PHYS 015 -- Week 5 Readng Jounals today fom tables WebAssgn due Wed nte Fo exclusve use n PHYS 015. Not fo e-dstbuton. Some mateals Copyght Unvesty of Coloado, Cengage,, Peason J. Maps.
Fundamental Tools and Defntons so fa: F k c q q 1 Coulomb s Law Foce exeted by pont chages on each othe F k q c 0 Q qn o k c dq da lectc feld ceated by a souce pont chage Q a dstance fom t. -hat = unt vecto adally outwad fom Q (Integaton ove a chage dstbuton) Foce exeted on a pont chage q 0 (the `subject chage) n an electc feld ceated by othe (souce) chages. Gauss s Law, lectc flux
Gauss s Law Re-cap: sphees, nfnte lnes & planes o n q o n o n o n A q A da L q L da q da ) ( and ) ( ) ( and ) ( 4 ) ( ) ( 4 L A
Fom Physcs I Wok constant foce Vaable foce, cuved path W W F f F d Knetc negy And Wok-negy Thm K W 1 mv K 1 1 mv f mv Some foces meet specal condtons to be desgnated as consevatve foces
Mathlde lfts a 4 kg book staght up a dstance of 0.5 mete at a steady speed. Mathlde does how much wok? 1. -0 J. 0 J 3. +0 J 4. Can t tell fom the nfo 57% 3% 7% 4% 1.. 3. 4.
Mathlde lfts a 4 kg book staght up a dstance of 0.5 mete at a steady speed. On the whteboads lst (wth appopate sgns): A) The wok done by Mathlde: B) The wok done by ath s gavtatonal foce on the book: C) The change n gavtatonal potental enegy of the ath-book system
Woksheet
Table Name A vey lage nsulatng sheet of chage has suface chage densty of +17.7 x 10-9 C/m. A dust patcle wth q= -1 x 10-1 C (-1 pc) and mass of m =.00 nanogams s 10 cm fom the sheet. How much wok does the electc foce do n pullng the dust patcle to the sheet? If statng fom est, how much knetc enegy does the patcle have just befoe t hts the sheet? How fast s t gong?
Two new quanttes and defnng elatonshps fom chapte 6: lectc potental enegy U (joules) Wok done by an outsde agent (e.g. you!) n assemblng a goup of chages (often fom nfnty) Changes n potental enegy, ΔU ae physcally mpotant. The electc potental enegy of two pont chages Q and q s gven by: U ( ) k c Qq lectc Potental V (joule/coulomb = volt) Potental enegy pe unt chage asng fom a souce chage Dffeences n electc potental, ΔV, between two locatons measues the wok to move a unt chage between those locatons. The electc potental ceated by a pont chage Q at the ogn s gven by: Q V ( ) kc Changes n U and V ae elated. o test chage) aound: U Keepng Q (souce) fxed and movng q (subject qv These ae SCALAR quanttes often ease to handle
f f d F W U U U 0 ) ( U K U K f f d q U q d q W q F 0 0 0 0 Defnton of potental enegy Consevaton of negy Wok done by electc foce o feld on a chage q 0 movng fom to f
lectc Potental negy of Pont Chages 1 0 0 0 1 1 0 1 ) ( ) ( Qq k Qq k d Qq k U U d Qq k U d F W U c c c c f q q U 1 0 4 1 ) ( LCTRIC POTNTIAL NRGY OF TWO POINT CHARGS
Toolbox da q q F dq k Q Q k q q k F o n c c c 0 1 o o ) ( ) ( x V dx dv V q U d V V V dq k Q k V Q k V q q k U x c c c c 1 1 1 ) ( ) ( ) ( Useful esults Fundamentals Basc laws, defntons Some Tools/Remndes fom Gen Phys 1 U K U K W U d F W U U U W K F d F W f f f const foce o "agent") (stoe enegy va wok by extenal (wok by consevatve foce) ext
Quck calculaton: In salt, Na + ons (+e) ae 0.6 nm away fom a patne Cl - on (-e). If you had just one pa of ons at ths dstance, what s the potental enegy of ths on pa? How much wok would you have to do to pull them apat to a lage dstance?
Woksheet- two potons
lectc Potental negy fo a system of electc chages, The electc potental enegy s the sum of the potental eneges of each pa of chages. The electc potental enegy U of a system (collecton of chages) can be ntepeted as the extenal wok needed to bng the chages fom nfnty to the fnal postons. If U > 0, the chages wll lkely fly apat spontaneously f eleased. If U < 0, t wll eque extenal wok to take the system apat (move the ndvdual chages so they ae all fa apat fom each othe)
Stat wth empty space dag n a chage fom nfnty. No electc felds aound, so NO wok equed!
