ELECTROSTATICS. JEE-Physics ELECTRIC CHARGE

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1 J-Physics LCTIC CHAG LCTOSTATICS Chge is the popety ssocited with mtte due to which it poduces nd epeiences electicl nd mgnetic effects. The ecess o deficiency of electons in body gives the concept of chge. Types of chge : (i) Positive chge : It is the deficiency of electons s comped to poton. (i) Negtive chge : It is the ecess of electons s comped to poton. SI unit of chge : mpee second i.e. Coulomb Dimension : [A T] Pcticl units of chge e mpee hou (6 C) nd fdy ( 965 C) Millikn clculted unt of chge by 'Highest common fcto' (H.C.F.) method nd it is eul to chge of electon. C 9 stt coulomb, bsolute - coulomb C, Fdy 965 C. NOD6 ()\Dt\4\Kot\J-Advnced\SMP\Phy\Unit-7\lectosttics\nglish\Theoy.p65 SPCIFIC POPTIS OF CHAG Chge is scl untity : It epesents ecess o deficiency of electons. Chge is tnsfeble : If chged body is put in contct with n nothe body, then chge cn be tnsfeed to nothe body. Chge is lwys ssocited with mss Chge cnnot eist without mss though mss cn eist without chge. So the pesence of chge itself is convincing poof of eistence of mss. In chging, the mss of body chnges. When body is given positive chge, its mss deceses. When body is given negtive chge, its mss inceses. Chge is untised The untiztion of electic chge is the popety by vitue of which ll fee chges e integl multiple of bsic unit of chge epesented by e. Thus chge of body is lwys given by ne n positive intege o negtive intege The untum of chge is the chge tht n electon o poton cies. Note : Chge on poton ( ) chge on n electon.6 9 C Chge is conseved In n isolted system, totl chge does not chnge with time, though individul chge my chnge i.e. chge cn neithe be ceted no destoyed. Consevtion of chge is lso found to hold good in ll types of ections eithe chemicl (tomic) o nucle. No eceptions to the ule hve eve been found. Chge is invint Chge is independent of fme of efeence. i.e. chge on body does not chnge whteve be its speed. Acceleted chge dites enegy v (i.e. t est) poduces only (electic field) Attction epulsion v constnt poduces both nd B (mgnetic field) but no dition Simil chges epel ech othe while dissimil ttct v constnt (i.e. time vying) poduces, B nd dites enegy

2 J-Physics MTHODS OF CHAGING Fiction: If we ub one body with othe body, electons e tnsfeed fom one body to the othe. Tnsfe of electons tkes plces fom lowe wok function body to highe wok function body. Positive chge Negtive chge Glss od Silk cloth Woollen cloth ubbe shoes, Ambe, Plstic objects Dy hi Comb Flnnel o ct skin bonite od Note : Clouds become chged by fiction lectosttic induction If chged body is bought ne metllic neutl body, the chged body will ttct opposite chge nd epel simil chge pesent in the neutl body. As esult of this one side of the neutl body becomes negtive while the othe positive, this pocess is clled 'electosttic induction'. Chging body by induction (in fou successive steps) chging body ' chging '-ve chging '-ve '-ve body body chged body is bought ne unchged body step- unchged body is connected to eth step- unchged body is disconnected fom the eth step- chging body is emoved step-4 Some impotnt fcts ssocited with induction- (i) (ii) (iii) Inducing body neithe gins no loses chge The ntue of induced chge is lwys opposite to tht of inducing chge Induction tkes plce only in bodies (eithe conducting o non conducting) nd not in pticles. Conduction The pocess of tnsfe of chge by contct of two bodies is known s conduction. If chged body is put in contct with unchged body, the unchged body becomes chged due to tnsfe of electons fom one body to the othe. The chged body loses some of its chge (which is eul to the chge gined by the unchged body) The chge gined by the unchged body is lwys lesse thn initil chge pesent on the chged body. Flow of chge depends upon the potentil diffeence of both bodies. [No potentil diffeence No conduction]. Positive chge flows fom highe potentil to lowe potentil, while negtive chge flows fom lowe to highe potentil. NOD6 ()\Dt\4\Kot\J-Advnced\SMP\Phy\Unit-7\lectosttics\nglish\Theoy.p65

3 J-Physics Chge diffes fom mss in the following sense. (i) GOLDN KY POINTS In SI units, chge is deived physicl untity while mss is fundmentl untity. (ii) Chge is lwys conseved but mss is not (Note : Mss cn be conveted into enegy mc (iii) The unt of chge is electonic chge while tht of mss it is yet not cle. (iv) Fo moving chged body mss inceses while chge emins constnt. Tue test of electifiction is epulsion nd not ttction s ttction my lso tke plce between chged nd n unchged body nd lso between two similly chged bodies. Fo non eltivistic (i.e. v << c) chged pticle, specific chge m constnt Fo eltivistic chged pticle deceses s v inceses, whee v is speed of chged body. m m ple When piece of polythene is ubbed with wool, chge of 7 C is developed on polythene. Wht is the mount of mss, which is tnsfeed to polythene. Fom ne, So, the numbe of electons tnsfeed n e m ple Now mss of tnsfeed electons n mss of one electon kg pticles (Nuclei of helium) pe second flls on neutl sphee, clculte time in which sphee gets chged by C. Numbe of pticles flling in t second t Chge on pticle e, So chge incident in time t ( t).(e) Given chge is C 6 ( t).(e) 8 t 6.5s 9.6 NOD6 ()\Dt\4\Kot\J-Advnced\SMP\Phy\Unit-7\lectosttics\nglish\Theoy.p65 COULOMB' S LAW The electosttic foce of intection between two sttic point electic chges is diectly popotionl to the poduct of the chges, invesely popotionl to the sue of the distnce between them nd cts long the stight line joining the two chges. If two points chges nd septed by distnce. Let F be the electosttic foce between these two chges. Accoding to Coulomb's lw. F nd F e k F F on F on 9 Nm whee k 9 4 C F on F on k coulomb's constnt o electosttic foce constnt

