Genel Physics (PHY 40) Lightning Review Lectue 3 Electosttics Lst lectue:. Flux. Guss s s lw. simplifies computtion of electic fields Q Φ net Ecosθ ε o Electicl enegy potentil diffeence nd electic potentil potentil enegy of chged conductos Cpcitnce nd cpcitos http://www.physics.wyne.edu/~ln/ Chpte 6 ΔPE. Potentil nd potentil enegy Δ B electosttic foce is consevtive q potentil ( scl) cn e intoduced s potentil enegy of electosttic field pe unit chge Review Polem: Pehps you hve noticed sudden gushes of in o hil moments fte lightning stokes in thundestoms. Is thee ny connection etween the gush nd the stoke o thunde? O is this just coincidence? cloud E F qe C mg Electosttic Pecipittion Gushes of Rin nd Hil fte Lightning Issn: 50-0469 0469 Jounl: Jounl of the tmospheic Sciences olume: Issue: 6 Pges: 646-665 665 uthos: Mooe, C.B., onnegut, B., lik, E.., McCig, D.. ticle ID:0.75/50 0.75/50-0469(964)0<0646:GORM>.0.CO;0469(964)0<0646:GORM>.0.CO; BSTRCT Osevtions of thundestoms in New Mexico wee mde with veticlly ticlly-scnning, 3-cm d on mountin top. Pio to cloud-to to-gound lightning dischge ney, the d echo ovehed ws usully quite wek, indicting low intensities i of pecipittion thee. Following the lightning it ws oseved sometimes tht in the egion of the cloud whee the dischge occued the d echo intensity pidly incesed, nd shotly theefte gush of in o hil fell ney. These studies confim elie d osevtions, mde y the uthos t Gnd Bhm Islnd, B.W.I., in which it ws found tht lightning is often followed f in the cloud y pidly intensifying echo nd then y gush of in t the gound. The inceses in d eflectivity in smll volumes of the cloud following lightning suggest tht the electic dischge is influencing the size of pticles in the cloud. n nlysis indictes tht within 30 seconds fte lightning dischge, d the mss of some doplets my incese s much s 00-fold s the esult of n electosttic pecipittion effect. 6. Electic potentil nd potentil enegy due to point chges Electic cicuits: point of zeo potentil is defined y gounding some point in the cicuit Electic potentil due to point chge t point in spce: point of zeo potentil is tken t n infinite distnce fom the chge With this choice, potentil cn e found s q ke Note: the potentil depends only on chge of n oject, q,, nd distnce fom this oject to point in spce,. 3 4
Supeposition pinciple fo potentils If moe thn one point chge is pesent, thei electic potentil cn e found y pplying supeposition pinciple The totl electic potentil t some point P due to sevel point chges is the lgeic sum of the electic potentils due to the individul chges. Rememe tht potentils e scl quntities! Potentil enegy of system of point chges Conside system of two pticles If is the electic potentil due to chge q t point P, then wok uied to ing the chge q fom infinity to P without cceletion is q. If distnce etween P nd q is, then y definition q P q qq PE q ke Potentil enegy is positive if chges e of the sme sign nd vice ves. 5 6 Mini-quiz: potentil enegy of n ion? Thee ions, N, N, nd Cl -, locted such, tht they fom cones of n uiltel tingle of side nm in wte. Wht is the electic potentil enegy of one of the N ions? Cl - N N q q q q q PE k k k q q [ ] N Cl N N N e e e Cl N ut : q q! Cl N qn PE ke qn qn [ ] 0 6.3 Potentils nd chged conductos Recll tht wok is opposite of the chnge in potentil enegy, [ ] W PE q No wok is uied to move chge etween two points tht e t the sme potentil. Tht is, W0 if B Recll:. ll chge of the chged conducto is locted on its sufce. electic field, E, is lwys pependicul to its sufce, i.e. no wok is done if chges e moved long the sufce Thus: potentil is constnt eveywhee on the sufce of chged conducto in uiliium B ut tht s not ll! 7 8
