Chapter 24, Problem 78GP

Capacitors can be used as “electric charge counters.” Consider an initially uncharged capacitor of capacitance C with its bottom plate grounded and its top plate connected to a source of electrons. (a) If N electrons flow onto the capacitor’s top plate, show that the resulting potential difference V across the capacitor is directly proportional to N. (b) Assume the voltage-measuring device can accurately resolve voltage changes of about 1 mV. What value of C would be necessary to detect each new collected electron? (c) Using modern semiconductor technology, a micron-size capacitor can be constructed with parallel conducting plates separated by an insulating oxide of dielectric constant K = 3 and thickness d = 100 nm. To resolve the arrival of an individual electron on the plate of such a capacitor, determine the required value of l (in μm) assuming square plates of side length l.