ELECTRIC CHARGES AND FIELDS nest CHARGE + An wecbale change ie an intrinsic property of acolan propo. Unit is counluml - le-= 1,60aQx107'%C Changer ane of tue kinds, Positive and negative Crerce Chee Mass | — 1) Can Le positive, : 1. Al Uttve. [ee megrmiie 1 Alone: poslit 2. Change can be iantined | As Not quantised 3. Change is conserned (3. Moss - energy is conserued, | | Home of the missing mass | . Lolkes the form of, energy. oa A Mawes aon | Of, speed. > speed. B+ Force Letweenrcan be | 5. Force Lehuen masses ie | Ottrockive cy repulsive | always attractive | 6 Force Petron changes 6. Fotce Reborn nv ae ds dependent on nabine Independent of medion. | Ah medium. _ i 7 FUNDAMENTAL Lew Or Cuaraes ! ‘MetHops OF CHaraunér: In Changing 24 Conduction } Tp om unchanged conductor (BD ie touched a changed trody (A) chosges ane shoned fy the tv Lodies (tite their potential is the same). Bs Changing 24 hiction : | Puibing two sultalle viraterials can electrify 2otin electrons while the then goles then and sus tne thectnons acdires O positive Chonge. e.g! wher a lass sod is subbed with stile, tre vetnens Toate Ail Wits neur hes a agateand Q ie Left Ath a positive | 3) Now the nod is sumed. So te negative won the and Pspreads ald even the conductor. Electroscepe is an instrument thot detects the presence G changes tn a body. | Peopeeties Or Cuaraeg : V\ donges one ywonlised . Chas Q a Dedy = ner near ee and e- Crexionag a. are additive . Toad chesge on an 2) fedy Ie the algebrale sum of the change on 3+ Changes ane conserued. The net chonge on an isolated | Aypten ds alurays a Constant » Covrour Ss Law : Coulomb» faus way Le stated os “Fovee of, interaction Letween tuo point changes is divectty Proportional to the product of tl changes and 3distance Lebroeen then’. bet quand qo Be the tivo Lee poink oA phanger separated fy a distance ae Detvoeen thom. ae point changes is geen by F 1 point changes Fae qqas Aeporroted nye distance ond Fe I “ a we FOO WY Ae or Fe k VY n> where kk is a constant wise value depends -on pod lve techn 20 clea es the tuo and also the wih in which Fy and + ane eT BY2%0 (Like )s the force on Bie omrny frome | and that en! i away Prom a. They repel ere another. On the other hand, if Yy2 £0 (untike chacrges), the force on Q is towards | 1, thar on lis towands 2, attract one anotten. | . Te ST system te value of constant k dn Vacuum is k= _t ATIEo The constant Eo ds cadled the perunistivily of the fre space. The oxperimentatty measured Vole of Akis 949x107 Nm cm, Ys Eo zt > ' ank AX 22 ¥AxI07 =; = 8. 85x 107! CON n> With thir choice Af constant k, the coomb's Brous can be written as AT éo ras xp charges wane situated fra midtiun and not in whine K is colted the dickectric constant xf the ST Unit of Change s Th the medium is aiv, then K =! Wee Qt = a=! conlomtb, T=! metre FeQ@xtotx IX! 2 QyioIN = nus, ene coulorwte is that vstich when phaced in airrat a distance of ene metre from an 2qpal and aimiban change, expertences a sepulsive force of AXIOIN. Redative | Pounittivity (Dielectric Constant) : The coulombic. ce Debiseen bo changed orticQe Leo made bee P 2 ot Wye | A Eokon Fo= 1 Ue | ire | where € is alscbute pereittiuity of tive median ond je equal Le Gok . Les € =KEéo Now >» Fae = &€ =K (or En) Fin E> [: Fue bo U2) TOUINAES yrleo Fro = Fae k | Thus» velative wtivt af a medium may Le defined o% the vatve 4, tht foros Leboen ture changes ata certain distance opart In air (or vacuum) to the force Letvown the same tier rhanges placed at ae Coulomb's Laur in Vector Forno p — _ « nH Sonal Suppose Luo Dike point charges SB au go are pla ata Yar fa Om divtance apant dn freespaee Ae ag ag | the ane alike , trey wild Fo Bop ° Tes changes '4192%0 mepee ee separates 24 0 distance Let Fia e the force onchange 4) nm duz te chonge 42 and Fai Le the force on change qa due Te q+ | | Let Ray do the wit vector from 4) te 42 - Then the force Fa $$ Roo tae F,] anéo | 67 Wynn > wwe Rar We the unit vector in the dimection of Far. mel &a4n [4 . a] Fou = lo Yor Vans “Te Ae a? 7 Siwitonty » 1f Fig de She wit vector from go te 41, the foror on change q) dit fb q> con Le wonition as > fer to M42 BR RL ae Feo rs alee ae | Since Min ond Ra; one sdk vectors pouting in x i ‘ drove Bo prec oenN caat c ae e Aw = = Are T. » Becomes Prenehore » cay | Fos 1. $4205.) 1 age 4, AMGy ye eresheos qrom 24h) LE fowewrs thot > => For = - Fin |. Taie shorrs thot fovees exerted by dre duo om zach other are uel and Ue The f oa the Newton's third Laur of motion i+ obeyed. a: Fora experienced one. due to r Letuater the twowhanges ds a cenbrar f : Soper POSITION Paineipe : | The Basic idea Athind the superposition. prtnetple ds that the porce ora duc 2 another chonge in LB neighbourhood je independent of the 2change qo is tue Bry iS > > 7 | Fre = Fit Fot--: + Fr presence of ore He ther changes in thein netghtourtood : Asa 2 result , the net force or due te all the dn Ue nee orheod, Spake te weston anon of nd foraes etc en it denik ait the individual changes in ite neighbourhood . In applying the auperpostiion POinrciple, all the indtuiduol forees must be colertatid teeeping Ln mind bet FFL, BS. Fh) be the forces: exerted ono | charge Ap dy the changes Yi4rs Jaro Gn in its | WahLoumo od: The net force which nour acts on the White applying tre above equation » the force Fr en qo due te qy is te Le caleulated assuming that the ster changes do vst affect this foree . Simitorly > the force Fa onde duc tg Js also te Le asuuned dndepundent ff the other changes. This is the essential feature of all the forces acting on dp. ContiNves s CHarare ‘DistRiBotion + A cotlection of Longe huunber of, Phennrentory changes js iu @ Cotinusis Change ‘Disteibutlon . | The «ontinucus change distnibutton Le one dimenitonal, two dinvensional or thot dimenstorncl.