PHY 114 A Gnral Physics II 11 AM-1:15 PM TR Olin 101 Plan for Lctur 4: 1. Introuction to th lctric potntial.rlationship btwn th lctric potntial an th lctric fil 1/31/01 PHY 114 A Spring 01 -- Lctur 4 1
Announcmnts: 1/31/01 PHY 114 A Spring 01 -- Lctur 4
i-clicr qustion Woul you attn a rviw sssion for nt Tusay s am on A. Monay aftrnoon at 4 PM B. Monay vning at 5 PM C. Sunay aftrnoon at 3 PM D. Sunay vning at 5 PM E. Non of ths 1/31/01 PHY 114 A Spring 01 -- Lctur 4 3
i-clicr rgistration problms: Campbll, Than Darmon, Ja Klbous, Sany Samsl, Davi Story, William 1/31/01 PHY 114 A Spring 01 -- Lctur 4 4
Consir a nutral (lctrically isolat) mtal sht: What happns whn you bring a point charg clos to th sht? Imag charg ffct u to mtal F ˆ ( ) sht 1/31/01 PHY 114 A Spring 01 -- Lctur 4 5
Somwhat rlat qustion from homwor: Suppos an lctrically nutral sht of mtal is plac in a uniform lctric fil. What is th rsultant charg istribution on th surfac of th sht? 1/31/01 PHY 114 A Spring 01 -- Lctur 4 6
1/31/01 PHY 114 A Spring 01 -- Lctur 4 7
Elctric fil insi an lctric isolat, nutral ial mtal 0. Gauss's Law for cylinr : 0 EA A in ε in 0 σ ε E 0 E 0 EA 1/31/01 PHY 114 A Spring 01 -- Lctur 4 8
Rviw of wor an potntial nrgy y r i s F r f F Wor : W r f F s r i For consrvativ F : W F s ( ) U f U i i 1/31/01 PHY 114 A Spring 01 -- Lctur 4 9 r r f
Application of wor principls to Coulomb s law forc r r q F ( r) W q r r q r r ( ) r' r' ( U ( r) U ) r rf r F r r r r 1/31/01 PHY 114 A Spring 01 -- Lctur 3 10
Potntial nrgy u to Coulomb's law with chargs q an : U ( r) q r r (jouls) Elctric potntial u to charg : V r r ( ) r (jouls/c Volt) Elctric potntial u to many chargs ( ) i V r r r i i i : 1/31/01 PHY 114 A Spring 01 -- Lctur 4 11
1/31/01 PHY 114 A Spring 01 -- Lctur 4 1
1/31/01 PHY 114 A Spring 01 -- Lctur 4 13 ), ( y y V ) ( ) ( ) ( ) ( ), ( a y a a y a y V Eampls of spatial istribution of lctric potntial
i-clicr rcis: Choos th prssion which corrspons to th valu of th lctrostatic potntial at th cntr of th squar in th iagram. A. B. C. D. E. 0 4 8 3 Non of ths. 1/31/01 PHY 114 A Spring 01 -- Lctur 4 14
i-clicr rcis: Choos th prssion which corrspons to th valu of th lctrostatic potntial at th cntr of th squar in th iagram. A. B. C. D. E. 0 4 8 3 Non of ths. 1/31/01 PHY 114 A Spring 01 -- Lctur 4 15
1/31/01 PHY 114 A Spring 01 -- Lctur 4 16 Calculation of th lctrostatic potntial at points A,B,C,D: V V V V D C B A 6 / / 3 / /
Rlationships btwn lctric potntial an lctric fil: E has units N/C V has units J/CVolt V ( r) r E( r') r' E( r) V ( r) ˆi Asi - - E ρ ε ( r) 0 V ( r) E( r) V ( r) V ˆ ( r) j ˆ y connction to Gauss's V ( r) ( r) V ( r) z 1/31/01 PHY 114 A Spring 01 -- Lctur 4 17 Law ρ ε 0
1/31/01 PHY 114 A Spring 01 -- Lctur 4 18 y r (,y) ( ) ( ) 3/ 3/ ˆ ˆ ) ( ˆ ) ( ˆ ) ( ) ( ) ( y y y y V V V y V j i r j r i r E r r
Elctric potntial for constant lctric fil: σ E σ ˆi σ ε 0 V E s rf σ ' ε 0 0 σ for 0 ε 0 0 1/31/01 PHY 114 A Spring 01 -- Lctur 4 19
Elctric potntial for constant lctric fil: σ E σ ˆi σ ε 0 V E s rf σ ' ε 0 0 σ for 0 ε 0 0 V i 0 V f σ ε 0 1/31/01 PHY 114 A Spring 01 -- Lctur 4 0
σ Elctric potntial for constant lctric fil: E σ ˆi ε 0 σ Suppos a proton having charg 1.610-19 C is initially at rst at 0, what is its final intic nrgy at? A. 0 B. -σ/ε 0 C. σ/ε 0 D. σ/ε 0 0 V i 0 V f σ ε 0 1/31/01 PHY 114 A Spring 01 -- Lctur 4 1
σ Elctric potntial for constant lctric fil: E σ ˆi ε 0 σ Suppos a proton is initially at rst at 0, what is its final intic nrgy at? K K K i f f U i K U K i U f f i U U V f f f σ ε 0 0 V i 0 V f σ ε 0 1/31/01 PHY 114 A Spring 01 -- Lctur 4
Uss for acclrat chargs: In an X-ray machin, lctrons ar acclrat bfor hitting a Cu or Mo targt that prouc X-ray raiation. Not: An lctron acclrat through a potntial iffrnc of 10V will hav K f 10V 1.6 10-18 J v f 10 6 m/s Elctron bam microscopy (almost atomic rsolution) Acclrat lctrons moving in a circl gnrat synchrotron raiation 1/31/01 PHY 114 A Spring 01 -- Lctur 4 3
σ Elctric potntial for constant lctric fil: E σ ˆi ε 0 σ Suppos a molcul with positiv an ngativ parts is plac in th fil E as show. A. It will mov to th right B. It will mov to th lft C. It will not mov D. It will rotat 0 V i 0 V f σ ε 0 1/31/01 PHY 114 A Spring 01 -- Lctur 4 4