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# cpt23-2 - The result een be entrusted with the eerie efe...

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Unformatted text preview: The result een be entrusted with the eerie efe peint eherge. The weri'. required re bring a will eherge Q ﬁetn inﬁnity te e peiet wheretise eleee'ie petentiel due te elite: eherges is Fweuldhe iii," = ﬂ I3“r . Therefere. fer e pneint eherge Q, the peteeﬁel energy is U=Qir". New. suppeeetwemelel sphere: with radii a; and r: ereeenneeteci byerhhteenemueg wire, as ﬂﬂewtt in Figure 4.3.3. -' \ ' _ in :'.' -._ __ "I . I}: \ﬁ ..-...___,..-'""'-——-1' | 1. Figure 1.3.3 Twe eerrlzhleting spheres eenneeted by a wire. Charge wil] eentinue te ﬂettr until equilibrium is artebiished Such 'Htel belit spheres 'ere at lite een're petenliel F1 - i"; I F’. Suppese the eitergee en the spheres at equilibrium are q. and "r'e- Neglecting lite efFeet eit'tlte wire that eenneete the tee spheres. ﬂteequipetentiei eentiitiest implies tr: ] 1:;Ea. ems" e 433,, r: at i=ﬂ {arse} lli J": assumingﬂtetlhetwesphereemwryi‘ereperteeﬂletlheeherge dishihruiertsenliie surfeees ef Ihe eenduetereere uniferrn. The electrie ﬁeldeleen he expressed as I r; e' 1 q er = _L=_LI 5:...4 J- 4.3.“) E‘ 44ml? e 1 marine ( i where er, and r:.II'J ere thesurl‘eee charge deeeitiee en spheres 1 and 2, respectively. The twe equeticsts can he eenrhined te yield {1.3.11} With the surfeee eherge r.’reneit:,-I being insereely mite-ml te lite radius. we eeneiude the the regime with rise smallest rerlii ef eunreture have the grease“ er. Thee the eleehieﬁeldsu‘engtit entiresurfeeeefeeendueteris greetestetmesherpeetp-ehttjhe design efe iightnhrg red: is M en this prineiple. 4—2I ...
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