ELECTROSTATICS. Syllabus : Einstein Classes, Unit No. 102, 103, Vardhman Ring Road Plaza, Vikas Puri Extn., Outer Ring Road PE 1

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1 PE ELECTOSTATICS Syllbus : Electic chges : Consevtion of chge, Coulumb s lw-foces between two point chges, foces between multiple chges; supeposition pinciple nd continuous chge distibution. Electic field : Electic field due to point chge, Electic field lines, Electic dipole, Electic field due to dipole, Toue on dipole in unifom electic field. Electic flux, Guss s lw nd its pplictions to find due to infinitely long unifomly chged wie, unifomly chged infinite plne sheet nd unifomly chged thin spheicl shell. Electic potentil nd its clcultion fo point chge, electic dipole nd system of chges; Euipotentil sufces, Electicl potentil enegy of system of two point chges in n electosttic field. Conductos nd insultos, Dielectics nd electic poliztion, cpcito, combintion of cpcitos in seies nd in pllel, cpcitnce of pllel plte cpcito with nd without dielectic medium between the pltes, Enegy stoed in cpcito. Einstein Clsses, Unit No.,, Vdhmn ing od Plz, Viks Pui Extn., Oute ing od

2 PE CONCEPTS C Popeties of chges : (i) (ii) (iii) (iv) (v) (vi) Two kinds of chges exist in ntue, positive nd negtive with the popety tht unlike chges ttct ech othe nd like chges epel ech othe. Excess of electons mens negtive chge nd deficiency of chge mens positive chge. Chge is conseved fo n isolted system. Chge is untized i.e. = ± ne whee n =,,... nd e =.6 9 C Chge is invint. On chging neutl body, the mss of the body will chnge. C Electic field : The mgnitude of electic field fo point chge t the distnce is given by 4 nd diection is towds the chge if it is positive nd wy fom the chge if it is negtive. = 8.85 C /Nm is known s bsolute pemittivity constnts nd is known s eltive pemittivity constnt. Pinciple of supe position : The electic field due to goup of chges cn be obtined using the supeposition pinciple. Tht is, the totl electic field euls the vecto sum of the electic fields of ll the chges t some point : E E E... Pctice Poblems : E. A positive chge is plced t the oigin. The minimum electic field poduced t the point (, 4, ) is given by.6( î 4 ĵ) N / C.6( î 4 ĵ) N / C.6(î 4 ĵ) N / C.6(î 4 ĵ) N / C. Five point chges, ech of vlue + coul, e plced on five vetices of egul hexgon of side L metes. The mgnitude of the foce on point chge of vlue coul plced t the cente of the hexgon is 5k /L k /L k /L. A cube of side b hs chge t ech of its vetices. The electic field due to this chge distibution t the cente of the cube is /b /b /b zeo [Answes : () d () c () d] C Coulomb Foce : E, whee is the test chge plced in the extenl electic field E. Column F Foce is centl, invese sue nd consevtive field. Coulmb s foce is vlid fo distnces fom cm to sevel kilometes. i.e. up to infinity. Pctice Poblems :. A liuid dop of mss m nd cying n electons cn be blnced by pplying n electic field. The diection nd mgnitude of the electic field is mg upwd, ne mg upwd, ne mg downwd, ne downwd, mg ne Einstein Clsses, Unit No.,, Vdhmn ing od Plz, Viks Pui Extn., Oute ing od

