Question

Using Coulomb's Law to Clean the Air Modern smokestacks use devices called scrubbers to remove large amount of pollution in the form of small particles (soot). Scrubbers use a two steps process: electrons are first added to the soot particle, and an electric force then pulls the particle out of the smoke stream. Acollectorsoo Consider a soot particle of mass msoot 1 nanograms (1e-12 kg), which corresponds to a diameter of a few micrometers. Some number of electrons have been added to give the particle a total charge qsoot- Suppose the collector has a total charge qcollector 1.65e-06 C. If the separation between Collector Soot the collector and the soot particle is r 0.2 m, particles moving What is the magnitude of qsoot in units of C) so that the electric force exerted on the particle is equal to its weight mg ? upward use: 9 - 10 m/s2, and k 9E9 N m2/c2. Ground Submit Answer Tries 0/2 How many electrons must be added to the soot particle? electrons Submit Answer Tries 0/2

Answer 1

Concept: we use Coulomb's law of force and Newton's law of motion and charge quantization for solving this problem as shown below, ***************************************************************************************************
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F_e = m g or, Vertical-bar q_collector Vertical-bar Vertical-bar q_soot Vertical-bar /4 pi element o r^2 = (m_soot) g or, Vertical-bar q_soot Vertical-bar = 2 . 69 times 10^- 17 c (if sign is needed, put a minus sign before answer) n (- e) = q_soot or, n (- 1.6 times 10^-19 c) = - 2 . 69 times 10^- 17 c or, n = 168 . 35 electrons .