Chapter 24, Problem 20P

(III) In an electrostatic air cleaner (“precipitator”), the strong nonuniform electric field in the central region of a cylindrical capacitor (with outer and inner cylindrical radii R_a and R_b) is used to create ionized air molecules for use in charging dust and soot particles (Fig. 24–21). Under standard atmospheric conditions, if air is subjected to an electric field magnitude that exceeds its dielectric strength E_S = 2.7 × 10⁶ N/C, air molecules will dissociate into positively charged ions and free electrons. In a precipitator, the region within which air is ionized (the corona discharge region) occupies a cylindrical volume of radius R that is typically five times that of the inner cylinder. Assume a particular precipitator is constructed with R_b = 0.10 mm and R_a = 10.0 cm. In order to create a corona discharge region with radius R = 5.0 R_b, what potential difference V should be applied between the precipitator’s inner and outer conducting cylinders? [Besides dissociating air, the charged inner cylinder repels the resulting positive ions from the corona discharge region, where they are put to use in charging dust particles, which are then “collected” on the negatively charged outer cylinder.]

FIGURE 24–21 Problem 20.