3 PE. A chge is divided into two pts nd the two pts e septed by cetin distnce d. Then the mximum foce between them will be k 4d k d k d k d [Answes : () b () ] C4 C5 Electic Field Lines : A convenient specilized pictoil epesenttion fo visulizing electic field pttens is ceted by dwing lines showing the diection of the electic field vecto t ny point. These lines, clled electic field lines, e elted to the electic field in ny egion of spce in the following mnne : The electic field vecto E is tngent to the electic field line t ech point. The numbe of electic field lines pe unit e though sufce tht is pependicul to the lines is popotionl to the mgnitude of the electic field in tht egion. Thus, E is lge whee the field lines e close togethe nd smll whee they e f pt. Fo positive point chge, the lines e diected dilly outwd nd fo negtive point chge, the lines e diected dilly inwd. The numbe of lines tht oiginte fom o teminte on chge is popotionl to the mgnitude of the chge. Motion of chged pticles in electic field When pticle of chge nd mss m is plced in n electic field E then the foce on the chge pticles is E E nd ccoding to Newton s second lw F E m m whee is the cceletion of the pticle. If the pticle is elesed fom est in unifom E o pojected with cetin speed long the diection of unifom E o opposite to the diection of unifom E then the pth is stight line othewise the pth is pbolic in unifom E. Pctice Poblems :. A chged pticle of mss m nd chge is elesed fom est in unifom electic field E. The kinetic enegy of the pticle fte time t is E t m E m t E t m Em t [Answes : () c] C6 Electic flux : Electic flux is popotionl to the numbe of electic field lines tht penette sufce. The electic flux though sufce is defined by the expession E.A EAcos E.dA If E is sufce unifom then whee is the ngle tht the electic field mkes with the noml to the sufce. C7 Guss s Lw : Guss s Lw sys tht the net electic flux though ny closed gussin sufce is eul E to the net chge inside the sufce divided by : E E.dA clculte the electic field due to vious symmetic chge distibutions. in. Using Guss s lw, one cn Einstein Clsses, Unit No.,, Vdhmn ing od Plz, Viks Pui Extn., Oute ing od

4 Pctice Poblems : PE 4. The electic chge is plced t the cente of cube of side. The electic flux though one of its fces will be 6 4 [Answes : () ] C8 Electic Field due to specil type of configution :. A ing of Chge E 4 E y =, x / ( x x ). A Disc of Chge E x x x. Infinite Sheet of Chge 4. Infinitely Long Line of Chge E x density, whee is the sufce chge E,E, whee is the line chge x density 5. A Spheicl Volume Chge Distibution (non-conducting solid sphee) E,E 4 is volume chge density 4 Einstein Clsses, Unit No.,, Vdhmn ing od Plz, Viks Pui Extn., Oute ing od

5 6. Spheicl Conducto (Hollow o Solid) PE 5 4 E = <, E Pctice Poblems :. A sphee of dius hs unifom volume chge distibution. At distnce x fom its cente, fo x <, the electic field is diectly popotionl to /x /x x x. One end of cm long silk thed is fixed to lge veticl sufce of chged nonconducting plte nd the othe end is fstened to smll bll hving mss of g nd chge of 4. 6 C. In euilibium, the thed mkes nd ngle of 6 with the veticl. The sufce chge density on the plte in µc/m is [Answes : () c () d] C9 Electic Potentil Enegy : The electic foce cused by ny collection of chges t est is consevtive foce. The wok W done by the electic foce on chged pticle moving in n electic field cn be epesented by potentil-enegy function U : W b = U U b. C Electic Potentil Enegy of two point chges : The potentil enegy fo two point chges nd septed by distnce is 4 U C C Electic potentil enegy of point chge in the electic field of sevel chges : The potentil enegy fo chge in the electic field of collection of chges i is given by i U whee i is the distnce fom i to. i i Totl potentil enegy of sevel chges : The totl potentil enegy U is the sum of the potentil ene- gies of intesection fo ech pi of chges. We cn wite this s U 4 i j i j ij Pctice Poblems :. Fou chges +,, + nd e plced t the cones A, B, C nd D espectively of sue of side. The potentil enegy of the system is k ( 4 ) k ( 4 ) 4 k [Answes : () ] 4 k Einstein Clsses, Unit No.,, Vdhmn ing od Plz, Viks Pui Extn., Oute ing od

6 C C4 PE 6 Enegy is n electic field : This enegy is stoed in the electic field geneted by the chges. i.e. in the spce whee the electic field exists nd it is found tht the enegy stoed in the field pe unit volume is given by E. Electicl potentil Electic potentil, scl untity, is the potentil enegy pe unit chge. Mthemticlly, Potentil, U V o U = V. The unit of potentil is volt (V) o J/c. Wok done by extenl souce to move chge ( ) vey slowly fom initil point to finl point in n electic field W = (V f V i ) whee V f is the potentil due to chge distibution t point nd V i is the find potentil due to chge distibution t initil point. C5 The potentil V due to point chge t distnce, C6 Potentil due to collection of point chges, V k C7 whee potentil will be clculted. i k V Electic potentil due to specil type of chge distibution. A ing of Chge i i, whee i is the distnce of chge i t the point V 4 x. A sphee of Chge V 8 8, V 4. Conducting Sphee (Hollow o Solid) V, V 4 4 Einstein Clsses, Unit No.,, Vdhmn ing od Plz, Viks Pui Extn., Oute ing od

