48 4aaa af2f 8f94620af36d(13). Show that for the plane parallel capacitor of Fig. P5.1.5, 2bdac43a 4184 4d05 b0e2 2e31c8441d56o205f74e7 940e 40c5 9418 dca0e80ed760, where A is the area of one of the electrodes.

(d) Use the integral form of charge conservation, (1.5.2), to show that 1ad4357d d82c 4d06 b5cc e66a08d79429

Fig. P5.1.5

b1dfc20b 5e88 459d 8aa8 f978126755c3

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