Hints: When moving at terminal velocity, the net force on an object is zero. The viscous drag force is on a spherical object is given by Stokes's law. Eq. (9-16), where v is the speed of the object with respect to the surrounding fluid, and the buoyant force is given by Archimedes' principle (Section 9.6).
An air ionizer filters particles of dust, pollen. and other allergens from the air using electric forces. In one type of ionizer (see diagram), a stream of air is drawn in with a speed of 3.0 m/s.The air passes through a tine. highly charged wire mesh that transfers electric charge to the particles. Then the air passes through parallel "collector" plates that attract the charged particles and trap them in a filter. Consider a dust particle of radius 6.0 urn. Mass 2.0 x 10-13 kg, and charge 1000e. The plates arc 10 cm long and arc separated by a distance of 1.0 cm. (a) lgnoringdrag forces . what would he. the minimum potential difference between the plates to ensure that the particle gets trapped by the f Iter? (b) At what speed would the particle be moving relative to the stream of air just before hitting the filter? (c) Calculate the Viscous drag force on the panicle when moving at the speed found in (b). (d) Is it realistic to ignore drag? Taking drag into consideration. should the potential difference be larger or smaller than the answer to (a)?