7 Pctice Poblems : PE 7. A hollow metl sphee of dius 5 cm is chged so tht the potentil on its sufce is V. Let the potentil t the cente of the sphee, t distnce cm fom the cente nd t distnce cm fom the cente e V, V, nd V espectively. Then V : V : V euls to : : : : : : : : 5. Two identicl thin ings, ech of dius metes, e coxilly plced t distnce metes pt. If coulomb nd coulomb e espectively the chges unifomly sped on the two ings, the wok done in moving chge coulomb fom the cente of one ing to tht of the othe is zeo ( ) ( )/(4 ) ( + )/4 ( + ) ( + )/(4 ) [Answes : () b () b] C8 eltion between electic field nd electic potentil : eltion between field nd potentil is given by dv E.d integting between points nd b, dv Vb V b b E.d whee V nd V b e the dv potentils t nd b. In diffeentil fom, we hve E ˆ d Pctice Poblems :. A nonconducting ing of dius.5 m cies totl chge of. C distibuted non-unifomity of its cicumfeence poducing n electic field E eveywhee in spce. The vlue of l the line integl E.dl (l = t the cente of the ing) in volt is : l + zeo [Answes : () ] C9 Euipotentil Sufce : Thee is nothe wy to demonstte the gphicl epesenttion of field using the concept of Euipotentil Sufces. An euipotentil sufce is thee dimensionl sufces on which the potentil hs the sme vlue t evey point. At point whee field line cosses n euipotentil sufce the two e pependicul. Note the following points : the field is stonge whee the euipotentil sufces e closely spced. the wok done to move chge on euipotentil sufce is zeo. the wok done to move chge fom one euipotentil sufce (hving potentil, (V ) to nothe euipotentil sufce (hving potentil V ) is (V V ). Pctice Poblems :. The figue shows lines of constnt potentil in egion in which n electic field is pesent. The vlues of the potentil e witten in bckets. Of the points A, B nd C, the mgnitude of the electic field is getest t the point is Einstein Clsses, Unit No.,, Vdhmn ing od Plz, Viks Pui Extn., Oute ing od

8 A B C eul t ll points [Answes : () b] PE 8 C Conductos nd insultos : In conductos chges e fee to move thoughout the volume of such bodies whees in cse of insultos o dielectics, the chges emin fixed t the plces whee they wee initilly distibuted. Hence chge given to conducto lwys esides on its sufce. In conductos electic chges e fee to move thoughout the volume of such bodies. When thee is no net motion of chge within conducto, the conducto is in electosttic euilibium. The following e the popeties of conducto in electosttic euilibium.. The electic field is zeo eveywhee inside the conducto (E = ). No volume chges exist inside conducto. The sufce of conducto is n euipotentil sufce nd lines of foces lwys meet conducting sufce nomlly. 4. Chge density is invesely popotionl to dius of cuvtue. 5. If thee is cvity inside conducto, the field stength inside the cvity euls zeo, whteve is the field outside the conducto. 6. The field intensity ne conducting sufce is lwys density t tht point. E, whee is the locl sufce chge 7. edistibution of Chge : If two conductos e bought into contct, the chges fom one of them will flow ove to the othe until thei potentils become eul. The eulity of potentil implies tht chges on ech sphee (s shown) is popotionl to its dius. i.e.,, the totl chge = 4, so the bove eution becomes. Fo unifom sufce chge density 8. Potentil of concentic conducting sphees : Supeposition Pinciple : Let us conside two concentic sphees of dii nd with unifomly distibuted chges nd. Using the pinciple of supeposition, the potentil of the smll nd lge sphee my be witten s Pctice Poblems : V k,. k V k k. A chge is distibuted ove two concentic hollow sphees of dii nd ( > ) such tht the sufce densities e eul. The potentil t the common cente is /4 times zeo. Two chges conducting sphees of dii nd, septed by lge distnce, e connected by long wie. The tio of the electic fields on the sufce of the two sphees is Answes : () b] Einstein Clsses, Unit No.,, Vdhmn ing od Plz, Viks Pui Extn., Oute ing od

