What is the magnitude of q soot (in units of C) so that the electric force exert

Question

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 ?.
Use: g = 10 m/s2, and k = 9E9 N m2/C2.

How many electrons must be added to the soot particle ?

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). qcollector 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. Collector Soot particles Consider a soot particle of mass m 1 picograms (1e-12 kg), soot- moving which corresponds to a diameter of a few micrometers. Some upward 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 the collector and the soot particle is r- 0.2 m Ground

Explanation / Answer

Fe = Fg

k*qs*qc/r^2 = mg

qs = mg*r^2/(k*qc)

Using the given values:

qs = 1*10^-12*9.81*0.2^2/(9*10^9*1.65*10^-6)

qs = 2.64*10^-17 C

B.

no. of electrons added to soot particle will be

qs = ns*e

ns = qs/e

ns = 2.64*10^-17/(1.6*10^-19) = 165 electrons

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