4 J-Physics Coulomb' s lw in vecto fom F foce on due to k ˆ F F k F ˆ (hee ˆ is unit vecto fom to ) y Coulomb' s lw in tems of position vecto F k ( ) O Pinciple of supeposition The foce is two body intection, i.e., electicl foce between two point chges is independent of pesence o bsence of othe chges nd so the pinciple of supeposition is vlid, i.e., foce on chged pticle due to numbe of point chges is the esultnt of foces due to individul point chges, i.e., F F F... Note : Nucle foce is mny body intection, so pinciple of supeposition is not vlid in cse of nucle foce. When numbe of chges e intecting, the totl foce on given chge is vecto sum of the foces eeted on it by ll othe chges individully k k... k k F... in vecto fom F k i n i n 4 n i ˆ i i i SOM IMPOTANT POINTS GADING COULOMB S L AW AND LCTIC FOC The lw is bsed on physicl obsevtions nd is not logiclly deivble fom ny othe concept. peiments till tody evel its univesl ntue. The lw is nlogous to Newton s lw of gvittion : F G () (b) (c) (d) m m with the diffeence tht : lectic foce between chged pticles is much stonge thn gvittionl foce, i.e., F >>F G. This is why when both F nd F G e pesent, we neglect F G. lectic foce cn be ttctive o epulsive while gvittionl foce is lwys ttctive. lectic foce depends on the ntue of medium between the chges while gvittionl foce does not. The foce is n ction ection pi, i.e., the foce which one chge eets on the othe is eul nd opposite to the foce which the othe chge eets on the fist. The foce is consevtive, i.e., wok done in moving point chge once ound closed pth unde the ction of Coulomb s foce is zeo. The net Coulomb s foce on two chged pticles in fee spce nd in medium filled upto infinity e F 4 nd F' 4. So F F ' K, Dielectic constnt (K) of medium is numeiclly eul to the tio of the foce on two point chges in fee spce to tht in the medium filled upto infinity. The lw epesses the foce between two point chges t est. In pplying it to the cse of etended bodies of finite size ce should be tken in ssuming the whole chge of body to be concentted t its cente s this is tue only fo spheicl chged body, tht too fo etenl point. Although net electic foce on both pticles chnge in the pesence of dielectic but foce due to one chge pticle on nothe chge pticle does not depend on the medium between them. lectic foce between two chges does not depend on neighbouing chges. NOD6 ()\Dt\4\Kot\J-Advnced\SMP\Phy\Unit-7\lectosttics\nglish\Theoy.p65

5 m p l e S o l u t i o n J-Physics If the distnce between two eul point chges is doubled nd thei individul chges e lso doubled, wht would hppen to the foce between them? () () F 4...(i) Agin, F' 4 o F' () 4 So, the foce will emin the sme F m p l e S o l u t i o n A pticle of mss m cying chge ' ' is evolving ound fied chge ' ' in cicul pth of dius. Clculte the peiod of evolution. 4 4 m m T T ( 4 ) (4 m) o T 4 m whee is the vecto dwn fom souce chge is test chge. m p l e The foce of epulsion between two point chges is F, when these e t distnce of m. Now the point chges e eplced by sphees of dii 5 cm hving the chge sme s tht of point chges. The distnce between thei centes is m, then compe the foce of epulsion in two cses. In nd cse due to mutul epulsion, the effective distnce between thei cente of chges will be incesed (d' > d) so foce of epulsion deceses s F d d d' NOD6 ()\Dt\4\Kot\J-Advnced\SMP\Phy\Unit-7\lectosttics\nglish\Theoy.p65 UILIBIUM OF CHAGD PATICLS In euilibium net electic foce on evey chged pticle is zeo. The euilibium of chged pticle, unde the ction of Colombin foces lone cn neve be stble. uilibium of thee point chges (i) K K Two chges must be of like ntue s F K K (ii) Thid chge should be of unlike ntue s F Theefoe nd 5 ( )

6 J-Physics uilibium of symmetic geometicl point chged system Vlue of t cente fo which system to be in stte of euilibium (i) Fo euiltel tingle (ii) Fo sue uilibium of suspended point chge system ( ) 4 Fo euilibium position Tcos mg nd T sin F e If is smll then tn ~ sin k mg k tn k mg F e mg k mg mg Tcos T F e Tsin mg If whole set up is tken into n tificil stellite (g eff ~ ) then T F k e 4 8 m ple Fo the system shown in figue find fo which esultnt foce on is zeo. Fo foce on to be zeo, chges nd must be of opposite of ntue. Net ttction foce on due to chges epulsion foce on due to k F A F k ( ) Hence (,) (,) F A (,) FA F m ple Two identiclly chged sphees e suspended by stings of eul length. The stings mke n ngle of with ech othe. When suspended in liuid of density.8 g/cc the ngle emins sme. Wht is the dielectic constnt of liuid. Density of sphee.6 g/cc. 6 5 mg F NOD6 ()\Dt\4\Kot\J-Advnced\SMP\Phy\Unit-7\lectosttics\nglish\Theoy.p65

7 J-Physics When set up shown in figue is in i, we hve tn 5 F When set up is immesed in the medium s shown mg in figue, the electic foce epeienced by the bll will educe nd will be eul to F nd the effective gvittionl foce will become mg F Thus we hve tn 5 s mg s F mg s 5 F mg effmg m ple Given cube with point chges on ech of its vetices. Clculte the foce eeted on ny of the chges due to est of the 7 chges. The net foce on pticle A cn be given by vecto sum of foce epeienced by this pticle due to ll the othe k chges on vetices of the cube. Fo this we use vecto fom of coulomb's lw F Fom the figue the diffeent foces cting on A e given s F k k ˆ A F ˆ k j k A ˆ, F ˆ k i j k A ˆ ˆ ; F k i ˆ kˆ A 4 (,,) 4 (,,) Z (,,) NOD6 ()\Dt\4\Kot\J-Advnced\SMP\Phy\Unit-7\lectosttics\nglish\Theoy.p65 F k i ˆ, A 5 F ˆ k i j A 6 k j ˆ, ˆ F A 7 The net foce epeienced by A cn be given s F net F A F A F A F A F 4 A F 5 A F k 6 A 7 7 X 5 A (,,) (,,) ˆi ˆ j k ˆ 6 (,,) 7 (,,) y

8 J-Physics m p l e Five point chges, ech of vlue e plced on five vetices of egul hegon of side Lm. Wht is the mgnitude of the foce on point chge of vlue coulomb plced t the cente of the hegon? S o l u t i o n If thee hd been sith chge t the emining vete of hegon foce due to ll the si chges on t O will be zeo (s the foces due to individul chges will blnce ech othe). Now if f is the foce due to sith chge nd F due to emining five chges. F f F f F f 4 L 4 L LCTIC FILD In ode to eplin ction t distnce, i.e., foce without contct between chges it is ssumed tht chge o chge distibution poduces field in spce suounding it. So the egion suounding chge (o chge distibution) in which its electicl effects e peceptible is clled the electic field of the given chge. lectic field t point is chcteized eithe by vecto function of position clled electic intensity o by scl function of position V clled electic potentil. The electic field in cetin spce is lso visulized gphiclly in tems of lines of foce. So electic intensity, potentil nd lines of foce e diffeent wys of descibing the sme field. Intensity of electic field due to point chge lectic field intensity is defined s foce on unit test chge. Lim F k ˆ k Note : Test chge ( ) is fictitious chge tht eets no foce on neby chges but epeiences foces due to them. p Popeties of electic field intensity : (i) It is vecto untity. Its diection is the sme s the foce epeienced by positive chge. (ii) lectic field due to positive chge is lwys wy fom it while due to negtive chge lwys towds it. (iii) Its unit is Newton/coulomb (iv) Its dimensionl fomul is [MLT A ] (v) Foce on point chge is in the sme diection of electic field on positive chge nd in opposite diection on negtive chge. (vi) It obeys the supeposition pinciple tht is the field intensity point due to chge distibution is vecto sum of the field intensities due to individul chge 8 NOD6 ()\Dt\4\Kot\J-Advnced\SMP\Phy\Unit-7\lectosttics\nglish\Theoy.p65

