Modern smokestacks use devices called scrubbers to remove large amount of pollut

Question

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. Consider a soot particle of mass m_soot= 1 picograms (le-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 q_soot. Suppose the collector has a total charge q_Collector = 1.5e-06 C. If the separation between the collector and the soot particle is r = 0.1 m, What is the magnitude of q_soot (in units of C) so that the electric force exerted on the particle is equal to its weight = mg ?. Use: g = 10 m/s^2, and k = 9E9 N m^2/C^2. How many electrons must be added to the soot particle ?

Explanation / Answer

mass of soot , m= 1 *10^-12 kg

total charge , Qc = 1.5 *10^-6 C

r = 0.1 m

let the charge on the soot is qsoot

Now , for electric force = m * g

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

9*10^9 * 1.5 *10^-6 * qsoot/.1^2 = 1 *10^-12 * 9.8

solving

qsoot = 7.26 *10^-18 C

the magnitude of charge qsoot is 7.26 *10^-18 C'

number of electrons = qsoot/charge on 1 electron

number of electrons = 7.26 *10^-18/(1.602 *10^-19)

number of electrons = 45

number of electrons is 45

Related Questions

Navigate

• Browse (All)
• Browse M
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.