Capacitors can be used as “electric charge counters.”

Chapter 17, Problem 6SL

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Problem 6SL

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 1mV. What value of C would be necessary to resolve the arrival of an individual electron? (c) Using modern semiconductor technology, a micron-size capacitor can be constructed with parallel conducting plates separated by an insulator of dielectric constant k= 3 and thickness d =100 n. What side length l should the square plates have (in μm)?