Electrodynamics: Maxwell's laws, Gauss's laws, Ampere-Maxwell law, Faraday's law., Study notes of Electrodynamics

Download Electrodynamics: Maxwell's laws, Gauss's laws, Ampere-Maxwell law, Faraday's law. and more Study notes Electrodynamics in PDF only on Docsity! FlEcTReNyWamice I THEORY Gavss's Law For .EvEctRic Fieuns (CHarree 1) @it THE reGRad Foes oF aauss's_ 1 aw. AGauss's LAw DEALS with Ereeraos7aTic FIELDS Micead |: Pr etecreic CHARGE PROdUCES = Aw ELECTRIC FlEtp, Amd THE Feux of THAT FIELD PASS NG THROVGH Any croskd svRFAcE 1S PROPORTION aL To THE TOTAL CHARGE. comTAred WITHin MAT SUR Pack = GF THE EvEctaic Fietp Pr. ELECTRicar FokcE RER varT CHARGE ExERTED Om A CHARGED oBIECT > e > =) ah Me: [a0 z MO Fe sebeceleal lpopee 4 w@ Jo 2 SMA Cw Ahor UE pencueen lw Nie ope NGS 5. THE DOT PRopuct 84-3 - AcsiB=| ASIBL + JA) By lt IALB Aes | LAMB) cos © 2 A a TM THE UNIT Moenar vector (EY vecree PERFEmDIicuLaR® TO THE syuRFAce iv Macmerupe oF 1 al level! t Bas 2 dal > We , a > <> Ee R THE conporév? oF E wormal 10 A surract Meehan ioe tHe | edccrese leon! lpeeravoledeak |r tuk cons stab | slumpace > ean = @e-lal: IENaleos@ = lElcose® 4 f, () da THE SuRFACE INTEGRAL a Mass | = fol, vy) da 4 | ee = Se ALAR Furetio~ ovER SuaFAce S 4 na a , Ae mda THE reux or A veeroe FiEup 6 g IAI *% Surrace Area , Muxreen VFeTOR FIELD A Arb 'searace S Pr RPERoicucaR To THE DiAFeriow OF THE FIEsD. A 15 PaRAuEL TO m = a =! a Oi Nol A x suas Mach, mR A unifokn pur por PERPEMicveAK ToS, [ere A 15 @ THE ¢omPoertns or z teRrErPicu AR To S ~ toh Wh riew THROVeHn EA TIRE SURFACE = L ALR, daj = ‘ Ren da = Dron A CLOSED subFace oS { Aen da = I hash 2 f, Ee nm do THE EvtEecrRi¢ Feu THeoven A closer SURFACE _ BL. Frux @, oF veerok Fibep E THRover surract Scar pe pETERMIMED ito, =F) x(Gunrace Anca) Is THE: Fools vay 5 Pty 16 UMIFOM And PERPEMDICUse To S > e > ‘al 2 Bo A) x (Suarrce ance) 7) Elis verronn Awd ar an arore To S > > Wa, 2) NE le & da, E16 Wom -uwiFoRM Apb AT A VaRIABLe AvcteE yo S$ We cvetrkicl ted (ak) El wonder de | eiet ints | pene rkatieG Isuerack Ciba veh) Bl g.! THE ENCLOSED CHARGE Wiora EMCtosED CriARGE = 2 i a 1-DIMENSiox Pek laladcr [peederh | (G7...) | a roAu 1 Li) EwcreseD LevoT oF cunecen cine ei i Maw. = nde + A_varies! AtoxG ALIKE Ds g 2 -_pinensiens “ : ance cuabaty pewsity (Chart) : cy Recta) ez] j gui saa _,— As Erevose> Arba oF A” cHAaRGed s-Rract a as (, oda +)-O_lv aries! over! A_|surrack M3 =| DIMEPSION S Miiveidad belated bevsiry P| (Clon?) i lest - cal ag | | sa | vhs Bal. = pV | | V = Evevosed rortiow or cancer voivnk NIST ba tells PL oh Pal > Chie Bo = I Pdv | |p lvaaies| OvER A VOuune THe. PE eae) (oF FREE SPACE a el 2 : w Gol: | glasanszeaze -|10° 1° | C/V | Bois Maa | | ee, ‘Ta | | | | Dh cha raditarce (ivrilts posoceen orbs: connor) | | Ea | | | fal ie | A LL Le a ao he a = Ho El fee | ie PLATE AREA FE d=] Plage cEPARATION E> TEAM DTVITY oF MaTERIAL at i | t : BETWEEY “PLATES WD rdenelr tiny oF A DIAL EcTRic (eecative- PERMirIMry) | fae] ash | hel eee era Ley | @  2. THE DIFFERENTIAL FORM oF Gauss’s LAW a BY¥-B =o BEE a3 DIVERGENCE OF Tue MAGMEric FIELD AT Ary Point 15 O THE DIVERGENCE OF THE MAGNETIC FIELD Te TEMDENCY oF A FIELD To “Flow” AWAY FROM A Pow? MoRE stRomery i THEY TowaRn THAT. Pam? > @ IN SPHERICAL Ccoondi~wares, Bovey WAS THE P= 6 OmPOWwENT BW victor FLELDS. WITH O. dIVERGEMCE ARE Sor EvoldDAr | Arr FIELDS ARE SOLENoIDAL ay ty 38 2B tek M7.8 é + (rb) + i oie ot — CYLIPDRICAL — CooRDIKATES THe Arpene | Mlaxwerw Law 4.1_THE iwTEeRAL ForM| oF THE AMPERE — Max weer Law ee 3 { Bee= lab (pene fies Ia) “acns = __MATHEMA rica DescRIPriow OF THE ciReULATiow oF TEE AanE Tic FIELD ARound pA closed parc Werus S_INcLupEs _rwe SovRCES FoR THE NAawETIC FIELD, A STEADY connverion CURRERT AND A CHAN Gin G ELECTRIC FLUX THROUGH Amy souRFACE S BeumoeD py Pare C Whe adele EvLEcTQic Frux = DISPLACE MEN? CURRENT 8, MAGMETIC CVURGErT OR A CHavGivG ELEcTRic Flux THRovGH A SYRFACE PRobUCcES A CIRCULATING MAGrEnc FIELD Arouvd AM7 PATH Tar povmds Tear suRFACE = &, MACMETIC FIEtb 15 PRobucEb AtowG A PATH IF Ary cuRREMT 18 EwccoseD By THE PATI OR WF THE ELecTRic Fuvx THROVGW AMY suRrACE Bourded) BY Tie PATH Cnawces OVER TIME, 0 BE USED To DFTERMiME THE ciRcuLATION OF THC MAGNETIC FIELD oR THE mAGmirude or ree B risen 5 > a { Bede THE nagwericc FtELD e1rcuration 4 MB acetic FI€ub STREMGTI4 DECREASES. AS BS, = DIstTArce FRom CURRENT CARRYING WIRE S| DP prorenriona. Te THE ENCLOSED CURRENT © Awd. RATE OF CHAMGE OF FLECTAIC Frux THrovoen AMY SURFACE RouwbED BY THE PATH OF INreGRaTiIow C « " @ B.. DETERMir~E THE B FrEtD A SPEcial AMPER: AW Loop Is RE@wRED aa ONLY HAS A P- ComPonENT  7 Me THE PERMEABILITY OF FREE SPACE Bes A MATERIALS REsPowSE To aw APPLIED NMAGHETIc FIELD => a 4 PRs! 44 10 V5 [Aan (sd N/A* on Ky /e* ) 3 Wkalehe FIELD 16 STRow GER Tran THE APPLIED FIELD owart4ee MAKY MAGKHETIC. MATERIALS a pe RELATIVE PERMEABILITY tS re. PB viabacwere Batemate te (Aah S$ fal (seigarey Isaadiea Tea 1) TW pAnanac were MATERIALS Wee (sileedzey ceraree! Tyab 1) a ates FERRONA@CNETIc MATERIALS L= L a M2 Magmweric PermeaBiury (ay = WuMPER oF TURMS LW TUE socEroid P| A_= cross - stcriowar AREA aL = LEME TH oF Te E core me FS ANDUcTAMCE ef A tore Sorewold oS AAT... The Evcrosenriberaie _evenenT 4 4 7 Evcvosed By part cI, > iE Toada ver CuRRENT ENCLOSED a 5 4 & { Fe ado THE RATE OF CHANGE OF Flux / B, CHANGING ELECTRIC FLUX THROUGK A SURFACE Witt Induck A <tRewt AMINE mAGHETIC FlecD