(a) Linea Change Density, : Suppox the change iv dintributed unbfownty aleng a Lines straight Or cunved Then the change disterbutien is called Linear. 4 Comiden a thin straight sod. - in in coutemi and R in metres . The Plectnostatile force on qo due te the change on infinitesimal orua dS is de 1 ox . Ai€o aen04 0 an eas RLS) anes yeThe teak fps cng on dee te change on | the whole > t aoe P+ Lae. SSO (©) Volume rity (2D) + Winer she change its distrituted tultorrns oe oO VRume , then it 46 called voliime vt a ore change 4 distributed NAA tee Volume Vs Then vobume chovge thosge density ans ar Soy it wade is coulonte fete’, element dV us dq = PAV. | lor examples Suppose the total chasige q is spread | The stotat force acting on Gp “aeteay avr the Aotal Noume is FL ft. ety 3 We. Evecteic Fieun : The space orrornd a change In which its electric influsnce ton Le fort is coved thy olectric field. Evectrie Feup Intensity Te electric field Intensity € ak any point In an eucroskatiec fterd is defined as the force expertencd Pr unit test chonge placed at that point, the "dest change being extremely mall. = aa |_| Ae the test ) Go produces its oun freed» Lt way dintul Be position of source . | Therefore, test ehrange should Le supfictentdy srratt , approaching Te Bev a.e. Yo tends to Zero. Therefore , E = tim F dvorn the Coulowk's Laur, the fore on thetert change is SE erent eee eee ak the origin geen Oe og | Felt Rae a ANen ye 7 Dectric pietd 3 tly ie oven 2. Fit es on qe (AMES— - C-1 Qe. es ANE a> re | The divaction of Fat a potnt Is along the Line Joining dine potnt and the Q, ining Cutvoasd AR QBs positive and poluting invoand if @ is negabive, Nate : Fon a. point chonge » vaph. for |e etcnite fila Downuty © iemus stance from k | / | | | 1 Evecrere Fieup Due To A Geove Or Charis : The slestnte feta due £0 0 Group af changes ob ab any Petit cam Se cabeutobed bap c Pietd dus te Lack chosige turn Ly ton Sovcidintig to oon clenqr Ste otaent are danSuperposition + Tf &, é&,.. En *s ' ar the filds due 2 Lrdividuat . po chongus and E is the nesutant i Jntemsitey » “e howe » a de sat errete as mouny P+ hee OF changes om ct Soe 1 Fe pa +t Gm Pop AME Hep Aigo TP AT Es Yop = See =~ cet mere, Enis the electaic field at tu peint P due Xp WY point chorige aund n= Qs8-.. Evectaic Leg Or Force : cul ar Lecbrte field tn a region i depicted , | agree electric Liner oh poner, a An electric Line force fee oo dm ot on. pout lpvan She dincton of tne aestnie ald Anienseeg at that pent Line of dovee Ps Electric ines ff Force | 1s Eveny Sine of force ie contimmous and smoot t \ curse originalin nerun Ss on <— Jpom- a Conte Ehonge at | - \ ending normally at o p Pe akonegative change. 2. The tomgent te the Line of force at any point giver the dinection & E at trot point. 3+ Liner of force never intersect 4, ERecdric Lines of force de wot ee cece hid inst — charged conductor i> Beno: 5. The mumber of Dines of foree per unit area Oo Aus Asraction, at euorg Pont a . ; = . seplond unlike eb changes cttrack toch alien. Th thes sawords glectsia Lines wf, force expand Latirally and. yy MAMARM [fxeea eee o + i i| yy yy yy |Longitndtnah cama he > se contrast Leargthucise, This explains, Y NE attraction Letweanr forces. / N Elecbrule fietd Lines com B. The Lines Pf force exert Lateral rir Intersect as shou, Prssine on one anther Le. they tend td repel each other. This xy 2xplaine Hepulsion. Se As The relative density of sthe [etol LX A Lines at different pornts indica = & a | the relative fteld strongrthe tenn pena et | points . Evecteic Diroces a A pain of 2qyol ond opposite point changes separate a distance de called an electric. dipole. ‘ The tuo changes ashich forun thre dipete are +9, ond ~GYond the = 3k distance Retroeen them is QL. “4 - Fg, Its electric dipole menment is defined as a vector quordity hoving magnitude 4.08 De the product of | change and distance Deroum the chonges and | dtnected from vepotive Ts positive charge: | Pe gx ae Thur, SI unit of electric dipole moment 1s Cm.The Ferd Or A Dirove - At A Pot On Its Axis (Axiac Line) Comiden own electric dipole changes 4 sepanated bape ; Arstance RL. Covsiden a point a dipcle Pot o distance x from the combrye of the dipele. The slectric field due 4, (44) at P Ero A 4 Girected atone BF) ANE» Ca-2)> ° The Lecteic fret Arse te (-g) ab P Eo- t 4 7 ibe Cas D> (Abrected aed ry As w+h > a-k Ei > én + The magnitude of aectric fietd ak Pig E+ €.