(Ill) In an electrostatic air cleaner (precipitator),

Chapter , Problem 20

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(Ill) In an electrostatic air cleaner (precipitator), thestrong nonuniform electric field in the central region of acylindrical capacitor (with outer and inner cylindrical radiiRa and Rb) is used to create ionized air molecules for usein charging dust and soot particles (Fig. 24-21). Understandard atmospheric conditions, if air is subjected to anelectric field magnitude that exceeds its dielectric strengthEs = 2.7 X 106N/C, air molecules will dissociate intopositively charged ions and free electrons. In a precipitator,the region within which air is ionized (the corona dischargeregion) occupies a cylindrical volume of radius R that istypically five times that of the inner cylinder. Assume aparticular precipitator is constructed with Rb = 0.10 mmand Ra = 10.0 cm. In order to create a corona dischargeregion with radius R = 5.0 Rb, what potential difference Vshould be applied between the precipitators inner and outerconducting cylinders? [Besides dissociating air, the chargedinner cylinder repels the resulting positive ions from thecorona discharge region, where they are put to use incharging dust particles, which are then collected on thenegatively charged outer cylinder.]