Chapter 7 Electrodynamics

Transcription

1 Cpt 7 Elctonics 7. Elctootiv Foc 7.. O s Lw Cunt Dnsity: ( n ) q ( n l) Q q qnv Fo lcton: n( )v nd d qnv Fo ost sustncs, t cunt dnsity is popotionl to t foc p unit cg: F ( E + v B) q. : conductivity, pfct conducto: : sistivity f t vlocity of t cgs is sufficintly sll, t foc du to gntic fild cn ignod. O s lw: E Sipl Undstnding: Fo xpintl sults, w v conducto, w y v t conducto s lngt nd coss sction s R. Considing unifo lctic fild in El R. W cn intuitivly liv tt R dpnds on Finlly w otin t ot fo of O s lw s l l R, so w v El. E, tt is E. H is sistivity. T conductivity is t invs of sistivity, i.. W usully wit t O s lw s E.. Sipl Clssicl Modl: Dfin t n f ti τ s t lpsd ti ft on collision nd fo nxt collision vnt.

2 T vg spd is n n τ v vg ( ) v E E vg Eτ τ. T cunt dnsity is. n τ Mtil Rsistivity (µω-c) Mtil Rsistivity (Ω-) Conductos Siconductos Silv.59 Gniu. X - Copp.68 Diond.7 Gold. Silicon. X 3 luinu.65 (ll vlus fo t, o C) E insid conducto fo sttiony cgs. Fo pfct conductos E vn if cunt is flowing. Usully w tt t conncting wis in lctic cicuit s quipotntil sinc tls good conductos. Expl: cylindicl sisto of coss-sctionl nd lngt L is d fo til wit conductivity. f t potntil is constnt ov c nd, nd t potntil diffnc is, wt cunt flows??,, O s Lw: R L L E # L L Expl: Two long cylind (dii nd ) sptd y til of conductivity. f ty intind t potntil diffnc, wt cunt flows fo on to t ot, in lngt L? λl Us Guss Lw: E ˆ π L λ λ d ln, π π λ λ E π L L π πl ln ( / ) Expl: T fild is unifo in cylindicl sisto wit constnt potntil

3 twn two nds. Pov it. On t cylindicl sufc n nˆ nd E, tfo E nˆ. By using uniqunss to, s w find solution ( z) z cli tt tis is t only solution. nd nc w cn L Expl: n vcuu-tu diods, lctons ittd fo ot ctod t zo potntil nd collctd y n nod intind t potntil, sulting in convction cunt flow. ssuing tt t ctod nd t nod plll conducting plts nd tt t lctons lv t ctod wit zo initil vlocity, find t ltion twn t cunt dnsity nd. dv F E, E( y) d d dv d d dv, v v d vdv v, v (ngy consvtion) E, n( ) v v is indpndnt on y., E d v / / d d ( d ) / d / / d d ( d ) / / / d d / / d / / / d / / 3 3 / / / y 3 3 / / / d / 3 / -- Cild-Lngui lw 9d

4 Conductnc: syol -> G, unit -> Sins (S) Rsistnc: syol -> R, unit -> O (Ω) Conductivity: syol ->, unit -> Ω-c o Ω- Rsistivity: syol ->, unit -> S / c o S / Rsistnc connctd in sis: R R + R... + Rsistnc connctd in plll: R R R Moility: Sinc t vg dift vlocity is dictly popotionl to t lctic fild, w wit u µ E nd u µ E fo lctons nd ols, spctivly. v ( µ + µ ) E E µ + µ Conductivity will ltd to t ci concnttion nd t ci s oving ility. oul Hting Lw: P R W dp P F u, P ( qe) u N ( qe) un v qnue E dv P E is pow dnsity, pow p unit volu Totl pow P E dv Edl d Boun Conditions fo Cunt Dnsity: E in t conducto fo st cunt: E, E, Cossing t oun:,, ov, low //, ov ov //, low low Expl: Two conducting di wit conductivity nd sptd y n intfc. T st cunt dnsity in diu s gnitud nd ks n ngl α wit t nol. Dtin t gnitud nd diction of t cunt dnsity in diu.

5 cosα cos α, sinα sin α Fo oognous conducting diu (not cossing t oun) t diffntil fo siplifis to cul f vcto cn xpssd s t gdint of scl potntil ψ ψ, Lplc s qution Rsistnc Clcultions: Expl: conducting til of unifo ticknss nd conductivity s t sp of qut of flt cicul ws, wit inndius nd outdius. Dtin t sistnc twn t nd fcs. -> ψ, ψ ψ ψ ψ + + φ φ z z t φ t φ π / d φ dφ π E ˆ φ ˆ φ φ π, d ln π π π R ln ( / ) 7.. Elctootiv Foc E E dl dl Wt ppns? f is finit, t wi (NiC lloy) ust zo. ting, ot f f s + E

6 f s : souc, odinily confind to on potion of t loop ( tty) E : n lctosttic foc, to soot out t cg flow nd counict t influnc of t souc to distnt pts E dl f dl f dl f dl, w is nd lctootiv foc (f) s E + - s E Expl: Estit t lxtion ti of volu cng in good conducto. E, +, E + + E + t t τ Rlxtion ti: 9. Fo copp τ ~.5 s. τ 7..3 Motionl f Mntion Pnon of nducd Cunts t Fist. u v f pull u v w E /cosθ θ. You pull t wi.. You found tt t wi is oving t constnt vlocity, v. 3. T ust on opposit foc cncl t pulling foc.. T foc gntd y t gntic fild nd doing on t cg y Lontz F foc. v is fo pulling nd u is fo lncing: E f pull ub q E dl ub sinθ u tnθb cosθ 5. T f is: ( ) vb Mgntic foc do not wok, wo is supplying t ngy tt ts t sisto? T pson wo is pulling on t loop is supplying t ngy.

7 Expssing t f y t gntic flux: dx Φ B B nd ˆ Bx, Bv B B T flux ul fo otionl f: Poof of t flux ul: Φ ( t + ) Φ( t) B cngd _ B nd ˆ, d v dl ( B ) dl is long t loop tt ounds t find t w wic is t coponnt of v nd is otogonl to dl B ( w dl ) ( w B) dl fg dl B Expl: tl disk of dius otts wit ngul vlocity ω out vticl xis, toug unifo fild B. cicuit is d y conncting on nd of sisto R to t xl nd t ot nd to sliding contct, wic toucs t out dg of t disk. Find t cunt in t sisto. B Φ Bπ B π dθd ωb B v d B ωd o f g dl ωb R Excis: 7., 7., 7.7, 7.