-ea (adeng BP) nn —- it & ATEo (m-2)% Aree (x4 a €- 4 Le _ & 4rté. | Ta-2)* aa B= 4 4a spe- 1 _SP* (1 p=qxan) AME, (a2 22)* 4I1E, (2 >- 9>\? In vector form > pet SP | eeSpectat Case i Ig point Pia fan from the dipots + ey L>>Q the teu 2? is UUole as comported De 2 40 tre npprerderate valu af, flatd 6 quer Hey > = P- op ATIEG 13 At A Fon Now mat To Ditove_ Axis (ow EquaToRiAl | Le) oy | Consider @ point P Dgting on dhe foul 2s x of the Ene foining He tuo ata distance o¢ Brom tre midpoint 0. / Saal | tot Fi and Es De she Pierd \ Intenricies af P due te +4 and oo. 8s 244 —4, changes. Ey is directed. “4 P isa por ne ow ay froin the positive change aapotdiod bina dhe ae Ex disuckd tousands dipole Hoe negative ew eee fevers point Pus a7 2 (oy Pagthagonas theorem): Noto, the magnitude ab each fidd Js given by Er- Gs = 4 4M Es (m4 2%) On sesclutng toch fied along X and y ones and adding then swspective Components ; tae find thot Hiss Y- components concel out and X- components 1g= aq 2 are 2) (134 2) Ve E= Ags —______.. AMEs (x74 27) 32 [ cee ee | e=-_! Pp ATES “(5004 D237 Tn vector fom . [> = } @-t-_p _ ames Ge 4 PYF The neqotine sign indicates thot Eis Co direction te P”. Pe Spectal Care } TZ %>>L, ther 12. _ _ Dirore In An Externac Evectric Fiera: ; Suppose an eleckute dipole The tuo changes £xpentence tie _— —_ sarod and opposite forces Fand -F Papen as shown, where F = UE. As the two | forces ane eqyah and opposite » having > ps ie Aiptenent Diner of action they form o pn dete. dipéle in an Couple, the roagnitude of moment of uunllerm dechic fiard the coupte or torque de given ty Ts [Fx ad | = 4F alsine - oy Ie Ac = Alsine] Stalte aqyilibediurn (9 = 05) L= PEsine Uns torgye acting on dre dipole dur tr external Held tends th altgn the 5 > AL nstatle equi tihstiorn dipake moment panollt Be the electuic feekd (© =180) Thefow » Weve equolior can Le woithen ar | [2.3] Dinedion of T : Direction of T is perperdioutar Se the Special Gare : ) Torque acting on a dipole is rroseiroum (= pe) when the Bipole us perpendicular Te the field ao(b) Torgue acting on an sicctate Alpole is zero urhen C2) Angte Letuacen Pand © is zero Le, = 20. In fiwcans te ee eee Gi) Angee Retrcwer pr and Ele 180" L.e, © =160°. Th thie case the dipole da In ventas aaystBtietann Tre number of fidld Vines passtng. Brough. a given onea js desouted ac the oLectrte flue Hvroigh the a and is denoted Ly O. Te isa seatan quantity . Therefore » [$= €Scose =F. | \Gaves Law # Lot Ws consider a sirbertoak surface of radius m valth a +4 at UR corte . The electric fidd ob ate the points co the surface is radially Reapere Ree oboe ua | outwond . Sine the Aadial dircction Jo evangurtane nevroad To tre surface of the sphere Hhe field ts normal te the surface ab all pects Hence » at point the electaic ea Eis in dhe Same direction ag the elemental arco Vector As (whith also normal Te the surface), T 2) the slumental Pur db through the ance element: a is Ger Gg ddg = €. aS = EAS a cst (at ate points on the sphere) ATED“dd = 1. 4 ds | AMEs The total ptux Gewun the surforce of the sphere ls a Auurornation (or integral) af te night hord side of He alove equatron, Hence » 6: Joe »% ds ATMEo n> New gq and a Being constant , we Ihave os + Jas Freon 6 = _4 Ana ATE oaA> [is Jas = 41: Austace b - a area of the apherw | fe o-oo (8) | Me cerca fom ay) abi shat Are total douing a change q ot its ene bo ee positcive and negative i 9, is negatives” The dotat electric flux through a closed surface S aurfact This susult developed LY Gours for ficlds by Maxwrel is called the Causes Low. Mathematically liv expressed os given Pelour | o- feds= 3 EoThe intagral on the Left Anand side of the eqpation giuer the total plc Horough a closed sunface Sand Yi won fhe sight bond side de dhe net change enclosed Inside the Posed sunfoce S+ ing the Gauss's Low t (i) This Lous ie applicable to hosed sinface dovrespectove of Ue sbape. ont (i Tre electric fiebls produced on the considerta surface ove produced by changes Inside, as-vaell as eutsiole thre Gil) The cLosed surface chosen fon the applicalron of Gauss’ ow 1s called the Gaussian 5 D Ye net draving any poluk changes on the Gaussian surface (iw) Gouss's taus le often used for colaWating electote fields duc Te symmetric bey Ao ropriate Gioussian ds ene ever which agDenetion Or © Covtoun’s lw Frou Giauss’s Law : “Lat us considen dure poiuk charges Grand go hept at a distance ra ~ The apart tn vocuim: ores expertenced | hig qe duc Te qa \ atte FeQie ---------- 0) Ne ww Fis tre electia field due — Changes! and Ao ane te Gp ak P. Hept ato. distance % eee crn anata nt cae Arunpace with the conbre Ab Fs and ince: radius 1. The Gaussian sunface passes Hvrough the point P. By Grawss’s. Law b= 4 aeen n-ne n- Ay | Eo hone @ 14 the atectnic flux poming Saough he Gawrsion "Ase ition Oh, electato peux b- $P. dg ------------- tn) Fave eqs. (11) and (1) EB. dS = Ge $ & SEGdS= Io (0 is constant in ro. a Prorvoughout the Gausstoan ee 2 surface) as > ect oo © Rie Ee Gy) From 2qive, (1) and Cw)Fea ame ATES ae The abeve expression of force 46 that of Coulomb's Row Ln electsrotabics. Gaussian surfece) afrout the Rint The change enclosed Ly the & Point Pis Located ot a Goussiown usface We 4 = MR. Azitance + prove 0 Aesonding te Gourwsl, throeoramn dong Aheoigit Dive of | net flux, ob. ange - ge.ds- 4% sw & & The cylindrical Gaussian