9 C PE 9 Electic Dipole : An electic dipole is pi of point chges with eul mgnitude nd opposite sign ( positive chge nd negtive chge ) septed by distnce d. The chcteistic of dipole is its dipole moment defined s p d, the diection is fom negtive chge to positive chge. Pctice Poblems :. Electic chges, nd e plced t the thee cones of n euiltel tingle of side l. The mgnitude of the electic dipole moment of the system is l l l 4 l [Answes : () c] C (i) (ii) Electic field due to dipole Along the Axis : The electic field intensity long the xis lwys point in the diection of the kp dipole. It mgnitude is given by E. x Along the Bisecto : The diection of electic field long the bisecto is lwys opposite to the kp y dipole moment. Mth emeticlly, Pctice Poblems : E. A given chge situted t cetin distnce fom shot electic dipole in the end-on position expeiences foce F. If the distnce of the chge fom the dipole is doubled then the foce cting on the chge is F. Then F /F euls to / /4 8. If E be the electic field intensity due to shot dipole t point on the xis nd E be tht on the ight bisecto t the sme distnce fom the dipole, then E E = E E = E E = E [Answes : () d () b] E C Electic potentil due to dipole (i) kp Along the Axis : The electic potentil long the x-xis is given by V x (ii) Along the Bisecto : The electic potentil long the bisecto is lwys zeo. C4 Dipole in n extenl electic field :. The net foce expeienced by dipole in n extenl unifom electic field is zeo.. When n electic dipole of dipole moment p is plced in n electic field E, the field exets toue on the dipole : p E.. The dipole hs potentil enegy U ssocited with its oienttion in the field : U p. E. This potentil enegy is defined to be zeo when p is pependicul to E ; it is lest (U = pe) when p is ligned with E, nd most (U = pe) when p is diected opposite E. Hence dipole is in stble euilibium when p is ligned with E. 4. The net foce on the dipole in the non-unifom field is non-zeo nd clculted by F du dx. Einstein Clsses, Unit No.,, Vdhmn ing od Plz, Viks Pui Extn., Oute ing od

10 Pctice Poblems : PE. The potentil enegy of n electic dipole in unifom electic field is U. The mgnitude of the toue cting on the dipole due to the field is N. Then U is minimum nd N is zeo when the dipole is pllel to the field. U is zeo nd N is zeo when the dipole is pependicul to the field. U is minimum nd N is mximum when the dipole is pependicul to the field U is minimum nd N is zeo when the dipole is nti-pllel to the field.. A dipole is plced in the field of infinite sheet of unifom chge density. Which of the following untity must be zeo? Foce Potentil Enegy Toue All the bove [Answes : () () ] C Vn De Gff Geneto It is used to genete the potentil in the ode of 6 volt which is used to cceletes the chged pticles. INITIAL STEP EXECISE. The tio of the electic foce between two potons to the gvittionl foce between them is of the ode of The wok done in otting n electic dipole of moment p in n electic field E though n ngle fom the diection of the field is pe ( cos ) pe zeo pe cos. The foce cting between two eul point chges distnce pt in i is F. If one of the chges is otted bout the othe in cicle of dius, the wok done will be F F F zeo 4. Thee cpcitos of cpcitnces µf, 9µF nd 8µF e connected fist in seies nd then in pllel. The tio of the euivlent cpcitnces in the two cses is 5/ /5 /9 9/ 5. The electic field t the oigin is long the positive X-xis. A smll cicle is dwn with the cente t the oigin cutting the xes t points A, B, C nd D hving coodintes (, ), (, ), (, ), (, ) espectivelty. Out of the points on the peiphey of the cicle, the potentil is minimum t A B C D 6. Ech of the fou cpcitos in the given cicuit is 5 µf. The chge on ech cpcito is 5 C 5 C.5 C.5 C 7. The seption between the pltes of pllel plte cpcito is d. A metl slb of thicknes d/ is inseted between the pltes. The tio of the cpcitnces befoe nd fte the intoduction of the slb is : : : : 8. The bob of simple pendulum of peiod T is given negtive chge. If it is llowed to oscillte bove positively chged plte, the new time peiod will be eul to T moe thn T less thn T infinite 9. A simple pendulum hs length l. The mss of the bob is m. The bob is given chge +. The pendulum is suspended between the pltes of chged pllel plte cpcito which e plced veticlly. If E is the electic field intensity between the pltes, then the time peiod of oscilltes will be Einstein Clsses, Unit No.,, Vdhmn ing od Plz, Viks Pui Extn., Oute ing od

