Physics 2113 Physics 2113 Lecture 14: MON 29 SEP CH25: Cpcitnce
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?
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. +
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.
+ 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 1-12 -6 F F (MicroMicroF) NnoFr nf 1-9 F
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
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Interior of 1989 Snyo Wlkmn Vrile cpcitor (tuner) Cermic cpcitors Tntlum Cpcitor Electrolytic cpcitors
Electrolytic (194-7) Electrolytic (new) Pper (194-7) Tigers Vrile ir, mic Tntlum (198 on) Cermic (193 on) Mic (193-5
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
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
Sphericl cpcitor: V Similr to cyliner,!! E A E V 2 4π r!! E l 4π 2 r E Er -q +q r r 1 1 1 2 4π 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
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).
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. Non-Polr ielectrics: Molecules cquire ipole moment when plces in the electric fiel. It is cuse ecuse of stretching of the molecules.
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 1 1.54 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.
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.