susfoce is divided Jivbe & pants # I,D ond Tl ar shoun. . SSS a ds. fea fea + [Pk a =z nD m8.48. Jess. low) Efds = ArAL "4 44 Constant en cused surface “Ee Ah cyttnden). Ex Qik = Ag eo ee AN eo Foem the Pique oH is chean that net edectric Bats at any polit f the Gaussian oylinder tras a dinecKon Ponperdicutan to the tclern outwards, oe = rd. vn aMEor Geragh shows Variation sh = : © wath dinlance 9. * Qs Fea ie ald tuo ae 2 0 sony Anfinie plane sheet. go io contcting ane shat baneg tye ee o's Tt Ws required the Bacto fald Intensity at a peint OSAurpace with area ef foce 's) A co Gauss’ Lavo ceed «4 nek Beas bE.ds- 4. ws & €& The Gousstan ace is divided inte SiGe ne into tree paris , $€.ds- Jed 4 fe Ke [eR . ws x T m Eo (ov) r vs - JEdscos4o* + J Edgcesn® + [edscoas? Eo = m m ® co = lakde eo = GES a REo So slectric field dus Te an infinite plata shed of Charge ls lundependat of distance of, pour of obseswvatiion . Aue Dike a Lex as shown Leth Aides lof the sheet. Chor enclosed the suspace We Ye TS. The cyindrical surface ls the Grausstan . at lds Dv Els comtauten tand ET] | Mm 1ol GerapR APriows Vasodilan = of Cvs distance ‘er’. — 7 Bain spherical shall | la) At a point oubside sheer : . aw sun beth on the rey cine ta anes bone ds suguired. te fird the Intensity at a point 'P! of -distamce ‘2! from Bre contre of thre shh (7>2D. A Gaussian sphere of ius in' le draun with '0’as contre (ss). oo i" \ Z According te Gauss Lous, net fer gé@.ds- 4 (rd bedseoo® = 4 &o Eo (6) de ds=% (or) EGdc- 4% -------@ &> Eo aeLD: Eis comtant on ‘S'] o. Ex €o + ec. my eer (by Aba peint on the surface of tre vhele : TEMP’ Les on the surface constden a Gaussian pwrface that is idenbleol Te the shell to dimension . a 2 Ad i Na 3 ek Net Hux Poy Games. Rous, €. dg =4% (sr) @Edscoso” = fede a tw Gessenc 4 Eo beds - 4 [m Eddes 4 ) ée Eo EE ds constant on S] EX 4nR>= % bo we ad qnéor*(2) com also Be Lwritter ac follows, ex4ane> = Tx gn o ee 8 pe P14 (c) At a point tnside : en, Ge. de As there ds no change within she shell, be. ds -=0 (x) E=0ELECTROSTATIC POTENTIAL AND CAPACITANCE Nteopuction : i Consider on electrostatic pisld E due cto a Phaced ot The vonigin. We being ae test sande he nom point R So the potut Pt us suepulstue force. So the roork done Ly the external Fext => External force a Fe =E~ectric force (due ew ~ -{ Fe. du Ae electric field) P ~ change (G2) The ST unit Ww volt (VY and ive Sle Tt bo collar quouitiey. Work done por annie positive tent chonge ly or en Ayorce Jun beirging oO unlk positive chrovrge dprom infinity Te o point is squat te the potential (Vv)at thak point: We ~[Wee] ree qe whew, [Wooletec ie the work done Ly the electric fitd on a chonged panticte as that pontcele Mewes in from infinity 1 0 point. A potentiat (V) com Le positives negative on gero, olepending on She «ign ound. magnitudes ef 4 and We. Evecteostatic Potentiac ‘Due To A Point CHarcit + bet P Le the potnt at a distance 1 from the The electric potential at oa point P is the omeurt of werk done Jin conning. o unit positive chonge from © Te P. As w0k done is indeperdent of Ahe path » woe choose 0 conventent pat the sradio£ orceeleration. het A 2e an intermediate petnt von tris patos where OA = me.Aw F_'_. & , adong on = wy Sroatt waernk dene Ln roving the lange Hvrough a distance doe fem Ato B. AW = Fda = Fdeccosigo’= - Fax [ev cos 1g0° = -1] —a) Aw: —Faw ee eae ee eee cae positive Con Le neghected . a atent[is a au DAs | + 22 cose) * Bee ae cove) ‘Ta Simtlantys so 7 x( . 2 cose \ le Pating thane aes By OY, we ebtain ve 2 [x ('- Beene) 3 “( Qa il ~+/142acese) 2 4AM Ee ma i ing Binomial theorem [(1+%)"= lene, 2 <6!) toe abba “ “aall worse) (1 Secon] - + Zee 1+ Feove] pee ie- w& (2222 =~ L% Aacese AMéon AMtEo™ | v= peose Le pe 4qxaa] | AM Eor* Az, peose =p, ater Bis unit Veckon abong the position vector oe- AL. Electrostatic. potentiol at P due te a Prout dipole (ed ) Le ve pe AM Eon” | The potential depends Jt net wor position vector o, Lut also on the ange Letoeen the position Vector s- The electric Potential due Ts an electric Aipete at peint P vosies Ln ott Aquane of 1, Lie, the istonce of, point P prem the centre of he dipole . © On the dipele axis © = 0° &L TL nVe bt Pp ATIEos™ 4 a QO- + - -0. ~ +- Axis D P i——— aa —— Positte sign for © = 0° and negative fe fon © = TL © On the equatorial plane =n a a Cos® = cos TL =0 aP \ —— LN, Lie., electrostatic potential ak anny point on the Etectesstanic Fotenmar Exeoay Or A Syetem / /\ 4 Or Crences Electrostatic potential a int ere geen yy ten tt done in Srnlnging the diprert changer Ab Brain Prespective petitions frem infiniters forge routrat Atponations+ Electrostatic Porential €: of oe Three Potint Changes t we seen“ het we now consider a a Aipstern Of these point changes §) fe ard Ja hotteg, poston tact Ay As and He i igin. a * nae o from ovgin Ys f%To tring Hy fievse from Infinite Be 1, No Worle 1s sugpired Lecouse when we Laing chorge 7) fem Anfinity Te 0 partioulan Localion where potential is Ber: ee Wi=z0 The work done tin Letingting qo pron infinity to perition a ix eet inftety Wa = Gav(va) Woe tage ANEe stig Bandqs produce a petinnal urtict at any potnt Pin given ty, Mas 2 [+ te 4néo ls Fas