A simple fuel level gauge can use the dielectric constant of the fuel to indicate its level in a tank. Consider the schematic drawn in the figure where the two rectangular plates of the capacitor have a width w, and a length L. The height of the fuel between the plates is h. The effective dielectric constant, keff, changes form a value of 1 when the tank is empty, to the value of the dielectric constant of the fuel, k , when the tank is full. The appropriate electronic circuitry can determine the effective dielectric constant of the system.

a) Ignoring any fringe effects, derive an expression for the keff as a function of h.

b) What is the dielectric constant for a tank that is ¼ full. ½ full, and ¾ full if the fuel is gasoline (k=1.95 )?

c) Repeat part b for the case of methanol as the fuel, (k= 33.0 ).

d) For which fuel is this a more appropriate gauge?