11 PE l / g l g E/m l g E/m l / [g (E/m) ] FINAL STEP EXECISE. Chges nd 8 e plced t the end points A nd B espectively of 9 cm long stight line. A thid chge is plced t point C of AB such tht the potentil enegy of the system is minimum. The distnce C fom A is cm cm 4 cm 5 cm. Two concente, thin metllic sphees of dii nd ( > ) be chges nd espectively. Then the potentil t dius between nd will be (k = /4 ) k k k k. Smll dops of the sme size e chged to v volt ech. If n such dops colesce to fom single lge dop, then its potentil will be nv v/n vn / vn / 4. A solid conducting sphee hving chge is suounded by n unchged concentic conducting hollow spheicl shell. Let the potentil diffeence between the sufce of the solid sphee nd tht of the oute sufce of the hollow shell be V. If the shell is now given chge of, the new potentil diffeence between the sme two sufces is V V 4V V 5. The dius of hollow metllic sphee is. If the potentil diffeence between its sufce nd point t distnce of fom its cente is V, then the electic field intensity t distnce of fom its cente is V/ V/ V/4 V/6 6. Two chged metllic sphees of dii cm nd cm hve 5µC positive chge ech. Now they e connected by conducting wie. The common potentil nd enegy lost e espectively 9 6 V, µj V, 6µJ.8 7 V, 5µJ none of these 7. An electic dipole is plced t the oigin long the x-xis. The electic field t ny point in the x-y plne is long the y-xis fo which position vecto mkes n ngle with the x-xis. Then tn euls to / ½ 8. The mgnitude of the electic field E in the nnul egion of chged cylindicl cpcito is sme thoughout is highe ne the oute cylinde thn ne the inne cylinde vies s /, whee is the distnce fom the xis vies s /, whee is the distnce fom the xis. 9. A metllic sphee is plced in unifom electic field. The lines of foce follow the pth(s) shown in the figue s 4 Einstein Clsses, Unit No.,, Vdhmn ing od Plz, Viks Pui Extn., Oute ing od

12 . Two smll blls hving eul positive chges coulombs on ech e suspended by to insulting stings of eul length L metes fom hook fixed to stnd. The whole set up is tken in stellite into spce whee thee is no gvity (stte of weightlessness). The ngle between the two stings nd the tension in ech sting e espectively PE 6, /, L 6 L, 8 L /, 8. A point chge moves fom point P to point S long the pth PS in unifom electic field E pointing pllel to the positive diection of the X-xis. The coodintes of the point P,, nd S e (, b, ), (,, ), (, b, ) nd (,, ) espectively. The wok done by the field in the bove pocess is given by E L b E b Eb E. Two identicl metllic sphees, septed by cetin distnce, cy chges + nd. The foce between them is F. The sphees e llowed to touch ech othe nd e moved bck to thei initil positions. Now the foce between them is F, then F /F euls to / /4 8. The cpcitnce of pllel plte cpcito is C. Now it is hlf filled with dielectic of constnt K s shown in figue, the new cpcitnce is C. Now the sme cpcitnce is hlf filled with sme dielectic s shown in figue. Then C : C : C euls to K K : : K K K : : K K K : : 4 K K K : : 5 K 4. Two pllel plte cpcitos of cpcitnces C nd C e connected in pllel nd chged to potentil diffeence V. The bttey is then disconnected nd the egion between the pltes of the cpcito C is completely filled with mteil of dielectic constnt K. The potentil diffeence coss the cpcitos now becomes V/(K + ) V/(K + ) 4V/(K + ) 6V/(K + ) 5. Foce between two identicl chges plced t distnce of in vcuum is F. Now slb of dielectic of dielectic constnt K = 4 is inseted between these two chges. The thickness of the slb is /. The foce between the chges will now become F F 4 6. In which cse the pticle my pefom Simple Hmonic Motion negtive chge plced, vey ne to the cente nd on the xis of unifomly positive chged ing. A shot dipole plced in unifom electic field with ny oienttion. F F Einstein Clsses, Unit No.,, Vdhmn ing od Plz, Viks Pui Extn., Oute ing od