Becuse the electic field is zeo inside the conducto, no wok is uied to move chges etween ny two points, i.e. [ ] 0 W q B If wok is zeo, ny two points inside the conducto hve the sme potentil, i.e. potentil is constnt eveywhee inside conducto Finlly, since one of the points cn e itily close to the sufce of the conducto, the electic potentil is constnt eveywhee inside conducto nd ul to its vlue t the sufce! Note tht the potentil inside conducto is not necessily zeo, even though the inteio electic field is lwys zeo! The electon volt unit of enegy commonly used in tomic, nucle nd pticle physics is electon volt (e( e) The electon volt is defined s the enegy tht electon (o poton) gins when cceleting though potentil diffeence of Reltion to SI: e.60 0 0-9 C.60 0 0-9 J 9 0 Polem-solving sttegy Exmple : ioniztion enegy of the electon in hydogen tom Rememe tht potentil is scl quntity Supeposition pinciple is n lgeic sum of potentils due to system of chges Signs e impotnt Just s in mechnics, only chnges in electic potentil e significnt, hence, the point you choose fo zeo electic potentil is ity. In the Boh model of hydogen tom, the electon, if it is in the gound stte, oits the poton t distnce of 5.9 0 - m. Find the ioniztion enegy of the tom, i.e. the enegy uied to emove the electon fom the tom. Note tht the Boh model, the ide of electons s tiny lls oiting the nucleus, is not vey good model of the tom. ette pictue is one in which the electon is sped out ound the nucleus in cloud of vying density; howeve, the Boh model does give the ight nswe fo the ioniztion enegy 3
In the Boh model of hydogen tom, the electon, if it is in the gound stte, oits the poton t distnce of 5.9 x 0 - m. Find the ioniztion enegy, i.e. the enegy uied to emove the electon fom the tom. 5.9 x 0 - m m e 9. 0-3 kg m p.67 0-7 kg e.60 0-9 C E? The ioniztion enegy uls to the totl enegy of the electon-poton system, e v E PE KE with PE ke, KE me The velocity of e cn e found y nlyzing the foce on the electon. This foce is the Coulom foce; ecuse the electon tvels in cicul oit, the cceletion will e the centipetl cceletion: v e m e c Fc o, e me ke o v ke, m e Thus, totl enegy is 6.4 Equipotentil sufces They e defined s sufce in spce on which the potentil is the sme fo evey point (sufces of constnt voltge) The electic field t evey point of n uipotentil sufce is pependicul to the sufce e m e kee e E ke ke me 8.8 0 J -3.6 e 3 convenient to epesent y dwing uipotentil lines 4 Exmples of Equipotentil Sufces 6.6 The definition of cpcitnce Cpcito: two conductos (septed y n insulto) usully oppositely chged Q -Q Positive nd Negtive Chge ( Dipole) Two Positive Chges The cpcitnce, C, of cpcito is defined s tio of the mgnitude of chge on eithe conducto to the mgnitude of the potentil diffeence etween the conductos Q C Δ 5 6 4
. cpcito is siclly two pllel conducting pltes with insulting mteil in etween. The cpcito doesn t hve to look like metl pltes.. When cpcito is connected to n extenl potentil, chges flow onto the pltes nd cete potentil diffeence etween the pltes. 3. Cpcitos in cicuits symols nlysis follows fom consevtion of enegy consevtion of chge Cpcito fo use in high-pefomnce udio systems. - - - 7 Units of cpcitnce The unit of C is the fd (F), ut most cpcitos hve vlues of C nging fom picofds to micofds (pf to μf). Recll, mico 0-6, nno 0-9, pico 0 - If the extenl potentil is disconnected, chges emin on the pltes, so cpcitos e good fo stoing chge (nd enegy). F C 8 6.7 The pllel-plte plte cpcito Polem: pllel-plte plte cpcito The cpcitnce of device depends on the geometic ngement of the conductos C ε0 d d Q -Q pllel plte cpcito hs pltes.00 m in e, septed y distnce of 5.00 mm. potentil diffeence of 0,000 is pplied coss the cpcito. Detemine the cpcitnce the chge on ech plte The electic field etween the pltes whee is the e of one of the pltes, d is the seption, ε 0 is constnt clled the pemittivity of fee spce, k e 4πε 0 3 6 E Δ / d 0000 / 5.0 0 m.0 0 / m ε 0 8.85 0 - /N m 9 0 5