AROundD A Bove bdDaRy OF THAT SURFACE PP olcpracemewr| duseer| | Dy | =| eh z ( i Boa de) 4,2 Tue DIFFEREATIAL FoRM. OF THE AMPERE- MAxwEti LAw Mie sau (Fale) : sud oS 2 Pius = MATHEMaricar DESCRIPTiIan oF THE CURL oF THE B FiEtb, THE TennErcy oF THE FIELD To ciRcuLATe AROun dD A_POWT x a hus = REPRESerrs Tee EttcrRic CURREnxT DEMSITY AND TIME RATE OF cnarce oF THE E Freud mt. CIRCULATING MAGWETIC FIELD 1S PRopucED BY AM BLECTRIc CcuRREwT AnD By Aw Eleeraic FIELD THAT @rAMoEs WITH TIME = MUxs THE curr oF THE MAGMwETIe FIELD 2 Bot *~ a > nr @ (s FIELD FoR AM IWFintTE tink SNEARAe 5 a Bs 3Be \r 26 a —= yp ee ober _ YBa) a A /X(HBe) _ oBe) 5 Mins = (7% ott me) al oe 2 at tos f VxB ZO = Expery AT THE Location Theoven wrict Ar ELECTRIC CURRENT Is FlowiNe @ Ok AT whHICH AM 6 FIELD 1S cHArGine Me hcl ode | Wee + de  > a 0 THE Evecraic current Dewsiry A ALSO CALLED Vorume CuRREMNT pEMwsiTy ) i} VEcToR CURREAT FlowirG THRove A umir CRoSE-SECTIOMAL AREA PERP EKA CULAR To THE DIRE cTIOn oF THE CURREWT a omits = Alan = BS ( M5 yy, Aza aCe) a DENSITY oF CHARGE CARRIERS i, = CHARGE PER cARRIER My, - AVECAGE DRIFT VELoaty oF CHARGE cARRIERS Beane DiREcTiow AS ecvRRENT Flow eS a T= 101% (Svarace Anca), J _umrotm avn ren PEwmicuraR Te S a 2 ie = res | Mrs. (suprace areca) , J vereRm AND a7 aw awere Te S @ Bi fseau aa E. a6 THE DISPLACEMENT cuRREMT DENSITY @... SA sone a. CuAMGE IN _E FIELD PRobucEsS A Cranaive B Fiecd Hd J wovutFoRm AND AT A VARIABLE ANGLE To S [ARAMA pe Law 3.4 THE WEG RAL FoORy oF | FARADAY eee ete a | e@ i Ent = - ie Renae Pale LUX RULE ih are é A 4 Fe IL al oad {2 ok da FARADAYS LAW ALTERNATE FORM Want WACWETIC Piyx THAover A SvREACE induces aw EMF tw any Boundary Pare oF THar SYREACE , AMD A CHANOIMG mAGwETic FIELD ImDveCES A C1 ROVATING EvecTRic piety _ a By THRovew a suRFAcE cuawGES, E-FIELD 1S ivpucED Atoms ITs BouwDARY- \F_combvetiw 6 mareéRia: |S PRESE~T Avom6: THAT BowndARY, yHE E-FiEun PRovibrs CURRENT CARRYING EMF a iwpuceb EF OPPOSES TINE CHANGE SIM Foux | lk > We THE 1NbdbUcED ExFe7Ric FiEtD | _ ee oF N/e ont W/o. wel-¥ ak 1s] | PAR LiwES LooP BAcic On THEMsecves (wo piveRoewer)  FvectRopywanics L Ewh @F CHAPTER QuESTIOns Gauss$ LAW for [ELecTRi¢ FlELds CeuaPTEe 4) @:4) SPHERE _, 42 15(4.6 :107"" Cc) Yt gt Yo (£4.¢|-107"* c) hd det 14a tga SE ole i122) cure spe L , O=-B xy Oe ae SNS FLAT PLANE Ey jes ela | {odo 3 [of eaxy Ted loti VES [er ded eal Fat ae Brae cd Ee SC ated ae Pa 2° 2 Tera Tae ee @ 6... ane 1.3) Uwe cHaece X= do(4- #2) Cas | lolee & he h hk (r URE it alle =) dx 2sha lab dx hath U1 : Greve Nevhe DB, > Fes babe [Vira EL 4) SPHERE F=aO, p= ps (£) qe =f pede = AL fy ptisive dtdeda: a fee sine didede ~ Pe Shae P if jaa) Jideds EI & ee (° fciawe de dé = Po ae Te (sue fa Xs 2 - Poker (4 Gn) 2 pees t 7 ; ; ene Powe Frne > Poke Or eae €. SA ie Fs PE be TOES oO Din Rei Bele SPO Vn Dianever 22 ai O- bel = liken ato? | C Al =\nsF* Gene SO Aaa ARE, aes =| 3or- aot |e KH a Ee 0.077 m > ): 6054 m 1.6) A= 100 en } b= Sem ft dork ea 0. <li oi (18 ib lelas| kh Coe) b, is Fa Op =| 483!.9 View (4 S\DE)  41.4) Wade cyerper |b pte Fwize Line » Ge rd 2 f ~Lde ls | NAL ®. a S + Ce Fuce cyernee | 9 OLE DR (tack) ZEo 1.8) katie! PL} | Ge ne ie7t ¢ (imagine Fue Bowe wih g Ar cewrer) UF Fulcl =. lee & [S| 44) op?t ier] V7 Ve tHave sy |G. f 121 4 esp 47071 Vay 1) SPECIAL GAUSSIA~ SURFACE FOR (Ar MFIMITE LINE | CHARGE CYILIMDER {s PERFECr (iris EiteeR PARALLEL of PERPEMDIevian To THE Ele ) 2 2 a B, 2 § Eendal |) for top ano Borron OF eyeinPER |F 2 REO sinck PEPEMDICW aR >, Sif SivcE| om rHe ibe | |E fo lai =! [EI S$ , i> a > > a ie {2 ee ee flake = NEW (arte) | (E- kabius oF cyemper | b3 LEneFis) t = ion a X pe her) > = + ME = t(ameud ose InP te 41.10) WFimi7e Feat rare > Prove trar__|E\ = eae (use A GUBE Tor met) oy = ss : Peneeh Ele Midd [Solilsleced BolAb prereaicy car FM pS fe fs (since Pom Paparcer) @, ede oe ed Hee Wnorren | 2 EIA eb ais ae % (Fa) 74k (r pay Tja — —*_IW| SPER eat CooRpinarrs : L | R He (Cmale Bie atl > Bl || spherical cosens <i ° >y c neat Se aN > —~ = > B a ba 43) _vecror! Fiery A= cos (7 ~ F)C 4 Sin (rnd i a Se Es “DIVERGENCE woud pE © ~- VA - yz (costry-&)) +/4 (uit ovel 0 az ~ ; a 444) Bo Pt be@ ter2 3 — Cyinperear cooars , Fim p <i is az Weilg l= (FS) + +o (be + % (era?) - OrotackZ- terre Lely yaelel ey lt Polat glarslele fT @ nw b Oa n = ~~ > 1.45) spueeical |Elzlat f+ 4 16) 4c @ pL Rsles | Vel ° : —A 0-2 =F iltab) + fro to (eetsess) 4 Kl JE bat paste) = p=(rot + ®(S2%)) e. Grieas, ba toe Haneeloldeleyns| 4 (chabrael ol) 24) B= Se-3i+4e nT Byron + Blecrren + Hisinrs = 0 @ig Ge Beebe a fale l ole Oras {bea da: if (Scbss flee) Mele Le = ig 4? de 2 4? Rn, We CNEL f, Berda = 5, (EUSSt ce ier el Lee ae haul 4 note Wo Beek ta) eaten (eae 4 Redeed |) We 2D APS Sep Tan bs ot mm Telstp.oo8 JA NTT solos if OL} Ria SP | Bel Ser 6 AS lis] paanwec| yo] | pea eB QS RPI PR BS ed BE Le ed ' eA eS EE { ehopeinad tb BEE (ot) Oa giant of? 1 NK Op Para ss ion lve 5 Oy, = 1.216 10°"? WK, AD. = 3.11 + 107" We > Ta = = 213) AB lolesilolalaloaseL. 7 } Bro $ Beada=oc rs x a Aas A 5 a ea eh. gat Uy in fea peta) ai ake |e T r io) a to T -0o7 = 3, = Be oatotae sth am demesne) loroe pe alee ol ons 1 (22so"1) 13 Sto We an “ = a ia 7 + t ot Bioi gatos? pimp, 2 later On] n= (Beet Pal z celisd (i aps soir = Oi, bo Sales | toby We pe) eh Intl = oso ls% | } T A 5 ~ Ty Ae gs o> IB eae Al = Faroe (oti 42.8%) ee ee a IS Ne ao DIG) tay eee pt al MI et Grease [37] ote nes ft Oy 