9 J-Physics GOLDN KY POINTS Chged pticle in n electic field lwys epeiences foce eithe it is t est o in motion. In pesence of dielectic, electic field deceses nd becomes F test Test chge is lwys unit ( ve) chge. test chge times of its vlue in fee spce. If identicl chges e plced on ech vetices of egul polygon, then t cente zeo. LCTIC FILD INTNSITIS DU TO VAIOUS CHAG DISTIBUTIONS Due to discete distibution of chge Field poduced by chge distibution fo discete distibution: k By pinciple of supeposition intensity of electic field due to i th chge ip i i 4 i i p Net electic field due to whole distibution of chge p i i Continuous distibution of chge d Teting smll element s pticle 4 d P d Due to line chge distibution k ds Due to sufce chge distibution k dv Due to volume chge distibution k s v [ chge pe unit length] [ chge pe unit e] [ chge pe unit volume] lectic field stength t genel point due to unifomly chged od P NOD6 ()\Dt\4\Kot\J-Advnced\SMP\Phy\Unit-7\lectosttics\nglish\Theoy.p65 As shown in figue, if P is ny genel point in the suounding of od, to find electic field stength t P, we conside n element on od of length d t distnce fom point O s shown in figue. Now if d be the electic field t P due to the element, then kd d Hee d L d lectic field stength in diection due to d t P is kd d d sin sin L k sin Hee we hve tn nd d sec d Thus d k L sec d sec d k sin, Stength L sin d 9 d L dcos P O d dsin

10 J-Physics Net electic field stength due to d t point P in diection is d k L sin d k L cos k L cos cos Similly, electic field stength t point P due to d in y diection is d y d cos k d L cos Agin we hve tn nd d sec d. Thus we hve d y k cos L Net electic field stength t P due to d in y diection is sec d k sec L cos d y d y k L cos d k L sin k sin sin L Thus electic field t genel point in the suounding of unifomly chged od which subtend ngles nd t the two cones of od cn be given s in diection : k L cos lectic field due to unifomly chged ing Cse I : At its cente cos nd in y diection y k L sin sin A B O C D Hee by symmety we cn sy tht electic field stength t cente due to evey smll segment on ing is cncelled by the electic field t cente due to the segment ectly opposite to it. The electic field stength t cente due to segment AB is cncelled by tht due to segment CD. This net electic field stength t the cente of unifomly chged ing is Cse II : At point on the is of ing C d P d sin d cos d NOD6 ()\Dt\4\Kot\J-Advnced\SMP\Phy\Unit-7\lectosttics\nglish\Theoy.p65

11 J-Physics Hee we'll find the electic field stength t point P due to the ing which is situted t distnce fom the ing cente. Fo this we conside smll section of length d on ing s shown. The chge on this elementl section is d d [ totl chge of ing] Due to the element d, electic field stength d t point P cn be given s d Kd The component of this field stength d sin which is noml to the is of ing will be cncelled out due to the ing section opposite to d. The component of electic field stength long the is of ing d cos due to ll the sections will be dded up. Hence totl electic field stength t point P due to the ing is p d cos O kd k d O k d / O k / / k lectic field stength due to chged cicul c t its cente : Figue shows cicul c of dius which subtend n ngle t its cente. To find electic field stength t C, we conside pol segment on c of ngul width d t n ngle fom the ngul bisecto XY s shown. d d C dsin d dcos Y The length of elementl segment is d, the chge on this element d is d.d NOD6 ()\Dt\4\Kot\J-Advnced\SMP\Phy\Unit-7\lectosttics\nglish\Theoy.p65 Due to this d, electic field t cente of c C is given s kd d Now electic field component due to this segment dsin which is pependicul to the ngul bisecto gets cncelled out in integtion nd net electic field t cente will be long ngul bisecto which cn be clculted by integting dcos within limits fom to. Hence net electic field stength t cente C is / k cos d / / k cos d / k sin / / k sin sin C k sin d cos

12 J-Physics lectic field stength due to unifomly sufce chged disc : If thee is disc of dius, chged on its sufce with sufce chge density we wish to find electic field stength due to this disc t distnce fom the cente of disc on its is t point P shown in figue. dy y P d To find electic field t point P due to this disc, we conside n elementl ing of dius y nd width dy in the disc s shown in figue. The chge on this elementl ing d. ydy [Ae of elementl ing ds y dy] Now we know tht electic field stength due to ing of dius, chge, t distnce fom its cente on its is cn be given s k / Hee due to the elementl ing electic field stength d t point P cn be given s d k d y / ky dy y / Net electic field t point P due to this disc is given by integting bove epession fom to s m ple d kydy / y k k y dy / y y Clculte the electic field t oigin due to infinite numbe of chges s shown in figues below. O fig () 4 (m) O fig (b) 4 (m) () k 4 6 k. ( / 4) 4k [ S, nd 4 ] m ple (b) k 4 6 k. / 4 4k 5 A chged pticle is kept in euilibium in the electic field between the pltes of millikn oil dop epeiment. If the diection of the electic field between the pltes is evesed, then clculte cceletion of the chged pticle. Let mss of the pticle m, Chge on pticle Intensity of electic field in between pltes, Initilly mg Afte evesing the field m mg m mg Acceletion of pticle g NOD6 ()\Dt\4\Kot\J-Advnced\SMP\Phy\Unit-7\lectosttics\nglish\Theoy.p65

