Solved: Capacitors can be used as electric charge

Chapter , Problem 78

(choose chapter or problem)

Capacitors can be used as electric charge counters.Consider an initially uncharged capacitor of capacitance Cwith its bottom plate grounded and its top plate connectedto a source of electrons, (a) If N electrons flow onto thecapacitors top plate, show that the resulting potentialdifference V across the capacitor is directly proportionalto N. (b) Assume the voltage-measuring device canaccurately resolve voltage changes of about 1 mV. Whatvalue of C would be necessary to detect each newcollected electron? (c) Using modern semiconductortechnology, a micron-size capacitor can be constructed withparallel conducting plates separated by an insulating oxideof dielectric constant K = 3 and thickness d = 100 nm.To resolve the arrival of an individual electron on the plateof such a capacitor, determine the required value ofi (in pm) assuming square plates of side length L