There are 2 flat metal plates, each of length L and width W. You place a tiny spacer of height 0.700h0 at one end of the plates, and at the other end, a distance L away, you place another spacer of height 1.300h0. Thus, the plate separation varies gradually from one end of the plates to the other.
(a) Calculate the capacitance of this not-quite-parallel-plate capacitor. (Hint: divide the plates strips, each having dimensions dx and W. A parallel plate capacitor is formed by each strip and the corresponding strip on the other side of the gap. The sum of these capacitances is the total capacitance of the device.)
(b) The tilt-plate capacitor you just analyzed (capacitance C) resembles a true parallel-plate capacitor made from the same plates, with a uniform distance h0 between them (capacitance
(C). On physical grounds, you expect their capacitances to be similar. In fact, they are related by C = aC||, where a is a constant. What is a?