2) bom ee oO policeman Helo Pe bh hol ob al we 2 ale aT < is wm x ~ at Bz 4: 10-5 (cos 30.3 4's 30 x) ero IS As ay Sony is fay " z ‘ oD es C3c46 ote ® yw ere deleders oyet |e lel we dolsbwll st La =a a Ss B borren Osha seuerdot® Wie Et roy GF Bune. k e@ Ba, rorac sO  L 4.6) B= asw (byle™ 2 — » = VxB - ws a B ~ bx = a yx 8B = eet = we t abcos(brie as abchatby ee d @ 23 pile ot ower™ (leds (oye. A sha lCisled/ FD) Ala dee Me = = 4.3) 7 BLE pl (est siege F VB! = weld a, a> 2Bs\ > a8 = E * . VxB = fra me le spot cosp)i t(2Bee™ sine) 3 > - 2 > 2 dl pas pes” {pose é +2swes) A fom Abe Me a 4.8) B-(S+beb ace’ 6 Se mee abe te bed > ef c 2 C Rye BS SST b ale X(r8)))2 = eT ibe epege mbes) Z Se Faber (ASR bE) 3 ANY pase e@ rues = Is ooo ee = sa IF Deceeaces as = et B= <6 7K Ee co.ns tAet Vix bolo th fey | aE Ze | Wesel ea pe, er | a = Fao Ay ces Coby x ah fs >, + - Steet ase rw i= 4.10) Se VxB = M, &. ge Een = VxB C 5 SES Pel pes OEP ARE Le bop e pape apd By = ee are se ea wt He t = 3 Sar er Flo z ( WAY Cos (aby sl peke avswoe Vine ota dey ® ere HENS - oe FaRapAy SLAW (CHAPTER 3) : 3.1) sovAre toor <wes- zoe Y-2 prark live, =) da = dy tal) 2 Sb a E: : R : ‘ed 1A a\_o < Bl) >B,e|% UC | | Stavping Atovg five x-axis), niru ,—FRR RerarB$ crock wise Fs oat +g Zora pyre $e g [2% 88 Era ge i, Bea do | =| i ioe {4 pclae | Haniel tJ d dy dz 3 BL qeal { e &dydz re 83) xv =8e =$s 3 IB ds = “BL & (ete - ) Sb Bebe Se ee ie) BSS at eo lee! VI bi be i eLLPALS = 3.2) SavakE covverivg tooP 2bes > L , Fixep B-Fievd (ile Rem IB bos 21) ale) | 2 o(£)_ rnp + 7k [tl 2) ei < (oslo, ) fae) =| Bh (-S si (o.£)- u) @ = Bot em lae) Vv to  3.3) Bae DESeewds wi Th sPERD v = 4 eemstanwT B iwTo Pack . d da a) tne - | Bea da = -[Bleslor iS, do = eb | So @ ASSVminG Wocwiprn , 7 = HEIGHT dL a > Eres! tees (wy) = -\~w & = |-|8lrw vy Ly hokeebrdiplewac Vs sdwicnlbeaelecd wee cua BL i Wael sie) pace 4 > 3.4) Square voop side = $ sreed v= Se B= Be 2 a > 7 dA = > Fe > oD rng e/- 4 J bea de > -% [Bal costo da 2-181 Se = 1B ge es) = -Bls $3 D-Bsyv — WHILE LooP ENTERS THE REGIOW EH ES) On Se wre etme las) tw sible Regia d >| 7 ow da Cxsy cr 7 Ene s - $f Benda = - 94 2 BIAS = ebis Bs Btw \Bisv- 3) 2¢ EF 4? —IBiev. 3.5) circu AR Loops f= 20cm = 0.2 mn Ri 42 a SoveEwerdD N=5 2= 3€ en = 0.38 m Se Foun od 4 let T,> 008 A bg RY ibe a) Nal sa Ae 4 7 ¢ 2" enpz- SB ea Ages = $f, ialde = - 2 (ink): - re? Se Jplolehs aa se bean LAV. iplee evs blo ee de ae oe ae dé 2 ie Le Ene: = 1B MeN 2= =-5.9-70°" V S) Tet pee EAP] 7 A Ee =R ret © A 3.6)| Nea2s | we Ie solgs Piel lg jon [BL= O35 T O@2we pone t d te d 7 ; Pabs |= 1s) (le Nipel able = eines da = -wieta * (eos we) - NIBLA (-w se (wOl> NIBIAW sin (we MAX EnF AT sim (wt) =1 EMF. => MIBIA w = 5Y SS = Wiss