In an electrostatic aircleaner("precipitator"), the strong nonuniform electricfield inthe central region of a cylindrical capacitor (with outerand innercylindrical radii Ra and Rb) is used to createionized airmolecules for use in charging dust and soot particles.Understandard atmospheric conditions, if air is subjected to anelectricfield magnitude that exceeds its dielectricstrength Es=2.7x10^-6,air molecules will dissociate intopositively charged ions and freeelectrons. In a precipitator, theregion within which air is ionized(the coronadischarge region) occupies a cylindrical volumeofradius R that is typically five times that of the innercylinder.Assume a particular precipitator is constructedwith Rb = 0.15 mmand Ra = 18.0 cm.
In order to create a corona discharge region withradius R=5.0Rb,what potential difference V shouldbe applied between theprecipitator's inner and outer conductingcylinders? [Besidesdissociating air, the charged inner cylinderrepels the resultingpositive ions from the corona dischargeregion, where they are putto use in charging dust particles, whichare then "collected" on thenegatively charged outer cylinder.]