Physics Lecture 14: MON 29 SEP


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1 Physics 2113 Physics 2113 Lecture 14: MON 29 SEP CH25: Cpcitnce
2
3 Von Kleist ws le to store electricity in the jr. Unknowingly, he h ctully invente novel evice to store potentil ifference. The wter in the jr forme the inner coting n his hns forme the outer coting of this evice, with glss s the meium isolting two conuctors (his oy n wter). Von Kleist switche on his genertor, chrge flowe to the glss jr, n he ecie to remove the glss jr from the mchine. Surprisingly, he receive n electric shock! Why?
4 Potentil irectly les to work. If evice cn store the potentil ifference, we cn use it to o necessry work. Cpcitors (or conensers s Volt clle them) re exmples of such evices. Potentil ifference generte t isolte chrge surfces, les to genertion of sttic electric fiel etween the surfces, which stores the energy. A ttery is evice tht mintins constnt potentil ifference cross its ens (through chemicl mens). A circuit is pth long which chrge flows. A switch is evice which if open oes not llow flow of chrge. Then the circuit is si to e open. If switch is close, circuit is close. +
5 When the switch is open, the circuit is incomplete n there is no flow of chrge. When the switch is close, the circuit is complete n electrons from plte h re ttrcte to the positive terminl of ttery, mking plte h positively chrge. Similrly, plte l ecomes negtively chrge. After some time, when the pltes re fully chrge, the potentil ifference etween the pltes is sme s V. There is no more flow of chrge.
6 + If the prllel pltes were unchrge n lter the ttery ws connecte to them, it will tke electrons from the + plte towrs the  plte. The prllel pltes re the simplest exmple of cpcitor. They pck n electric fiel mong them. Appropritely constructe, the fiel cn e very intense. The chrge on ech plte is proportionl to the potentil mong the pltes: q CV Whenever these quntities re proportionl, the constnt C is efine s the cpcitnce of the evice in question. This unit is typiclly too lrge. Most common re: Units: Coulom [ C] Volt Fr MicroFr µ F 1 PicoFr pf F F (MicroMicroF) NnoFr nf 19 F
7 The cpcitnce of evice is completely etermine y the chrcteristics of the evice (geometry, mterils). It oes not epen on pplie potentils, chrges or fiels. Computing cpcitnce: Strtegy: compute V s function of q, re off the proportionlity fctor! Prllel pltes: E If the seprtion is smll compre to the size of the pltes we cn pproximte the fiel for tht of infinite plnes: V σ A E!! E s A E A Are of pltes. A V C C
8 Motheror of Iphone S
9 Interior of 1989 Snyo Wlkmn Vrile cpcitor (tuner) Cermic cpcitors Tntlum Cpcitor Electrolytic cpcitors
10 Electrolytic (1947) Electrolytic (new) Pper (1947) Tigers Vrile ir, mic Tntlum (198 on) Cermic (193 on) Mic (1935
11 Cylinricl pltes: q +q r Agin, we pproximte the fiel for tht of n infinite cyliner. To compute this, we surroun the interior cyliner with cylinricl Gussin surfce. V!! E A V L 2π rl E!! E l Er E 2π L 2π rl r r 2π L 2π L [ ln( ) ln( ) ] ln
12 L ln 2 V π so L C ln 2 π Cylinricl cpcitor n rius lrge, seprtion is smll, If for lrge. 1 ln ln ln ln like plne cpcitor. 2 A L C π
13 Sphericl cpcitor: V Similr to cyliner,!! E A E V 2 4π r!! E l 4π 2 r E Er q +q r r π r 4π r 4π π 4 Now V V V, therefore C 4π Limit cses: If R, noting tht we hve, C 2 4π R A 4π R 2, A Plnr If, C 4π Cpcity of conucting sphere
14 Dielectrics: We know tht in insultors, electrons cnnot move freely s in conuctors. However, they o exhiit limite rnge of motion. Molecules re not sphericlly symmetric n they tilt in response to n pplie electric fiel. As ll polriztion effects, it hs the consequence of iminishing the fiel insie the insultor (extreme cse: conuctor, no fiel). Tht is, if one inserts n insultor etween the pltes of cpcitor, ue to polriztion effects the fiel (n the potentil) will e smller for given chrge, thn if one h vcuum mong the pltes. q CV Implies tht q is fixe, V is smller, therefore C is igger! Inserting ielectric is prcticl wy of incresing the cpcitnce of cpcitor. It lso llows to tolerte higher V mong pltes without sprks flying etween them (some ielectrics rek own less thn ir).
15 Different types of Dielectrics: Polr ielectrics: The molecules of these mterils hve permnent electric ipole moment. These electric ipoles lign long the electric fiel when it is externlly pplie on the mteril. NonPolr ielectrics: Molecules cquire ipole moment when plces in the electric fiel. It is cuse ecuse of stretching of the molecules.
16 Given two ienticl cpcitors, one with ielectric n the other in vcuum, we write, κ Ciel κ C vcuum for prllel plte cpcitor : C A iel So we cn sor the constnt κ in the efinition of κ All equtions we erive up to now re correct in the presence of ielectrics if one replces in plce of! Some vlues: κ κ vcuum ir κ κ pper wter 35 8 Electric fiel of point chrge in ielectric E q 4π r 2 Guss lw:!! E s q q q q' If one uses, there is no nee to tke into ccount explicitly inuce chrges.
17 Summry: We ve seen wht cpcitor is: evice tht pcks electric fiel in confine region. Next clss we will lern wht hppens when you connect more thn one such evice, n how they ctully store energy.
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