13 m ple S o l u t i o n J-Physics Clculte the electic field intensity which would be just sufficient to blnce the weight of n electon. If this electic field is poduced by second electon locted below the fist one wht would be the distnce between them? [Given : e.6-9 C, m 9. kg nd g 9.8 m/s ] As foce on chge e in n electic field F e e So ccoding to given poblem F e W e mg mg V e.6 m As this intensity is poduced by nothe electon B, locted t distnce below A. e 4 e 4 So, m m ple S o l u t i o n A block hving mss m 4 kg nd chge 5 C is connected to sping hving foce constnt k N/ m. The b lock li es on fi ctionless hoi zontl tck nd uni fom electi c fi eld 5 5 V/m cts on the system s shwon in figue. The block is elesed fom est when the sping is unstetched (t ) () By wht mimum mount does the sping epnd? (b) Wht is the euilibium position of the block? (c) Show tht the block's motion is simple hmonic nd detemine the mplitude nd time peiod of the motion. () As inceses, electic foce will ccelete the block while elstic foce in the sping k will oppose the motion. The block will move wy fom its initil position till it comes to est, i.e., wok done by the electic foce is eul to the enegy stoed in the sping. So if m is mimum stetch of the sping. k () m m m k m 6 5 (5 ) (5 ).5 m (b) In euilibium position F, so if is the stetch of the sping in euilibium position NOD6 ()\Dt\4\Kot\J-Advnced\SMP\Phy\Unit-7\lectosttics\nglish\Theoy.p65 k (/k) m.5 m (c) If the displcement of the block fom euilibium position ( ) is, estoing foce will be F k( ± ) k [ k ] nd s the estoing foce is line the motion will be simple hmonic with time peiod nd m 4 T.4 s k mplitude m m

14 J-Physics LCTIC LINS OF FOC lectic lines of electosttic field hve following popeties A B (i) Imginy (ii) (iii) Cn neve coss ech othe Cn neve be closed loops A> B (iv) (v) (vi) (vii) (viii) The numbe of lines oiginting o teminting on chge is popotionl to the mgnitude of chge. In tionlised MKS system (/ o ) electic lines e ssocited with unit chge, so if body encloses chge, totl lines of foce ssocited with it (clled flu) will be / o. Lines of foce ends o stts nomlly t the sufce of conducto. If thee is no electic field thee will be no lines of foce. Lines of foce pe unit e noml to the e t point epesents mgnitude of intensity, cowded lines epesent stong field while distnt lines wek field. Tngent to the line of foce t point in n electic field gives the diection of intensity. So positive chge fee to move follow the line of foce. GOLDN KY POINTS Lines of foce stts fom (ve) chge nd ends on ( ve) chge. Lines of foce stt nd end nomlly on the sufce of conducto. fied point chge ne infinite metl plte s edge effect s The lines of foce neve intesect ech othe due to supeposition pinciple. The popety tht electic lines of foce contct longitudinlly leds to eplin ttction between opposite chges. The popety tht electic lines of foce eet ltel pessue on ech othe leds to eplin epulsion between like chges. lectic flu () The wod "flu" comes fom Ltin wod mening "to flow" nd you cn conside the flu of vecto field to be mesue of the flow though n imginy fied element of sufce in the field. lectic flu is defined s da This sufce integl indictes tht the sufce in uestion is to be divided into infinitesiml elements of e da nd the scl untity da is to be evluted fo ech element nd summed ove the entie sufce. Impotnt points bout electic flu : (i) It is scl untity (ii) Units (V m) nd N m /C Dimensions : [ML T A ] (iii) The vlue of does not depend upon the distibution of chges nd the distnce between them inside the closed sufce. 4 NOD6 ()\Dt\4\Kot\J-Advnced\SMP\Phy\Unit-7\lectosttics\nglish\Theoy.p65

15 lectic Flu though cicul Disc : J-Physics Figue shows point chge plced t distnce fom disc of dius. Hee we wish to find the electic flu though the disc sufce due to the point chge. We know point chge oigintes electic flu in dilly outwd diection. The flu is oiginted in cone shown in figue psses though the disc sufce. To clculte this flu, we conside on elementl ing n disc sufce of dius nd width d s shown. Ae of k this ing (stip) is ds d. The electic field due to t this elementl ing is given s If d is the flu pssing though this elementl ing, then ds d d S co s k d k d / d d / d / The bove esult cn be obtined in much simple wy by using the concept of solid ngle nd Guss's lw. NOD6 ()\Dt\4\Kot\J-Advnced\SMP\Phy\Unit-7\lectosttics\nglish\Theoy.p65 lectic flu though the ltel sufce of cylinde due to point chge : Figue shows cylindicl sufce of length L nd dius. On its is t its cente point chge is plced. Hee we wish to find the flu coming out fom the ltel sufce of this cylinde due to the point chge. Fo this we conside n elementl stip of width d on the sufce of cylinde s shown. The e of this stip is ds.d L 5 ds C

16 J-Physics The electic field due to the point chge on the stip cn be given s k. If d is the electic flu though the stip, then d ds cos K d K d / Totl flu though the ltel sufce of cylinde d This sitution cn lso be esily hndled by using the concepts of Guss's lw. L / d / L / 4 GAUSS' S LAW It eltes with the totl flu of n electic field though closed sufce to the net chge enclosed by tht sufce nd ccoding to it, the totl flu linked with closed sufce is / times the chge enclosed by the closed sufce i.e.,.ds S n ds O GADING GAUSS'S LAW IT IS WOTH NOTING THAT : Note : (i) Flu though gussin sufce is independent of its shpe. (ii) (iii) (iv) (v) Flu though gussin sufce depends only on chges pesent inside gussin sufce. Flu though gussin sufce is independent of position of chges inside gussin sufce. lectic field intensity t the gussin sufce is due to ll the chges pesent (inside s well s out side) In close sufce incoming flu is tken negtive while outgoing flu is tken positive. (vi) In gussin sufce does not employ but employs. (vii) Guss's lw nd Coulomb's lw e euivlent, i.e., if we ssume Coulomb's lw we cn pove Guss's lw nd vice ves. To pove Guss's lw fom Coulomb's lw conside hypotheticl spheicl sufce [clled Gussin sufce] of dius with point chge t its cente s shown in figue. By Coulomb's lw intensity t point P on the sufce will be, And hence electic flu linked with e ds.ds 4 Hee diection of nd ds e sme, i.e.,.ds S 4 6 ds S 4 4.ds S.ds 4 Which is the euied esult. Though hee in poving it we hve ssumed the sufce to be spheicl, it is tue fo ny bity sufce povided the sufce is closed. NOD6 ()\Dt\4\Kot\J-Advnced\SMP\Phy\Unit-7\lectosttics\nglish\Theoy.p65

