Electric Potential Energy

Transcription

1 Electic Ptentil Enegy Ty Cnsevtive Fces n Enegy Cnsevtin Ttl enegy is cnstnt n is sum f kinetic n ptentil Electic Ptentil Enegy Electic Ptentil

2 Cnsevtin f Enegy f pticle fm Phys 7 Kinetic Enegy (K) nn-eltivistic Ptentil Enegy () etemine y fce lw K mv f Cnsevtive Fces: K+ is cnstnt ttl enegy is lwys cnstnt exmples f cnsevtive fces gvity; gvittinl ptentil enegy spings; cile sping enegy (Hke s Lw): (x)½kx electic; electic ptentil enegy (ty!) exmples f nn-cnsevtive fces (het) fictin viscus mping (teminl velcity) ( x, y, z )

3 Exmple: Gvity t sufce f eth. Gvittinl fce cnsevtive. F mg cnst. mgy gvittinl ptentil enegy + K cnstnt p ll fm est t : lge; K ze t : K lge; smll eveywhee: + K cnst. + K + K Enegy cnseve. y F mg Cn slve this plem tw wys: using fces n Newtn s Lws using C. f E. me ptentil enegy

4 Exmple: Chge in unifm E fiel. Electicl fce ls cnsevtive. F unifm electic fiel: F E cnst. Ey electicl ptentil enegy elese chge fm est t : E n F wnw s it cceletes wn, K inceses; eceses. E y F E me ptentil enegy + K cnstnt nifm gvity nifm E fiel mgy Ey Tw plems vey simil.

5 Wk n ptentil enegy. W wk ne y fce in ging fm t lng pth. W F l Δ ( ) - W + W Fl csθ F θ l W F u exmple: F l El E + W E(y y ) E l l E y El y cs E( y y ) E F E let y n chse t y ( ) y l Ey Ptentil enegy in unifm E fiel.

6 Electic ptentil enegy Imgine tw psitive chges, ne with chge, the the with chge : Initilly the chges e vey f pt, s we sy tht the initil ptentil enegy i is ze (we e fee t efine the enegy ze smewhee) Cnsie fixe n mves illy fm t W F l E E Cn ientify: 4πε 4πε 4πε ( ) Like: cs Gmm An inepenent f pth! Diffeence? Ptentil enegy f tw pint chges.

7 Electic ptentil enegy Wht if is psitive n is negtive? Pticles ten t mve t smlle. like chges epel. unlike chges ttct. 4πε Cn ls think f the s the wk ne y n utsie gent t ssemle the chge istiutin stting with the pticles t infinity. Define t infinity. F O F E F O - F E W O -W E Wht if me thn tw chges?

8 Electic Ptentil Enegy Exmple: Wht is the ptentil enegy f this cllectin f chges? + Step : Bing in + fm infinity. This csts nthing. - - Step : Bing in ne - chge. The fce is ttctive! The wk euie is negtive: ()( ) 4πε Step 3: Bing in n - chge. It is ttcte t the +, ut epelle fm the the - chge. The ttl wk (ll 3 chges) is ( )( ) ( )( ) ( )( ) πε 4πε 4πε 4 πε A negtive munt f wk ws euie t ing these chges fm infinity t whee they e nw (i.e., the ttctive fces etween the chges e lge thn the epulsive nes).

9 I5PF 5: A Tw chges which e eul in mgnitue, ut ppsite in sign e plce t eul istnces fm pint A. ) If thi chge is e t the system n plce t pint A, hw es the electic ptentil enegy f the chge cllectin chnge? ) inceses ) eceses c) esn t chnge

10 IL5A Cnsie the 3 cllectins f pint chges shwn elw. Which cllectin hs the smllest ptentil enegy? -Q -Q -Q +Q -Q +Q -Q +Q () () (c) +Q

11 IL5A Cnsie the 3 cllectins f pint chges shwn elw. Which cllectin hs the smllest ptentil enegy? -Q -Q -Q +Q -Q +Q -Q +Q () () (c) +Q We hve t psitive wk t ssemle the chges in () since they ll hve the sme chge n will ntully epel ech the. In () n (c), it s nt cle whethe we hve t psitive negtive wk since thee e ttctive pis n ne epulsive pi. () πε Q () 4πε Q (c) 4πε Q () (c) ()

12 V(x,y,z) is scl fiel, efine eveywhee in spce. Electic ptentil Cnsie tht we hve thee chges fixe in spce. The ptentil enegy f n e test chge t pint P is just Q Q Q 3 f t P k + k + k p p 3p Q Q Q 3 p p 3p Nte tht this fcts: x (the effects f ll the chges) Just s we peviusly efine the electic fiel s the fce/chge, we nw efine the electic ptentil s the ptentil enegy/chge: V(x,y,z) (x,y,z)/ ( V) epens n wht is, ut V is inepenent f (cn e + -) nits f electic ptentil e vlts: V J/C

13 ELECTRIC POTENTIAL f pint chge V () ( ) πε 4 4 πε ) Wht is electic ptentil istnce m fm +C chge? QC m ELECTRIC POTENTIAL f pint chges: supepsitin! ) Wht is electic ptentil istnce L fm fm tw +C chges? L L L V () 4 + πε L 4πε L 4 ) Wht if the tw chges e +C n C?? Esie thn ing E fiels. πε L

14 ELECTRIC POTENTIAL We cn euivlently cnsie the Wk t mve the chge fm t s, W ( ) ( V V ) SO, the wk pe unit chge t mve fm t euls, Als W F l E l V V W V V E l The ptentil iffeence, V V, is line integl Genel. Cn fin V fm E.

15 Exmple; Clculte vltge iffeence etween tw psitins eltive t pint chge + se the line integl efinitin l E V V K E ˆ ) ( 4 4 cs E E l E V V πε πε T etemine ptentil enegy f chge t pint P. V ) ( 4 V πε ) ( 4 πε