We present a theory that describes the scenarios of equations of motion of clustered air ions entering into specific systems. The system analyzed here is composed by two or three conductive parallel plates. In the first case (system of two parallel plates) one plate collects air ions which enter into the area between these plates. In the second case (system of three parallel plates) the collector plate is the middle one.Air ions usually are classified into several categories according to their electrical mobility (size). The main categories are: cluster ions (mobility 0.5-3.2 cm2/V.s), intermediate ions (mobility 0.034-0.5 cm2/V.s), and large ions (mobility 0.0042-0.034 cm2/V.s).This theory has an important application on ion counter operations. Usually the apparatus measures the concentrations of only cluster air ions (mobility > 0.5 cm2/V.s). Air ions are deflected by the electric field established by a potential difference of polarized plates. Air ion concentrations are derived from measurement of electrical current caused in the system.Based on this theory, we can determine analytically the efficiency of the collection of air ions of different electrical mobility by above mentioned systems