Workdone In Letinging 9s) Ne is ap times Vizo at wm a Ws> 4s Vijalvs)= 1/43 4 4243 Anes ( 8 Pas The total werkdone in assem bing Changes ot Are given Locations (Anal Lp the potential tneng | Ph the ayster) is obtained Ly adding the woedone U = Wit WatWs = 0+ tl UG 4 1 (282+ a AME Mia ATEol Hi Aas wba 4 4 492 + G4 wie cams tsa ATES Tie nesurt can also Le expressed din summation foun as b= [a = S #44] AMEo tot Te aij Dare te the comerwabiue nature of olectrostatic jorce » “tre value of, U ie independent -0f the rrannen ir suhich thre configuiation is assemtted . Forennian Eneraiy In An Externar Fle Fre UW) Potential Enengy ob & Lingle Charge bn External Freadd 3 Potentiot energy of a sigh change gq.) at a point Luith postition vectors ttn an extesunrat frerd = aV(~) whores V[or) is the polential ot the -potnt dus Lo Axbernal electric field E- 0) Potentiad Energy of a Systenn of Aus charges dn an Externar Hietd + Ue Qe (4 qeeV (v2) + AF ATEe Tia ashore, G14 2 = too peinis changes ot posiic'en Vectors #11 ond Ho prospectively V(ai) = potentiolat 1 due te Uhe external field vss) = potential at %2duse to Thre external field 4fotentiac. Enerey Or A Dirove_ In AN Externe eon : Comsiden vo. dipele wuith changer +4 and -9 placed Lin a aniforun external eectete field as shown Jin the figure + In 0 unifoun -electaic Held, the Aipele -experierces roferce, Lut experiences a Sorgue(T) given 24 T= Pxt This torque soll tend te state the dipole Suppose an external torque Text le appeied te the dipole - So that, it sotates foun Oc Le ©: swith sespect ke The ebectoulc. Ateld CE). —_« Dipole in Muiform extenmrod prepa Une amount of wonkdone by the external torque We Pre (ede Go- [Pre strode Ge We PE [-cose J: W = PE (ces®o - cos6:) Ve werk done Wits stoned as the potential energy A, the systenr, Thersfore, the potentiol energy Ue) = PE (cos®e - cose) Spector Case 3 © When the dipole ts initionty aligned along the electric Aled , 1:2) 8 = 0° and we drove te seb Ae ok ought, Owith Ey Ley Or =e. . We -PE (cos® - ceso®) Ws —PE (cose - 1) This work done is stoud tn the dipole in the foun of potential energy: | (When the dipole ix initlady at night Ine, ie, 01 = Q0° ard we have Ts set ib at ange © swith E, ive, 62-0 "We -pE (coc - cosdo*) = -PEcoe . Potential tnenqy of dipole, 0 = W= -PpEcose U=-PE Olniousty » petentiol energy of an electric dipete te o sealon Quantity Ib le measuned in joule. IoEquireten Tiny Sveraces : ¢ Tt is a surface walt a constant value of petntiol at all polnis on the surface. Fon a singte change potential is ve ka So if ris constant ) Vis constant - en sunfaces, af a airefe change one concentricNo work is done in moving dhe test change from one point Ie another on an tqulpotentiot Aunpace + Tp AL nw the smate distance -on the “quipoentin£ surface throug wuttoh o Unie pe ae dw: Bak Dur dw-o P.di-0o kur E#O ALtO "C050 = FD" Eley ab The okectuic field Eis aloays nounal te the Revation Berween Evectare re Fier> Ano Forenrriae + Consider tw. equipotential ausfaces A and B Apoced Clery o% shou, The potential A is V and that + Bas Vidv. der us Ahe perpendicular distance Antuowr the tive equipotentiol surfaces. When o sanik positive 4s taken along tris distance from Bto A The electric field. Wea = Va- Va = t+dvu P.dy -- dv Le = ig0°] | 1gan For uniform field E.da = adv € [lan - Jav EX =v = -dy iel- | a] Electric fiskd isin the dtruction in uvtich the potentio£ clecreases + Magnitude of electric feta is Giver Ly die magnitude ef -potentiat grodient . For a given dv, 80 the eqyipotintiol surfaces dund fosr opont Jn the neaton of weal stechrie tata - Fotenrtiac Enteay In Ax Externat Fleum : The potential energy do a hosp q at pt. Pin the external field as qv. Potential energy of o aystem of Achonges qi and {> Located at 91 and mo sold suspeck te mome ovigin, Ys Wor) is the sro done din Detinging 41 fem co te or Wark dene Jun Letnging ga from ce te A. Ww, Yo V(rs) + YF 4m Eerievs Potentia£ Energy = qivlritqovloa)+ Vd ATES Tia Foopennies Or Convertors | & Ak the susrtoce of wo conductor He slectnle field must De renmal te Dre sustorce , 3 The interior of a conductor can boave no sxcers change in the static condin'en . By Gauss Louw, Covalder ony small velure : > Ge. da ~ gy [Becosse alectric ptetd Insider > be cenducter is zero] ge da =O me Y=° 4. The 2hecterostatic potentiad is constant Hrrvoughout the volume of the conductor ound Jrar the some value on Le purtace. aoSunfoce of, __ the conductts To find te electric fetd at ary point P, on We choose a pitt Lex (a short cuts Jaro Goumsiown sustace. The pile Lex i partly a bbe ond pp ouside the surface of the con / Tt has a Arnall azo of eros 4 te, A& and mepigiote hetghe Inside Bre sungace Ets 0, Ontsicle » tre field Ie novmal to the surpace . The r i , : é ; Outstole cross Aection Bay resting Q , EAS 26 2 q d = 8.4 a 7 EAS T=4 TAS _ EAg a & E = T/2. Pomanty cutwandsEvectrostatic GHiet DING ! Electaic field Inside thre conthy of the conductor is Zero Whatever Le the size ard shape of tHe ard the abectite fEetd In whith. ib rray Pe pleced (Dingrann nefer text Lock pg: 40) Thin pack im vscd rave wo change Commies They one caaastpeed thee © Polar © New - polo Nen potavannd Potarr