pllel plte cpcito hs pltes.00 m in e, septed y distnce of 5.00 mm. potentil diffeence of 0,000 is pplied coss the cpcito. Detemine the cpcitnce the chge on ech plte 6.8 Comintions of cpcitos Δ0,000.00 m d 5.00 mm C? Q? Solution: Since we e deling with the pllel-plte cpcito, the cpcitnce cn e found s.00 m C ε0 ( 8.85 0 C N m ) 3 d 5.00 0 m 9 3.54 0 F 3.54 nf Once the cpcitnce is known, the chge cn e found fom the definition of cpcitnce vi chge nd potentil diffeence: ( )( ) 9 5 Q CΔ 3.54 0 F 0000 3.54 0 C It is vey often tht moe thn one cpcito is used in n electic cicuit We would hve to len how to compute the uivlent cpcitnce of cetin comintions of cpcitos C 5 C 3 C 3 C 4. Pllel comintion By definition, Thus, C would e Q Q Q C Q C C Q Q Connecting ttey to the pllel comintion of cpcitos is uivlent to intoducing the sme potentil diffeence fo oth cpcitos, The totl chge tnsfeed to the system fom the ttey is the sum of chges of the two cpcitos, Q Q Q Q Q Q Q Q Q Q Q Q Q C C C C 3 Pllel comintion: notes nlogous fomul is tue fo ny nume of cpcitos, It follows tht the uivlent cpcitnce of pllel comintion of cpcitos is gete thn ny of the individul cpcitos C C C C (pllel comintion) 3... 4 6
Polem: pllel comintion of cpcitos 3 μf cpcito nd 6 μf cpcito e connected in pllel coss n 8 ttey. Detemine the uivlent cpcitnce nd totl chge deposited. 3 μf cpcito nd 6 μf cpcito e connected in pllel coss n 8 ttey. Detemine the uivlent cpcitnce nd totl chge deposited. 8 3 μf 6 μf Q Q Q Q C? Q? Fist detemine uivlent cpcitnce of nd : C C C μf 9 Next, detemine the chge ( )( ) 6 4 Q CΔ 9 0 F 8.6 0 C 5 6. Seies comintion By definition, C Thus, C would e c Q Q Q Q Q C Q C Connecting ttey to the seil comintion of cpcitos is uivlent to intoducing the sme chge fo oth cpcitos, Q Q Q voltge induced in the system fom the ttey is the sum of potentil diffeences coss the individul cpcitos, C Q Q Q Q Q Q Q Q Q C C C Seies comintion: notes nlogous fomul is tue fo ny nume of cpcitos,... (seies comintion) C C C C 3 It follows tht the uivlent cpcitnce of seies comintion of cpcitos is lwys less thn ny of the individul cpcitnce in the comintion C 7 8 7
Polem: seies comintion of cpcitos 3 μf cpcito nd 6 μf cpcito e connected in seies coss n 8 ttey. Detemine the uivlent cpcitnce nd totl chge deposited. 3 μf cpcito nd 6 μf cpcito e connected in seies coss n 8 ttey. Detemine the uivlent cpcitnce. 8 3 μf 6 μf c Q Q Q Q C? Q? Fist detemine uivlent cpcitnce of nd : CC C μf C C Next, detemine the chge ( )( ) 6 5 Q CΔ 0 F 8 3.6 0 C 9 30 6.9 Enegy stoed in chged cpcito Exmple: electic field enegy in pllel-plte plte cpcito Conside ttey connected to cpcito ttey must do wok to move electons fom one plte to the othe. The wok done to move smll chge Δq coss voltge is ΔW Δq. s the chge inceses, inceses so the wok to ing Δq inceses. Using clculus we find tht the enegy (U) stoed on cpcito is given y: Q U Q C C q Find electic field enegy density (enegy pe unit volume) in pllel-plte cpcito Recll U C ε volume d Thus, u U/ volume enegy density ε0 ( Ed ) /( d ) d nd so, the enegy density is u ε0e 0 C d Ed Q 3 3 8
Exmple: stoed enegy In the cicuit shown 48, 9μF, 4μF nd C 3 8μF. () detemine the uivlent cpcitnce of the cicuit, () detemine the enegy stoed in the comintion y clculting the enegy stoed in the uivlent cpcitnce, C 3 In the cicuit shown 48, 9μF, 4μF nd C 3 8μF. () detemine the uivlent cpcitnce of the cicuit, () detemine the enegy stoed in the comintion y clculting the enegy stoed in the uivlent cpcitnce. C 3 48 9 μf 4 μf C 3 8 μf C? U? Fist detemine uivlent cpcitnce of nd C 3 : C C C μf 3 3 Next, detemine uivlent cpcitnce of the cicuit y noting tht nd 3 e connected in seies CC 3 C C3 5.4 μf C C3 The enegy stoed in the cpcito 3 is then ( 5.4 0 )( 48 ) 5.9 0 6 3 U C F J 33 34 6.0 Cpcitos with dielectics dielectics is n insulting mteil (ue, glss, etc.) Conside n insolted, chged cpcito Q Q Q Q Inset dielectic 0 Notice tht the potentil diffeence deceses (k 0 /) Since chge styed the sme (QQ 0 ) cpcitnce inceses C Q Q κq 0 0 0 0 κ 0 κc 0 dielectic constnt: k C/C 0 Dielectic constnt is mteil popety 35 9