13 positive chge plced, vey ne to the cente nd on the xis of unifomly positive chged ing. ll e coect 7. Two -pticles e t est when 4 m pt. They stt moving unde thei electosttic foce of epulsion. The speed of ech -pticle when they e 4 4 m pt is (mss of -pticle = kg).9 8 ms.8 8 ms.4 8 ms 8 ms 8. A block of mss m nd hving chge is plced on smooth hoizontl tble nd is connected to wll though n unstetched sping of sping constnt k s shown in figue. A hoizontl electic field E pllel to the sping is switched on. The mplitude of the esulting SHM of the block nd its time peiod e espectively E m, k k E, k m k E, k none of these m k 9. A dipole is locted in the field of long thed chged with line unifom chge density. In which oienttion the foce cting on dipole is zeo? dipole is plced pllel to the thed. dipole is plced pependicul to the thed. in both oienttions. none of these. The inne of two concentic spheicl shells of dii nd b(b > ) hs chge. The oute sphee is mintined t zeo potentil (ething). The chge on the oute sphee. b/ PE. Two identicl point chges e suspended by insulted stings of eul length. The stings mke n ngle of 6 with ech othe. When suspended in liuid of density.8 gm/cm the ngle emins the sme. The density of the mteil of the sphee is.6 gm/cm. The dielectic constnt of the liuid is A cpcito C is chged to p.d V. The chging bttey is then emoved nd the cpcito is connected to n unchged cpcito C. Let U is the initil stoed enegy in cpcito C, then finl stoed enegy in the combintion is C U C C C C U C C C U C C U C C. A cpcito of µf withstnds mximum voltge of 6 kilovolt while nothe cpcito of µf withstnds mximum voltge of 4 kilovolt. If the two cpcitos e connected in seies, the system will withstnd mximum voltge of kv 4 kv 6 kv 9 kv 4. Fou metllic pltes, ech hving sme e, e plced s shown in figue. The distnce between the consecutive pltes e eul. Altente pltes e connected to points A nd B. Let the euivlent cpcitnce of this system is C. Now the sme fou metllic pltes e nged s shown in figue. Let the euivlent cpcitnce of the system is C Then C /C euls to : : : : 5 5. A pllel plte cpcito with slb of dielectic constnt filling the whole spce between the pltes is chged to cetin potentil nd isolted. Then the slb is dwn out nd nothe slb of eul thickness but dielectic constnt is intoduced between the pltes. The tio of the enegy stoed in the cpcito lte to tht shoed initilly is : : 4 : 9 9 : 4 Einstein Clsses, Unit No.,, Vdhmn ing od Plz, Viks Pui Extn., Oute ing od

14 6. Two identicl pllel plte cpcitos connected in pllel to bttey with switch S closed. The switch is now opened nd the fee spce between the pltes of the cpcitos is filled with dielectic of constnt. The tio of the totl enegy stoed in both cpcitos befoe nd fte the intoduction of the dielectic is 5/ /5 5/ /5 7. A pllel plte cpcito is connected to bttey. The untities chge, voltge, electic field nd enegy ssocited with this cpcito e given by, V, E nd U espectively. A dielectic slb is now intoduced to fill the spce between the pltes with the bttey still in connection. The coesponding untities now given by, V, E nd U e elted to the pevious ones s E V Kd KAV d AV W d K PE 4 9. The cpcities of two conductos e C nd C nd thei espective potentils e V nd V. If they e connected by thin wie, then the loss of enegy will be CC (V V ) (C C ) = V > V E > E U > U 8. A pllel plte cpcito of plte e A nd plte seption d, is chged to potentil diffeence V nd then the bttey is disconnected. A slb of dielectic constnt K is then inseted between the pltes of the cpcito so s to fill the spce between the pltes. If, E nd W denote espectively, the mgnitude of chge on ech plte, the electic field between the pltes (fte the slb is inseted), nd wok done on the system, in uestion, in the pocess of inseting the slb, then CC (V V ) (C C ) CC (V V ) (C C ) ( C C)(V V ) C C AV d ANSWES (INITIAL STEP EXECISE) ANSWES (FINAL STEP EXECISE). c 6. b. b. d.. 7. c. c. d.. d 8. c. d.. d 4. b 9. d d 5. b 5. b 6. d b b 7. d 8. c c 9. d 9. b 9. c.. b Einstein Clsses, Unit No.,, Vdhmn ing od Plz, Viks Pui Extn., Oute ing od