molecules 3 @ New polar : Centers of positive and negative changes coincide. The molecule has no dipole moment. Ee 3 Oxygen, nibogen . «Polar t Lt is oneinuttolh the centres of posticive aud negative changes ore separated and Une role cles (@) Polar molecules (a) Non-polar molecules A diclectrle dA diddectric saith polon molecutes also develop a net dipole memant . In the absence of On 2x ternal electric Pteld., thre differork dipoles ane oriented Arordomly dive to thermal motion. So the total dipole Mement is 0. Whur an external flerd ts applied, the individual moments Tend te align with the field. So thou iso net dipole moment which is thse, Atscotion of tre field ard tre dielectric Ly said te Le Polarised. The dipete moment per uudit volume is called polorisation and is denoted Pp. A steckan dietectste stat ts placed tin an unidorm eectric Le as shoum. Consider a 4rall volume Mement AV. eau innide the volume element the net te 0. This te leecause the post tive change of the first dipole ts lose De the we of the Other dipole. But at the edges the positive ends of thre dipole remain wneubralised and thre negative charges at the Left susface . The tunbalanced changes produce an wectoic fiebd In the Aiclecbute . Therdores tre total feetd Inside the disdoctric is reduced. be > H co, 6 /& Some examples of polar and non-polar molecules,Capacitan ce | A capacitor ds a system of dco conductors separated Ly an Insulator. Let Q Le the charge on the plates of tne capaclton: Ure potenttiol difference Vis proportional te Qs Quay Q =cv where C is capacitance Capacitance C depends on SGeomericol configuration (Shope sige ond the Aeporation of, tue Aipstem of uo Conductors) © Natwee of insutator ST unit of capacitance : Fanad (F) | Forad = lopudunt- | wot Thee de a Limit te dhe amount of that Low Le stored on & giver capacitor. Ae sire quantity mf; charge Ireneasess electra petd plates ineseases ond PD also increases The Chases “tant Baking | Thi i known a Leaking of changes.Devecteic (STRENGTH : The maximum electric feta thar oa dielectric medium can wittstond witheut Leuokdoun i% called diekectaic atrengin- _Poraccer Poste _Crpaertor : Te comsinte of treo ttn conducting plater each of | one & one hata pasvallid Te each tthe. ob & diatonce posit. The Plates ort Separated Ly lnsulac® 9 medium Like air on paper: lt o Leite anal change dawily of place T and * ~o’ of poe Tr. We arsume thd d < Ot Qo 4+ Qa CVs CIV+CoVtCaV C= CitCatCa Co 2fhectinve capacitance Eneray Stozen IN A Capacrtor : Desig chasiging Let ‘q) Le the change. on ie plates | Of, the capacitor ond V' Be the pot: Acpt. Retro the plates of the capacitor. The workdone din giving on iz dw = vidq > Adg — 6% Apacitoures Of capacitor. the | Tom wontons Bn gtaing: 2 toe a? space Pa ye LTT The de atored as pots erenay 1 O2 @> Buc @=cv Ve ac cv 4 AEs, Ed oa = 1 €oe> Ad Cs Tota Exerey Sropep IN_A Compination Or Capacitors t Totat Energy stored in series or parallel combination Stata Fe ol Copocitors . Tn sorter eral Q— Constont }Total Enenay vb et @ 2 Q@, 1b ®t 2 Cs be Qfay tat 2 (Cr Co ca (Ee yw aQcr QC AQC2a UV =i4+0a4Va Th porattet combinatior V-¥ constant | Vet coye a oP ov? (cr Co+ Cs) 2 Lowey 1 2 4 . ay +t cant, 1 | 2 a CNM Cav U= Uj+U0a403 | Common Potentiat : “When dive capactton : ie ome conasted Bio eondunering wore, then flows fev capacitor of digi wr potential te the A | ok Lower potential. Unie pour of changes continue | phen trete potential Lecomes equols Aris quot | prtential is called Common potentias « Common potential ,\V = CN + Cove shore, epee ane Copacitis awe e { Changed Te potentials Vi and Vo. sespeotiuely. 3°Lee, Common potentiat a Totakchonge Tetat capacity CiVi4CaVea = CiVtCon OF CW —-C1V = CaV-CoNo trey change Lok Ly one capacitor = Change gotred capacitor Lost Or Enerey On SHaring CHarces: Whew do Bpacitors ane Cennected LE each | Other, Arey shore » thee thes acquire a Commen Potential. On showing charges, tere ts alroaiys owe oss of energy. Hovowien ) Lobat change of te Aryster ermal pe conseied » Consider tsp copactions rowing capacttonces Ci, Ca ond potentials Vy Vo mespectiuely » Then, Lchere tre two capacitors one connected together, tre total tnengy stored tn the ture copacttors » Ds Uta = RON + dave —— 0) When the two capacitors ane Connected together » otal change on the capacitor, Ha Wr Yr = Crit CoVa, Torar Capacitance 4 He tuo capaciterss C= Ci+Co | o, Setar the tuso Bt oe energy of capac bons paften trey connected, 692s (Ci+Caved? Dred 5 ac 2 Citce utSubbracting Eq: (N) from &q + ft) » we qe O-O'= [Lows oyy\ —- b Git Cove)? (a = ) 3 (o1+es) CPR 4 CC a Wi + CiCaNe™ 4 Cx*ya*— (C14 Cave)® aw (Cr+ C2) C102 (WA 4VF — QVived Q(C1+Ca) Av = Cio (Ve-ve>* | Q(C1+C2) | Since) U-U' is posiecue > there de abvoays a Lose of | dogerner » An Aetorm of deot radiation dure te | clectrte cwvnent utibte changing and electromagnetic Acris OF Seep Poisrs : | Winer a spherical conductor of cradius SL Comes a change 7) Ht surface density As given fey T = Change 2 4 Arex A4Na> tor a pointed ands 1 is Ney Wey Amail) trorebore is a positive quantity.CURRENT ELECTRICITY eovititubes on electric vvent. Ip a chr DQ passes -Hureugh an osteo bn tine te t+ Ot, The