17 J-Physics (viii) () If closed body (not enclosing ny chge) is plced in n electic field (eithe unifom o non unifom) totl flu linked with it will be zeo. sphee (A) (B) (b) If closed body encloses chge, then totl flu (A) (B) (C) (D) (/ ) (/ ) (/ ) (/ ) linked with the body will be.ds S Fom this epession it is cle tht the flu linked with closed body is independent of the shpe nd size of the body nd position of chge inside it.[figue] Note : So in cse of closed symmeticl body with chge t its cente, flu linked with ech hlf will be nd the symmeticl closed body hs n identicl fces with point chge t its cente, flu linked with ech fce will be n n (i) Guss's lw is poweful tool fo clculting electic intensity in cse of symmeticl chge distibution by choosing Gussin sufce in such wy tht is eithe pllel o pependicul to its vious fces. As n emple, conside the cse of plne sheet of chge hving chge density. To clculte t point P close to it conside Gussin sufce in the fom of 'pill bo' of coss section S s shown in figue. NOD6 ()\Dt\4\Kot\J-Advnced\SMP\Phy\Unit-7\lectosttics\nglish\Theoy.p65 n n Sheet of chge (A) n 7 in n Conducto (B) The chge enclosed by the Gussin sufce S nd the flu linked with the pill bo S S S (s is pllel to cuved sufce nd pependicul to plne fces) So fom Guss's lw, (), S S n

18 J-Physics () If,.ds, so but if,.ds So my o my not be zeo. If dipole is enclosed by closed sufce then,, so.ds, but Note : If insted of plne sheet of chge, we hve chged conducto, then s shown in figue (B) in. So S nd hence in this cse. This esult cn be veified fom the fct tht intensity t the sufce of chged spheicl conducto of dius is, 4 with 4 So fo point close to the sufce of conducto, 4 4 m ple If point chge is plced t the cente of cube. Wht is the flu linked () with the cube? (b) with ech fce of the cube? () Accoding to Guss's lw flu linked with closed body is (/ ) times the chge enclosed nd hee the closed body cube is enclosing chge so, T () (b) Now s cube is symmeticl body with 6 fces nd the point chge is t its cente, so electic flu F T 6 6 linked with ech fce will be Note: (i) (ii) Hee flu linked with cube o one of its fces is independent of the side of cube. If chge is not t the cente of cube (but nywhee inside it), totl flu will not chnge, but the flu linked with diffeent fces will be diffeent. m ple If point chge is plced t one cone of cube, wht is the flu linked with the cube? In this cse by plcing thee cubes t thee sides of given cube nd fou cubes bove, the chge will be in the cente. So, the flu linked with ech cube will be one eight of the flu. Flu ssocited with given cube 8 8 NOD6 ()\Dt\4\Kot\J-Advnced\SMP\Phy\Unit-7\lectosttics\nglish\Theoy.p65

19 J-Physics FLUX CALCULATION USING GAUSS LAW ds ds ds in nd out totl in cicul nd out cuved totl y ds ds ds in nd out totl z nd in out totl k Note : hee electic field is dil 4 hemisphee cylinde NOD6 ()\Dt\4\Kot\J-Advnced\SMP\Phy\Unit-7\lectosttics\nglish\Theoy.p65 9 cube 8 4

20 J-Physics m ple As shown in figue closed sufce intesects spheicl conducto. If negtive chge is plced t point P. Wht is the ntue of the electic flu coming out of the closed sufce? close sufce conducto P Point chge induces chge on conducto s shown in figue. Net chge enclosed by closed sufce is negtive so flu is negtive. m ple Conside î (N/C) then wht is the flu though the sue of cm side, if the noml of its plne mkes 6 ngle with the X is. Scos [ ] cos6 ½ 5 Nm /C m ple Find the electic field due to n infinitely long cylindicl chge distibution of dius nd hving line chge density t distnce hlf of the dius fom its is. point will be inside so k k F I HG K J 4 LCTIC FILD DU TO SOLID CONDUCTING O HOLLOW SPH Fo outside point ( > ) Using Guss's theoem.ds At evey point on the Gussin sufce ds ;.ds ds cos ds.ds [ is constnt ove the gussin sufce] 4 p 4 Fo sufce point : S 4 Fo Inside point ( < ) : Becuse chge inside the conducting sphee o hollow is zeo. (i.e. ) So.ds in O P da Gussin sufce NOD6 ()\Dt\4\Kot\J-Advnced\SMP\Phy\Unit-7\lectosttics\nglish\Theoy.p65

21 LCTIC FILD DU TO SOLID NON CONDUCTING SPH Outside ( > ) Fom Guss's theoem At sufce ( ).ds 4 P 4 s Put S 4 Inside ( < ) : Fom Guss's theoem s.ds Whee chge contined within Gussin sufce of dius...(i) 4 (4 ) J-Physics O P ds Gussin sufce P ds O Gussin sufce As the sphee is unifomly chged, the volume chge density (chge/volume) is constnt thoughout the sphee chge enclosed in gussin sufce 4 put this vlue in eution (i) in (4 ) LCTIC FILD DU TO AN INFINIT LIN DISTIBUTION OF CHAG NOD6 ()\Dt\4\Kot\J-Advnced\SMP\Phy\Unit-7\lectosttics\nglish\Theoy.p65 Let wie of infinite length is unifomly chged hving constnt line chge density. P is the point whee electic field is to be clculted. Let us dw coil Gussin cylindicl sufces of length. Fom Guss's theoem.ds.ds.ds s s s ds so.ds nd ds so.ds [ ds ] Chge enclosed in the Gussin sufce So o. ( f ) Chged cylindicl nonconducto of infinite length k lectic field t outside point ˆ A lectic field t inside point B k whee k 4 > < ds ds Gussin Sufce Gussin sufce ds

22 J-Physics DILCTIC IN LCTIC FILD Let be the pplied field, Due to polistion, electic field is. p The esultnt field is. Fo homogeneous nd isotopic dielectic, p the diection of p is opposite to the diection of. So, esultnt field is P lectic field inside solid conducto is lwys zeo. GOLDN KY POINTS lectic field inside hollow conducto my o my not be zeo ( if non zeo chge is inside the sphee). The electic field due to cicul loop of chge nd point chge e identicl povided the distnce of the obsevtion point fom the cicul loop is uite lge s comped to its dius i.e. >>>. m ple Fo infinite line distibution of chge dw the cuve between log nd log. A whee A constnt log log A m ple tke log on both side log log A log A point chge of.9 C is plced t oigin. Clculte intensity of electic field due to this point chge t point 4 ; whee i yj i 7 j, LCTOSTATIC POTNTIAL NGY, 7, ( ˆi 7 ˆj) () log ˆi 7 ˆj NC Potentil enegy of system of pticles is defined only in consevtive fields. As electic field is lso consevtive, we define potentil enegy in it. Potentil enegy of system of pticles we define s the wok done in ssembling the system in given configution ginst the intection foces of pticles. lectosttic potentil enegy is defined in two wys. (i) Intection enegy of chged pticles of system (ii) Self enegy of chged object lectosttic Intecti on negy lectosttic intection enegy of system of chged pticles is defined s the etenl wok euied to ssemble the pticles fom infinity to the given configution. When some chged pticles e t infinite seption, thei potentil enegy is tken zeo s no intection is thee between them. When these chges e bought close to given configution, etenl wok is euied if the foce between these pticles is epulsive nd enegy is supplied to the system, hence finl potentil enegy of system will be positive. If the foce between the pticle is ttctive, wok will be done by the system nd finl potentil enegy of system will be negtive. NOD6 ()\Dt\4\Kot\J-Advnced\SMP\Phy\Unit-7\lectosttics\nglish\Theoy.p65