15 AIEEE ANALYSIS []. A chge pticle is plced t the cente O of cube of length L (ABCDEFGH). Anothe sme chge is plced t distnce L fom O. Then the electic flux emeging fom t O is 4 4 ( ) 4 4 PE 5 / zeo / L / L. On moving chge of coulomb by cm, J of wok in done, then the potentil diffeence between the points is. V 8 V V.5 V. If thee e n cpcitos, ech of cpcity C, connected in pllel to V volt souce, then the enegy stoed is eul to The wok done in plcing chge of 8 8 coulomb on condense of cpcity micofd is 4 joule joule 6 joule 6 joule 9. Thee chges, + nd e plced s shown in the figue. The x-component of the foce on is popotionl to CV ncv CV CV n 4. Cpcitnce (in F) of spheicl conducto with dius m is If chge is plced t the cente of the line joining two eul chges such tht the system is in euilibium then the vlue of is / / /4 /4 AIEEE ANALYSIS [] 6. A sheet of luminium foil of negligible thickness is intoduced between the pltes of cpcito. The cpcitnce of the cpcito becomes infinite incese decese emins unchnged 7. A thin spheicl conducting shell of dius hs chge. Anothe chge is plced t the cente of the shell. The electosttic potentil t point P distnce / fom the cente of the shell is b b b b cos sin cos sin. If the electic flux enteing nd leving n enclosed sufce espectively is nd, the electic chge inside the sufce will be ( )/ ( + ) ( ) ( + ) Einstein Clsses, Unit No.,, Vdhmn ing od Plz, Viks Pui Extn., Oute ing od

16 AIEEE ANALYSIS [4/5]. Two spheicl conductos B nd C hving eul dii nd cying eul chges in them epel ech othe with foce F when kept pt t some distnce. A thid spheicl conducto hving sme dius s tht of B but unchged is bought in contct with B, then bought in contct with C nd finlly emoved wy fom both. The new foce of epulsion between B nd C is F/4 F/4 F/8 F/8 [4]. A chged pticle is shot towds nothe chged pticle which is fixed, with speed v. It ppoches upto closest distnce nd then etuns. If wee given speed v, the closest distnce of ppoch would be / /4 [4]. Fou chges eul to e plced t the fou cones of sue nd chge is t its cente. If the system is in euilibium the vlue of is ( ) ( ) 4 4 ( ) ( ) [4] 4. A chged bll B hngs fom silk thed S, which mkes n ngle with lge chged conducting sheet P, s shown in the figue. The sufce chged density of the sheet is popotionl to PE 6 8 L 4 L L L/4 [5] 6. Two thin wie ings wch hving dius e plced t distnce d pt with thei xes coinciding. The chges on the two ings e + nd. The potentil diffeence between the centes of the two ings is zeo 4 d / 4 d d [5] 7. A pllel plte cpcito is mde by stcking n eully spced pltes connected ltentively. If the cpcitnce between ny two djcent pltes is C then the esultnt cpcitnce is C n C (n )C (n + ) C [5] 8. A fully chged cpcito hs cpcitnce C. It is dischged though smll coil of esistnce wie embebded in themlly insulted block of specific het cpcity s nd mss m. If the tempetue of the block is ised T, the potentil diffeence V coss the cpcitnce is mst C mst C mct s mct s [5] AIEEE ANALYSIS [6] sin tn cos cot [5] 5. Two point chges +8 nd e locted t x = nd x = L espectively. The loction of point on the x-xis t which the net electic field due to these two point chges is zeo is 9. Two spheicl conductos A nd B of dii mm nd mm e septed by distnce of 5 cm nd e unifomly chged. If the sphees e connected by conducting wie then in euilibium condition, the tio of the mgnitude of the electic fields t the sufces of sphees A nd B is : : 4 4 : : Einstein Clsses, Unit No.,, Vdhmn ing od Plz, Viks Pui Extn., Oute ing od