Bng n q fom nfnty
wok by extenal foce o "agent"
4 pont-chages (same magntude, sgns shown) ae aanged n a squae. (Ignoe ponts labeled A, B, C). The total electc potental enegy U fo ths system s: (wth U=0 when patcles ae at nfnty) 1. Negatve. 0 3. Postve 4. Can t tell 64% 3% Adapted fom Unv. Coloado Boulde 4% 0% 1.. 3. 4.
PHYS 015 -- Week 5 Readng Jounals today fom tables U ( ) k c Qq lectc Potental negy assocated wth q beng nea Q - (O the extenal wok needed to bng q gently n fom nfnty to a dstance fom Q (assumed fxed). ) Measued n joules. V ( ) k c Q lectc Potental ceated by Q n ts neghbohood. An altenatve to usng the electc feld n descbng Q s nfluence on othe chages aound t. Measued n joules/coulomb = volt We wll most often thnk about dffeences: ΔV. 1 ev (electon-volt) = 1.6 x 10-19 J = enegy ganed/lost by a chage of +/- e movng though a electc potental dffeence of 1 volt Fo exclusve use n PHYS 015. Not fo e-dstbuton. Some mateals Copyght Unvesty of Coloado, Cengage,, Peason J. Maps.
lectc Potental V fo a system of pont chages, (Dvde chages nto souce chages and a subject chage -- electc potental V s ceated by the souce chages) The electc potental s the sum of the electc potental ceated by each (fxed) souce chage Q. V k V(x,y,z) s lke an electc topogaphc map fo chages. Measued n unts of Volts = joules/coulomb Q U s to V as F s to The potental enegy of a subject (o test) chage q 0 nea othe souce chages s U=q 0 V
Two basc appoaches to fndng the potental V (1) Gven a dstbuton of chages, use supeposton: V Q kc o V k c dq (Ths chooses V=0 at nfnty) () Gven an electc feld, calculate changes n V (potental dffeence) (Ths only tells us the change n potental, and lets us set V=0 wheeve t may be convenent.)
4 pont-chages (same magntude, sgns as shown) ae aanged n a squae. The electc potental, V, at pont A s: 1. Negatve. 0 3. Postve 4. Can t say. 81% 19% 0% 0% Adapted fom Unv. Coloado Boulde 1.. 3. 4.
4 pont-chages (same magntude, sgns as shown) ae aanged n a squae. The electc potental at pont B due to the fou chages s: 1. Negatve. 0 3. Postve 4. Can t tell 88% (And now tell me about the electc feld at B.) 1% 0% 0% Adapted fom Unv. Coloado Boulde 1.. 3. 4.
4 pont-chages (same magntude, sgns as shown) ae aanged n a squae. The total wok you must do to bng a poton fom nfnty to B s 1. Negatve. 0 3. Postve 4. Can t tell 96% 0% 0% 4% 1.. 3. 4. Adapted fom Unv. Coloado Boulde
4 pont-chages (same magntude, sgns as shown) ae aanged n a squae. The total wok you must do to move a poton fom C to A s 1. Negatve. 0 3. Postve 4. Can t tell 89% 11% 0% 0% 1.. 3. 4. Adapted fom Unv. Coloado Boulde
ach stuaton contans the same total chage Q. The ng and half ng ae unfom and of adus R. The pont chages (Q n C, and both Q/ n D) ae R fom the axs. Whch poduces the lagest electc potental V at the pont P on the z axs? 1. A. B 3. C 4. D 5. All the same 6. Impossble to say A B C D P P P P 89% 7% 4% 0% 0% 0% 1.. 3. 4. 5. 6.
lectc potental on the axs of a unfom ng of chage, wth total chage Q, adus R. z dq R
Woksheet V of lne of chage
λ lectc Potental Dffeence nea a vey long we 1
λ lectc Potental Dffeence nea a long we 1
lectc Feld lnes and equpotental lnes /sufaces) qupotentals ae analogous to contous on a topogaphc map. The electc feld s pependcula to the lnes of constant potental (equpotentals). Conductos n electostatc equlbum ae equpotentals. (dv=0 snce =0 nsde a conducto) When the tny step d taken s pependcula to the feld dv=0
qupotental lnes ae shown. A poton s caed fom pont to pont f at constant speed. The wok done by the extenal agent movng the chage s 1. 115 ev. +85 ev 3. -85 ev 4. Between 0 and 85 ev 93% 0% 4% 4% Adapted fom Unv. Coloado Boulde 1.. 3. 4.
x f x y x x y z z z lectc Feld as slope (o gadent) of V dx v v V(x) x V dv d dx dv dx dv d V x ( dx V y dy V dz)
Woksheet paallel plates