23 Intection negy of system of two chged pticles J-Physics Figue shows two ve chges nd septed by distnce. The electosttic intection enegy of this system cn be given s wok done in binging fom infinity to the given seption fom. d F It cn be clculted s W F.d k d [ ve sign shows tht is decesing] W k U [ intection enegy] If the two chges hee e of opposite sign, the potentil enegy will be negtive s U Intection negy fo system of chged pticles k When moe thn two chged pticles e thee in system, the intection enegy cn be given by sum of intection enegies of ll the pis of pticles. Fo emple if system of thee pticles hving chges, nd is given s shown in figue. The totl intection enegy of this system cn be given s U k k k NOD6 ()\Dt\4\Kot\J-Advnced\SMP\Phy\Unit-7\lectosttics\nglish\Theoy.p65 LCTIC POTNTIAL m p l e S o l u t i o n lectic potentil is scl popety of evey point in the egion of electic field. At point in electic field potentil is defined s the intection enegy of unit positive chge. If t point in electic field chge hs potentil enegy U, then electic potentil t tht point cn be given s V U joule/coulomb Potentil enegy of chge in electic field is defined s wok done in binging the chge fom infinity to the given point in electic field. Similly we cn define electic potentil s "wok done in binging unit positive chge fom infinity to the given point ginst the electic foces. A chge C is tken fom infinity to point in n electic field, without chnging its velocity, if wok done ginst electosttic foces is 4J then potentil t tht point is? V W 4J C et V Note : Alwys emembe to put sign of W nd.

24 J-Physics lectic Potentil due to point chge in its suounding : p The potentil t point P t distnce fom the chge V P U. Whee U is the potentil enegy of chge t point p, U k lectic Potentil due to chge od :. Thus potentil t point P is V P k Figue shows od of length L, unifomly chged with chge. Due to this we'll find electic potentil t point P t distnce fom one end of the od s shown in figue. Fo this we conside n element of width d t distnce fom the point P. L d P Chge on this element is d L d The potentil dv due to this element t point P cn be given by using the esult of point chge s dv kd k L d Net electic potentil t point P : V lectic potentil due to chged ing Cse I : At its cente dv L k d k L L ln L To find potentil t the cente C of the ing, we fist find potentil dv t cente due to n elementl chge d on ing which is given s dv kd Totl potentil t C is V dv kd k. d C 4 As ll d's of the ing e situted t sme distnce fom the ing cente C, simply the potentil due to ll d's is dded s being scl untity, we cn diectly sy tht the totl electic potentil t ing cente is k. Hee we cn lso stte tht even if chge is non unifomly distibuted on ing, the electic potentil C will emin sme. NOD6 ()\Dt\4\Kot\J-Advnced\SMP\Phy\Unit-7\lectosttics\nglish\Theoy.p65

25 Cse II : At point on is of ing J-Physics We find the electic potentil t point P on the is of ing s shown, we cn diectly stte the esult s hee lso ll points of ing e t sme distnce fom the point P, thus the potentil t P cn be given k s V P P lectic potentil due to unifomly chged disc : Figue shows unifomly disc of dius with sufce chge density coul/m. To find electic potentil t point P we conside n elementl ing of dius y nd width dy, chge on this elementl ing is dy dy. Due to this ing, the electic potentil t point P cn be given s dv y kd k..y dy y dy y P Net electic potentil t Point P due to whole disc cn be given s V y dy dv y y LCTIC POTNTIAL DU TO HOLLOW O CONDUCTING SPH At outside sphee NOD6 ()\Dt\4\Kot\J-Advnced\SMP\Phy\Unit-7\lectosttics\nglish\Theoy.p65 5 > P Accoding to definition of electic potentil, electic potentil t point P V.d d out 4 4 ; V d 4 4 4

26 J-Physics At sufce V.d d out 4 4 ; V d 4 V 4 4 Inside the sufce : dv Inside the sufce V constnt so V d 4 LCTIC POTNTIAL DU TO SOLID NON CONDUCTING SPH At outside spheesme s conducting sphee. At Sufce Sme s conducting sphee. Inside the sphee V.d k k V d d V k V d d k V k k V Potentil Diffeence Between Two points in electic field Potentil diffeence between two points in electic field cn be defined s wok done in displcing unit positive chge fom one point to nothe ginst the electic foces. AVA B V B If unit ve chge is displced fom point A to B s shown wok euied cn be given s VB V A B.d A If chge is shifted fom point A to B, wok done ginst electic foces cn be given s W (V B V A ) If in sitution wok done by electic foces is sked, we use W (V A V B ) If V B < V A, then chges must hve tendency to move towd B (low potentil point) it implies tht electic foces cy the chge fom high potentil to low potentil points. Hence we cn sy tht in the diection of electic field lwys electic potentil deceses. m p l e S o l u t i o n C chge is shifted fom A to B nd it is found tht wok done by etenl foce is 8J ginst electostic foces, find V A V B W AB (V B V A ) 8 J C (V B V A ) V A V B 8 V uipotentil sufces Fo given chge distibution, locus of ll points hving sme potentil is clled 'euipotentil sufce'. uipotentil sufces cn neve coss ech othe (othewise potentil t point will hve two vlues which is bsud) 6 NOD6 ()\Dt\4\Kot\J-Advnced\SMP\Phy\Unit-7\lectosttics\nglish\Theoy.p65

27 uipotentil sufces e lwys pependicul to diection of electic field. If chge is moved fom one point to the othe ove n euipotentil sufce then wok done W AB U AB (V B V A ) [ V B V A ] Shpes of euipotentil sufces J-Physics VV VV VV VV VV VV fo unifom electic field euipotentil sufces e pllel plne fo point chge, spheicl conducto euipotentil sufces e spheicl fo line distibution of chge euipotentil sufces e cylindeicl The intensity of electic field long n euipotentil sufce is lwys zeo. lectic Potentil Gdient The mimum te of chnge of potentil t ight ngles to n euipotentil sufce in n electic field is defined s potentil gdient. V gd V Note : Potentil is scl untity but the gdient of potentil is vecto untity In ctesin co odintes V L NM V i V y j V z k O P m ple If V 5 y 5 z then find mgnitude of electic field t point (,y,z). m p l e V ˆ V ˆ V i j k ˆ y z ( 5 i j 5 k ) unit The fou chges ech e plced t the cones of sue of side. Find the potentil enegy of one of the chges NOD6 ()\Dt\4\Kot\J-Advnced\SMP\Phy\Unit-7\lectosttics\nglish\Theoy.p65 The electic potentil of point A due to chges B, C nd D is V Potentil enegy of the chge t A is P V 7 4.

