Using Coulomb\'s Law to Clean the Air Modern smokestacks use devices called scru

Question

Using Coulomb's Law to Clean the Air

Modern smokestacks use devices called scrubbers to remove a 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.

Consider a soot particle of mass msoot= 1.5 picograms (1.5e-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 = 1.95e-06 C. If the separation between the collector and the soot particle is r = 0.2 m,

(a) 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.

(b) How many electrons must be added to the soot particle? ________

Explanation / Answer

mass of soot , m= 1.5*10^-12 kg

total charge , Qc = 1.95*10^-6 C

r = 0.2 m

g = 10 m/s^2

let the charge on the soot is qsoot

Now , for electric force = m * g

k * Qc * qsoot/r^2 = m * g

9*10^9 * 1.95*10^-6 * qsoot/.2^2 = 1.5*10^-12*10

qsoot = (((0.04)*(1.5*10^-12)*(10))/((9*10^9)*(1.95*10^-6))

solving

qsoot = 3.419*10^-17 C

the magnitude of charge qsoot is 3.419*10^-17 C'

number of electrons = qsoot/charge on 1 electron

number of electrons = 3.419*10^-17/(1.602 *10^-19)

number of electrons = 213

number of electrons is 213

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