tweunt I at time aA in vgn. dng T+ lim AQ, dQ bt>o Ak Ob df cwunt electricity is shady , then r= kh ST Unit? Ampou - Tf one coulumt of change wonresses 01 wren in ene second, then the \Azicso' Orm's Law The cust powing vo. conductor Us dinectby ce Te the potential olipperence] flo -of, changes Hough Le - GT Anit of sesistance ! ofr (2) Stuce R= V/r, susistonce us said tm Le IP if 1A corvrent fows va conductor uirrose Lrrds ane Maintained at 2 potential difference of Iv. tao = IVA! Faetor’s Arrecting Resistance : \. Length (Ra DS a} Area of cross acotion (Ro '/n) 3 Nature of material -Raet/y R= PL | where P is constant of A Leboulty vor sae pesiztamce of the material of the conductor . Tt depends von che mate of the wraterial vond on Sarmperotio Lut is independint of Us size on Ahape| Units OF Resistivity br): Resistdut aw 5 be at athe veeend, by ondunctan oy at eenaine af that motentol.Corrent Density (5) : Cunnent dinsity Tot ing point Je Ws alefined vas a wit area Held nownal Te the nection ».f The plow of Change at Hat point. Tr direction T= 2/a Sy osve vector vmakes ong © wilh the curvent duction, Ian I= Jrcose = 7.4 Thus ewwent ds 0 Acalan quality whereas Leu ent denslly Vector. Linit vol cunment density Js Ar? Consvetance (Gi) t Conductance wf A conductor ib the ease swith which changes flow through it . Tt is equal t Khe neciprocal of ils sesistance . G='/R Unit = ohm" emo or elemer(s) Conrpvetivity (> : | Ta seclprocal of musinbidiy Of material is eatted Ue cond w= '/p Unit tobe ns-' (or) mem! (ov) Sr-tNi CommerciaL Resistors: 1. Wire Lound seststors | monganin» constantan Or nichstome. are used. MV) pelotively Lnvsersttive JS Teperotune 2. Carbon mesistors | mace from mixture of var Black ond nesin Linden 2rlosed Jn a ceramic or plastic jacket . dv: Monge of voles poritte » cheap, compact . Cou Resigtors ! The fiert doo bonds indicate the first two Alguificont numbers. The thind Land indicates Bre power of ten asa multiplier The fourth Rromd indicates the tolerance. Colour Nuwpber Multiption Tekestance (*/*) Bracke ° ! —_ B Il lol Ded 2 (o> Onange 3 | 10% Vebleovs 4 | \o* Green 5 | lo Boue G | lo® Vieder 7 | lo" ere 2 fo te Whir ci 104 Got | lor! 5 Biluer tom to No colour | - | 20 4Eq: Sk the colours are yotlouss violet, Leon and goed» dhen nesistonce Us RAX1O7'O + By. Caeeiees Or CuRReNT : \. Solids } electrons thn metals uvtite electsons and Anoles in srumiconductors. a Liquids : positive and negative lens 3. Gases : postitue ions , negative dons and xlectsrons Deiet Verocity An Ant RELAKATION Time + meee ho- Oe et | fied» dese alestnons ane bea a | motion dus tle theniad energy - Heovoevert y thone ie | Mae re uae direction of motion. a hy, Ds, a, Thy. Um ane the Hondom udlocittes | 1h Nueckrones Huon oounage Vabootley of stectrons oll Le, = (4 Tit..... +0) /N = 0 Tas thane is ne mak plow ah charge dn ony dintcrion. Tn the presence tf on exbonat fied © Zach tecknon experiences wo force ~eE” in the oS gee tye at we eel Whene no is the mass of an electron. Ae the electron metal Lows on -otiren electrons of thre metal. Biron dhe caltinions an elechen gains 2 vi in a dinzction opposite te ©. a Svelocity Lots venty for a short poled of Time. velodity Wire a+ oT Similorky velocities of the wthen Lectrons vill be, Va = Wn + A To .... Woe Unt QIN Thre average velocity Ua = (4 ++ 08) /N = [(@? + at) + (i+ Sta) 4... + (RA RIN)] [N = (Ur+ Ob 4 -..t a) /N 4&(TitTat--- +TN)/N = O04 aT were T= (Ti+ Tat. +IN) /N ds the werage ti an tine Retro £100 cottistons, The average dime thot lapses Leboeen two successive time . The welocity gained Ly on Pectron duning this time is Va = OT =-eFT/m Vd ds cabled athe dnife vetocltey aaa mt Prue rlectrons of 2 conductor in the eppostte pea.Revtation Between Current An / let a potential difference VLE appeted acer o conductor of Lengin 2 amd of wnriforir cross Aection. A. The electric field E set up inside the Aovductor ds given Ly E=V/2 Under the inftuence of tre field Es free electrons chegin Te Arif Be eppons. dination. salts te ownage Anift velocihy Va Let the number of, oectrons per unit volume Len. let chonge on an electron Le e- Tren unter of electrons in Length 2 of the conductor =n x valume of Conductor = KAL. Total change contained tn length 2 of the conductor bay = mar Age the electrons which enter the conducter at the sight end volil pass terough the conductor at the Rept end in time += LI va. “Covent T= A = NAL 2 neAva + five » T= neAva Current Density (pe at‘Depvction Or Onis Law : Whin .o potential diffrence V is applied across a conductor of Longin £5 the doigt velocity Jn Lown -of Vis given by Vd = CET [me Ty the aren af cross Section of the conductor through tht conductor voll be T= neAlah | zenaeVT[me (or) V/T = ML/ne>TA Ak a fixed temperature the quantiiies m,L,n, er T ond A all dave constant values for a given Conductor: SN[D = a ecomstant, 2 the resistance (which is chins Lave) - Thus R= mL[nerTta Resistivity : The susistance R of a conductor of 2, oven of Cross Atctton A ond resistivity, Cis gon Oy R= PLIp But Qe m2 [ne2 TA »Pe m |[ne>T P depends on» re Electron density of the conductor (1) 2. Rekaxation time (T)Microscopic Foam Or Onn's Law + Flor an