28 J-Physics m p l e A poton moves with speed of m/s diectly towds fee poton oiginlly t est. Find the distnce of closest ppoch fo the two potons. Given : N m C ; m p.67 7 kg nd e.6 9 C S o l u t i o n As hee the pticle t est is fee to move, when one pticle ppoches the othe, due to electosttic epulsion othe will lso stt moving nd so the velocity of fist pticle will decese while of othe will incese nd t closect ppoch both will move with sme velocity. So if v is the common velocity of ech pticle t closest ppoch, by 'consevtion of momentum'. mu mv mv v u And by consevtion of enegy mu mv 4 e So, 4e 4 mu [s v u ] And hence substituting the given dt, (.6 ).67 (7.45 ) 7 m LCTIC DIPOL A system of two eul nd opposite chges septed by cetin distnce is clled electic dipole, shown in figue. vey dipole hs chcteistic popety clled dipole moment. It is defined s the poduct of mgnitude of eithe chge nd the seption between the chges, given s p d d - p In some molecules, the centes of positive nd negtive chges do not coincide. This esults in the fomtion of electic dipole. Atom is non pol becuse in it the centes of positive nd negtive chges coincide. Polity cn be induced in n tom by the ppliction of electic field. Hence it cn be clled s induced dipole. Dipole Moment : Dipole moment p d (i) (ii) p Vecto untity, diected fom negtive to positive chge Dimension : [LTA], Units : coulomb mete (o C-m) (iii) Pcticl unit is "debye" Two eul nd opposite point chges ech hving chge fnkline ( e) nd seption of Å then the vlue of dipole moment (p) is debye. C m Debye F m 9. C m 8 NOD6 ()\Dt\4\Kot\J-Advnced\SMP\Phy\Unit-7\lectosttics\nglish\Theoy.p65

29 m p l e S o l u t i o n J-Physics A system hs two chges A.5 7 C nd B.5 7 C locted t points A: (,,.5 m) nd B ; (,,.5 m) espectively. Wht is the totl chge nd electic dipole moment of the system? Totl chge lectic diople moment, p Mngitude of eithe chge seption between chges.5 7 [.5.5] C m C m. The diection of dipole moment is fom B to A. Dipole Plced in unifom lectic Field Figue shows dipole of dipole moment p plced t n ngle to the diection of electic field. Hee the chges of dipole epeience foces in opposite diection s shown. F net ( ) p Thus we cn stte tht when dipole is plced in unifom electic field, net foce on the dipole is zeo. But s eul nd opposite foces ct with seption in thei line of ction, they poduce couple which tend to lign the dipole long the diection of electic field. The toue due to this couple cn be given s Foce seption between lines of ctions of foces d sin p sin F d d p Wok done i n ottion of Dipole in lectic field When dipole is plced in n electic field t n ngle, the toue on it due to electic field is Wok done in otting n electic dipole fom to [ unifom field] p sin dw d so W dw d nd W W p sin d p (cos cos ) NOD6 ()\Dt\4\Kot\J-Advnced\SMP\Phy\Unit-7\lectosttics\nglish\Theoy.p65 e.g. W 8 p [ ( )] p W 9 p ( ) p If dipole is otted fom field diection ( ) to then W p ( cos) p p 9 p 9 8 minimum mimum p minimum W minimum W p W mimum p

30 J-Physics lectosttic potentil enegy : lectosttic potentil enegy of dipole plced in unifom field is defined s wok done in otting dipole fom diection pependicul to the field to the given diection i.e., W9 p sin d 9 p cos p. is consevtive field so wht eve wok is done in otting dipole fom to is just eul to chnge in electosttic potentil enegy W U U p (cos cos ) Wok done in otti ng n electic dipole i n n electic field Suppose t ny instnt, the dipole mkes n ngle with the electic field. The toue cting on dipole. d ( sin) p sin The wok done in otting dipole fom to W d p sin d W p (cos cos ) U U ( U p cos) B d A C Foce on n electic dipole in Non unifom electic field : If in non unifom electic field dipole is plced t point whee electic field is, the intection enegy of dipole t this point U p.. Now the foce on dipole due to electic field F U If dipole is plced in the diection of electic field then F p d d m p l e Clculte foce on dipole in the suounding of long chged wie s shown in the figue. In the sitution shown in figue, the electic field stength due to the wie, t the position of dipole s k Thus foce on dipole is F p. d d - p k p kp Hee ve chge of dipole is close to wie hence net foce n dipole due to wie will be ttctive. NOD6 ()\Dt\4\Kot\J-Advnced\SMP\Phy\Unit-7\lectosttics\nglish\Theoy.p65

31 J-Physics LCTIC POTNTIAL DU TO DIPOL At il point lectic potentil due to chge V k ( ) O P lectic potentil due to chge V k ( ) Net electic potentil V V V k k k ( ) ( ) ( ) kp kp If > > > V At euitoil point lectic potentil of P due to chge V k P lectic potentil of P due to chge V k Net potentil V V V k k V O At genel point p cos p. V 4 4 p d electic dipole moment y lectic field due to n electic dipole Figue shows n electic dipole plced on is t oigin. Hee we wish to find the electic field nd potentil t point O hving coodintes (, ). Due to the positive chge of dipole electic field t O is in dilly outwd diection nd due to the negtive chge it is dilly inwd s shown in figue. net O NOD6 ()\Dt\4\Kot\J-Advnced\SMP\Phy\Unit-7\lectosttics\nglish\Theoy.p65 V kp cos nd V kp sin k p Thus net electic field t point O, net cos If the diection of net is t n ngle fom dil diection, then tn Thus the inclintion of net electic field t point O is ( - tn

