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 fine, 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 μ m, mass 2.0 × 10ˆ’13 kg, and charge 1000 e. The plates are 10 cm long and are separated by a distance of 1.0 cm.
(a) Ignoring drag forces, what would be the minimum potential difference between the plates to ensure that the particle gets trapped by the filter?
(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 particle 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)?

Transcribed Image Text:

Charged dust particle 10 cm Airflow 1 cm Fine metal mesh (charging region) Collector plates with filter