Chpte 5 lectic Potentil consevtive foces -> potentil enegy - Wht is consevtive foce? lectic potentil = U / : the potentil enegy U pe unit chge is function of the position in spce Gol:. estblish the eltionship between the electic fiel n electic potentil. clculte the electic potentil of vious continuous chge istibution. use the electic potentil to etemine the electic fiel 5. lectic Potentil n Potentil Diffeence U F l U F l l potentil enegy iffeence U U l electic potentil iffeence Continuity of lectic Fiel lectic Potentil + + + l The potentil function is continuous eveywhee. Units _ olt J / C _ e _ N / C _ / m.6 9 J
K =? e visible light:? e 5. Potentil iffeence in unifom electic fiel l U Wht is euipotentil sufce?? mple: The electic fiel between two pllel pltes of opposite chge mple: Motion of poton in unifom electic fiel = 8. /m =.5 m Fin the chnge in electic potentil between the points n. b Fin the chnge in potentil enegy. 5. lectic Potentil n Potentil negy Due to Point Chges let n --> n U mple: Potentil negy of Hyogen tom Wht is the electic potentil t isce =.59 X - m fom poton? b Wht is the electic potentil enegy of the electon n the poton t this seption? e U e 9 9.6.59 7. _ e 9 7. _ b
mple: Potentil negy of Nucle-Fission Poucts In nucle fission unium-5 nucleus cptues neuton n splits pt into two lighte nuclei. Sometimes the two fission poucts e bium nucleus chge 56e n ypton nucleus chge 6e. ssume tht immeitely fte the split these nuclei e positive point chges septe by.6 enegy of this two-chge system in electon volts. U 5 _ m. Clculte the potentil 9 9 9 9 9 9 56.6 6.6 9 56.6 6 99 _ Me.6 5 J.6 5 e i i -> esie fo clcultion without consietion of vecto ition mple: Potentil Due to Two Point Chges P: P: 5nC 5nC.. 5nC 5nC..6 mple: point chge is t the oigin n secon point chge is on the - is t =. Fin the potentil eveywhee on the -is. 5. Obtining the lue of the lectonic Fiel fom the lectic Potentil U F l --> l --> l The electic fiel points in the iection in which the potentil ecese most pily. D? D? D? l l tl l t / l
If the potentil epens only on thee will be no chnge in fo isplcements in the y n iection. l i i j i y --> If isplcements pepenicul to the il iection give no chnge in l --> mple: Fin the electic fiel fo the electic potentil function given by 5 _. mple: Potentil Due to n lectic Dipole n electic ipole consists of positive chge on the -is t i n negtive chge on the -is t i. Fin the potentil on the -is fo in tems of the electic ipole moment p. --> p --> Genel eltion etween & y & y i j i y y j n i j y Obtining electic fiel fom electic potentil i y j y y y
5 Potentil ue to n electic ipole p? 5.5 lectic Potentil Due to Continuous Chge Distibutions Due to n Infinite ine Chge: MTHOD : let sec ln ln MTHOD : Obtin by pplying Guss s lw:
6 ef P P ef ef P ln on The is of Chge ing Q s /? on The is of Unifomly Chge Dis: fo --> Q / mple: Fin the electic fiel long iection. 5.6 lectic potentil Due to Chge Conucto insie conucto -> const The conucto is thee imensionl euipotentil sufce. The potentil hs the sme vlue eveywhee on n euipotentil sufce. Due to n Infinite Plne of Chge MTHOD : Obtin by pplying Guss s lw: P + Q
p p --> l eff p p --> l eff eff eff Insie n Outsie Spheicl Shell of Chge MTHOD : Obtin by pplying Guss s lw: Q Q fo Unifomly Chge Sphee > Q b < Q Q Q Q mple: hollow unchge spheicl conucting shell hs n inne ius n n oute ius b. positive chge is in the cvity t the cente of the sphee. Fin the chge on ech sufce of the conucto. b Fin the potentil. Q b Q b 7
b b b mple: The two sphees e septe by isce much gete thn n. Fin the chges Q n Q on the two sphees if the totl chge is Q. Fin the tio of the mgnitues of the electic fiels t the sufces of the sphees. Q Q Q Q Q --> Q Q Q Q chge is plce on conucto of nonspheicl shpe. Q smll --> ge 8
5.7 The Millin Oil-Dop peiment 5.8 pplictions of lectosttics The n e Gff Geneto The lectosttic Pecipitto Xeogphy n se Pintes 9