32 J-Physics At point on the is of dipole : O k lectic field due to chge ( ) k lectic field due to chge ( ) k k Net electic field ( ) ( ) k 4 ( ) [ p Dipole moment] kp ( ) kp If >>> then At point on euitoil line of dipole : k k lectic field due to chge ; lectic field due to chge Veticl component of nd will cncel ech othe nd hoizontl components will be dded So net electic field t P sin cos cos [ ] k cos cos cos nd O k k kp kp kp ( ) ( ) If > > > then o P sin GOLDN KY POINTS Fo dipole, potentil is zeo t eutoil position, while t ny finite point In unifom, dipole my feel toue but not foce. If dipole plced in field (Non-Unifom) geneted by point chge, then toue on dipole my be zeo, but F Distibution Pointchge Dipole Potentil popotionl to popotionl to Foce between Point chge Dipole nd point chge Dipole-dipole 4 Popotionl to m ple A shot electic dipole is situted t the oigin of coodinte is with its is long is nd euto long y is. It is found tht the mgnitudes of the electic intensity nd electic potentil due to the dipole e eul t point distnt P P kp V 5 m fom oigin. Find the position vecto of the point in fist udnt. cos kp cos Position vecto of point P is 5 ˆ i ˆj cos 5 cos cos 45 NOD6 ()\Dt\4\Kot\J-Advnced\SMP\Phy\Unit-7\lectosttics\nglish\Theoy.p65

33 m p l e J-Physics Pove tht the feuency of oscilltion of n electic dipole of moment p nd ottionl ineti I fo smll mplitudes bout its euilibium position in unifom electic field stength is p I Let n electic dipole (chge nd t distnce pt) plced in unifom etenl electic field of stength. F F - P estoing toue on dipole p sin p (s is smll) Hee ve sign shows the estoing tendency of toue. I ngul cceletion I P I Fo SHM comping we get p I Thus feuency of oscilltions of dipole n p I LCTOSTATIC PSSU Foce due to electosttic pessue is diected nomlly outwds to the sufce. Foce on smll element ds of chged conducto df (Chge on ds ) lectic field ( ds) ds ds NOD6 ()\Dt\4\Kot\J-Advnced\SMP\Phy\Unit-7\lectosttics\nglish\Theoy.p65 Inside Just outside ( is field due to point chge on the sufce nd is field due to est of the sphee). The electic foce cting pe unit e of chged sufce is defined s electosttic pessue. P eleectosttic df ds

34 J-Physics uilibium of liuid chged sufces (Sop bubble) Pessues (foces) ct on chged sop bubble, due to (i) Sufce tension P T (inwd) (ii) Ai outside the bubble P o (inwd) (iii) lectosttic pessue P e (outwd) (iv) Ai inside the bubble P i (outwd) in stte of euilibium inwd pessue outwd pessue P T P o P i P e m ple cess pessue of i inside the bubble (P e ) P i P o P T P e but P T 4T nd P e P 4T if P e i P o then 4T Bss hs tensile stength.5 8 N/m. Wht chge density on this mteil will be enough to bek it by electosttic foce of epulsion? How mny ecess electons pe sue Å will thee then be? Wht is the vlue of intensity just out side the sufce? We know tht electosttic foce on chged conducto is given by df ds So the conducto will bek by this foce if, i.e. min C / m > Beking stength i.e., Now s the chge on n electon is.6 9 C, the ecess electons pe m Futhe s in cse of conducto ne its sufce V/m CONDUCTO AND IT' S POPTIS [FO LCTOSTATIC CONDITION] (i) (ii) (iii) (iv) (v) (vi) Conductos e mteils which contins lge numbe of fee electons which cn move feely inside the conducto. n electosttics, conductos e lwys euipotentil sufces. Chge lwys esides on oute sufce of conducto. f thee is cvity inside the conducto hving no chge then chge will lwys eside only on oute su fce of conducto. lectic field is lwys pependicul to conducting sufce. lectic lines of foce neve ente into conductos. (vii) lectic field intensity ne the conducting sufce is given by fomul (viii) A A nˆ ; B B nˆ nd C When conducto is gounded its potentil becomes zeo. C nˆ nˆ NOD6 ()\Dt\4\Kot\J-Advnced\SMP\Phy\Unit-7\lectosttics\nglish\Theoy.p65

35 J-Physics (i) () When n isolted conducto is gounded then its chge becomes zeo. When two conductos e connected thee will be chge flow till thei potentil becomes eul. (i) lectic pessue t the sufce of conducto is givey by fomul P density. whee is the locl sufce chge m ple Pove tht if n isolted (isolted mens no chges e ne the sheet) lge conducting sheet is given chge then the chge distibutes eully on its two sufces. Let thee is chge on left side of sheet nd chge on ight side of sheet. Since point P lies inside the conducto so P O A O A O A O A So chge is eully distibuted on both sides O - A P - A m ple If n isolted infinite sheet contins chge on its one sufce nd chge on its othe sufce then pove tht electic field intensity t point in font of sheet will be lectic field t point P : nˆ A nˆ A A O, whee nˆ A nˆ A NOD6 ()\Dt\4\Kot\J-Advnced\SMP\Phy\Unit-7\lectosttics\nglish\Theoy.p65 [This shows tht the esultnt field due to sheet depends only on the totl chge of the sheet nd not on the distibution of chge on individul sufces]. m ple Thee lge conducting sheets plced pllel to ech othe t finite distnce contins chges, nd espectively. Find electic field t points A, B, C, nd D - A B C Sol. A. (i) Hee mens electic field due to. A ( ) A A A, towds left 5

36 J-Physics (ii) B ( ) A, towds ight (iii) C ( ) () A 4 A A, towds ight A towds left ( ) (iv) D A A A, towds ight m ple Two conducting pltes A nd B e plced pllel to ech othe. A is given chge nd B chge. Pove tht the chges on the inne fcing sufces e of eul mgnitude nd opposite sign. Also find the chges on inne & oute sufces. Conside Gussin sufce s shown in figue. Two fces of this closed sufce lie completely inside the conducto whee the electic field is zeo. The flu though these fces is, theefoe, zeo. The othe pts of the closed sufce which e outside the conducto e pllel to the electic field nd hence the flu on these pts is lso zeo. The totl flu of the electic field though the closed sufce is, theefoe zeo. Fom Guss s lw, the totl chge inside this closed sufce should be zeo. The chge on the inne sufce of A should be eul nd opposite to tht on the inne sufce of B. A B P A B The distibution should be like the one shown in figue. To find the vlue of, conside the field t point P inside the plte A. Suppose, the sufce e of the plte (one side) is A. Using the eution / ( ), the electic field t P due to the chge A (downwd); due to the chge A (upwd), due to the chge A (downwd), nd due to the chge A (upwd). The net electic field t P due to ll the fou chged sufces is (in the downwd diection) p A A A A As the point P is inside the conducto, this field should be zeo. Hence, 6 This esult is specil cse of the following esult. When chged conducting pltes e plced pllel to ech othe, the two outemost, sufces get eul chges nd the fcing sufces get eul nd opposite chges. NOD6 ()\Dt\4\Kot\J-Advnced\SMP\Phy\Unit-7\lectosttics\nglish\Theoy.p65