electron, 4.2 -€ and Va += -ePT m . qe ngVvae = nt-e) (21) 2 nereL m Bur ner>T = lo sag ww 8 Jac? ME- Mosiurty OF CHarsié Canciers : | Mate Pb a. charge Cossler de the doift velocity | cgquined Ly Lc tna sult electric field» Ttw | , Me lvdl/e = eT/m S.T anit! m/v. TEMPERATURE E “DEPENDANCE Or Resistivity ‘ Crm|nemt Is Metals 3 for metals n is not dependant on temperature Te ony apprectalte 2xtent Lut as mune dncneases , the thermal specd of; fue electrons Inewases ond alse the vibration ompeitude of metal Lens increases. Thus the free electrons collide more frequentty wollte. he metal Lons > The mean stelaration tine T decreases, Hence sestotivity Increases Resistivity ? at temperature THs giver P= 0 [r+ w(t ra] met where Co ie the sestativkty ot tempera Te 9and % is the coefficient of sesistiuity: ve x = (P- Co) | Po (T-T0) Thus the cosifictent of susistiuity of & may Le The unit X45 °C-!, For metals % is tve- As R- PLlA Ree RoLi+ K(t-o] = Re li4 xe] Whee Re = sesistance at t°c Re = stesintonce at O° t= subse tin temperature as Tnsukatere and Semiconductors 1 Tn inwlators ond ‘semiconductors , the number . ok fru electrons Lncrtaser tx volth Une Jncrense din temperate This tnoase more than compensates ony decrease Ln - So far Aucl matertals, conductivity Increases on sresistietty decreasesLuartation OF Onm’s Law: ty Obmic Conductors : Those whith Ohm's ~ Rowe. V- graph fon wehmic conductors is a straight Line passing Hvrough ontgin. |¢ | a +t n Qi Non- ofa conductors : These donot obey Olin ie Low: Now - ohmic Altuations may *f fottarwing types : @)V-L graph dees not pase onlgin ayy- 2 graph slotionship de non - linear. (W) I depends on sigin of V for some abselute Voli. of V. | (WY -L sutationsnip de men - unique. | oe : a + n Pron: Qireag vgn Fi | ; | tay | 4 Ts } | | if, \ | | ; , 8 6 7 —¥ I —— >Vv Pot iiyy (ob tiafarn. connenbeV- (yp nae Somowete (ame ree Ca nistance o96) yN-E WoT groph doesnt pars no ian qroptavatonge tinted tere wp Tee att1 (me) ” Tunckion diode (wen - Uinear value of T depends on sign of V) ComBin ation OF Restore : By Oln's Law, potinttol drops accors the swsistors one, VizTRi: , Vo =TRe » Va=IRa Th Res the equivalent seristance then Ve IRs tli Ne Akso Ve VitVo4Va ae Vie vate Va | STRe = IRD Ro +TRs - | 1 Ree RitRot+Ra | i | lor 1 susistancesy RA =RItRad---4 Pn VY Equivalent resistance = Sum Bw One —WWy— AL individual swsintomces. |YW Porter Combination : Internat Resisrance O Or A Ceu : When vo cele ds dn a circuit, cunvent flours tn the ustres ferom +ve teuninal tovearils the ne | terminel. But instole Ane celd, tn the tkecboliyta ; tue tows flow from the Lora te che Aighen potantinr, of current inside He cell. The seristonce offered dhe okectrolyte ab o cobs collect inkernal sesistonce af the cell.+ Temperature of the electrolyte. Teeminac Forentian “Dirrerence : The potential cbrep actors tie tesuminals of % cele dhe o cuvunt ls being drawn from it is called Ue keuninal potential diffence (v)- Retation Between €Me ‘€! AND TERMINAL let a cetk of errf €& ond Internal resistance s Le connected Ts van external suststance 2» Let o. ewvent T flour thvvougie thie cicrewik. Lote a WW Emp E= semen Ly dhe colt ie Atreuit Also, | Emge E = awerkclone in caring a snik change from At B thro! extounal sUesistance(e) + uprkdene in Fm tunik change fever Bi A ngein: etmek soststatce (or) @=vev'By obs Law, VeIe omd V'> In “@ 2IR+ In = I(R+H) So, jT= € | R+or — A&o, V= Ie ve Ve ER LR | Also, Vz e-y' = €- IR lve e@-24] “Ws E-v e-vio. E-Ve I Special Cases : OY Whenr cel ie in open cincuit » I =O Ten Vepen = €. Thus, Pid across the Leouminal Of 2 col ue aquol Te ute emf ache no cuvwrent dn Being | drown from the colt - | Or) Wier cet te in closed. cht» T is Leing drawn. | eo DTxo vee (“vse e-a7) Thus pid across the terminals of a ce ina osed cht ds always tess than tt ong - Gn) Max. cuwment that can Le Aran from a cepe ie for R=O0 5 Go Tnoax = re aComminietion OF Cetus ' DL Cells tn Series t Lot Tote the cunt dtivrorigh the seer combination of Hoo cells Of mf &1 ancl Ba wollte ae eee Pi aud Ma especial: oise ee = —- + tm a eee Ler Va, Ve ond Ve Le the potentials ot points As B onde mesp. pid across the troo celts will Le, Vae = Va-Ve= €:-Iam Vac =Va_- Vez E2-Tan New Vac Ws the prd ccross the series Combdiatar| Vac = Va-Ve = (Va-Va dt (ve- Ve) = (€1-Tai)+ (€2-Ta.) lov) Vac = (€1+€2)- 2 (1+ 12) —O the equivalent cele » Vac = beq- Ineg, —@ from D ond @ Eeq = Ett la and Heq = S14 He Th gen, fe nm colts, Hono Jatebreat clin, =E2 =Ex= En is Ceqy = C1+€ar---+Orn Ceqr eit ever E=n€ ii. Pegs Hit Hate. + Ato Aeqe H¢ Mt M$ HOM Tp one of Bhe cells (say of emf eo) t+ Connected Bre other woay ctoundYD eq = 61 -Catlat--. + En Ti) meq? Sup tat Hat 9+ ton Poratteh bet Ti and To fe the cwvuents Leaving the Ve. Lkectmodes of the cells and sesult Ln ov current I! &: se coy ar Ke =z — 1 A << ° ema =~ RI é Be e DYKE, ain Ne pen, an Fe Ls TitTo Nevo ) Prd CV) Letrocen the teuninals of Both certs must Le tome (" they ane Parcarece) So, V= Vei-Veo= €r-Tiai =) t= E,-v war and W= Ver - Veo > €2-Ta%e =) Ta. el iy Aa vo Tos €1-V4 €n -v Pu Ae 2 ( Ea Eo a+ t te Cat Sa) YR am) ® prem the equivelent cell 1s Eeq -v © rt Peg From © and © |