17 . Two insulting pltes e both unifomly chged in such wy tht the potentil diffeence between them is V V = V, (i.e. plte is t highe potentils. The pltes e septed by d =. m nd cn be teted s infinitely lge. An electon is elesed fom est on the inne sufce of plte. Wht is its speed when it hits plte? PE 7 4. Chges e plced on the vetices of sue s shown. Let E be the electic field n V the potentil t the cente. If the chges on A nd B e inte chnged with those on D nd C espectively, then.87 6 m/s 9 m/s.65 6 m/s 7. m/s. An electic dipole is plced t n ngle of to non-unifom electic field. The dipole will expeience toue s well s tnsltionl foce toue only tnsltionl foce only in the diection of the field tnsltionl foce only in diection noml to the diection of the field AIEEE ANALYSIS [7]. An electic chge µc is plced t the oigin (, ) of X Y co-odintes system. Two points A nd B e situted t (, ) nd (, ) espectively. The potentil diffeent between the points A nd B will be 4.5 volt zeo 9 volt volt. A bttey is used to chge pllel plte cpcito till the potentil diffeence between the pltes becomes eul to the electomotive foce of the bttey. The tio of the enegy stoed in the cpcito nd the wok done by the bttey will be 4 E chnges, V emins unchnged E emins unchnged, V chnges Both E nd V chnge E nd V emin unchnged 5. The potentil t point x (mesued in µm) due to some chges situted on the x-xis is given by V(x) = /(x 4) volt. The electic field E nd x = 4 µm is given by /9 volt/µm nd in the +ve x diection 5/ volt/µm nd in the ve x diection 5/ volt/µm nd in the +ve x diection /9 volt/µm nd in the ve x diection 6. A pllel plte condense with dielectic of dielectic constnt K between the pltes hs cpcity C nd is chged to potentil V volt. The dielectic slb is slowly emoved fom between the pltes nd then einseted. The net wok done by the system in this pocess is zeo (K )CV CV (K ) / K ( K )CV 7. If g E nd g M e the cceletions due to gvity on the sufces of the eth nd the moon espectively nd if Millikn s oil dop expeiment could be pefomed on the two sufce, one will find the tio electonicchgeon themoon electonicchngeon theeth g m /g E g E /g M ANSWES (AIEEE ANALYSIS )... b d 6. d b 9. d.. d. d. b 4. b 5. c 6. d 7. c 8. b 9.. c.. b c Einstein Clsses, Unit No.,, Vdhmn ing od Plz, Viks Pui Extn., Oute ing od

18 PE 8 TEST YOUSELF. The tio of the electic foce between two electons to the gvittionl foce between them is of the ode of A pticle A hs chge + nd pticle B hs chge +4, ech hving the sme mss m. When llowed to fll fom est though the sme electic potentil diffeence, the tio of the speed of A to tht of B will be : : 4 : : 4. The insultion popety of i beks down when the electic field is 6 V/m. The mximum chge tht cn be given to sphee of dimete 5 m is ppoximtely C C 4 C 5 C 4. The dii of two sphees foming spheicl cpcito e.5 m nd.6 m. If medium of dielectic constnt 6 is completely filled in between, the cpcity of the cpcito will be. F 9 F F 8 F 5. Two pticles A nd B, ech hving chge, e plced distnce d pt. Whee should pticle of chge be plced on the pependicul bisecto of AB fom its mid-point so tht it expeiences mximum foce? d d d/ d 6. A thin conducting ing of dius hs n electic chge +. The chge is distibuted unifomly ove the ing. A point chge + is plced t the cente of the ing. The intection foce between the chged pticle nd the ing is 8. A cpcito hving cpcity of. micofd is chged up to V nd its pltes e joined to wie. The het poduced in joule will be An infinite numbe of chges, ech eul to coulomb, e plced long the x-xis t x (in metes) =,, 4, 8,...nd so on. The potentil nd field in SI units t x = due to this set of chges e espectively /4 times, 4,4 4,, 4/. Thee chges,, e locted t the vetices of n euiltel tingle. At the cicumcente of the tingle field is zeo but potentil is non-zeo field is non-zeo but potentil is zeo both field nd potentil e zeo both field nd potentil e non-zeo k k 4k 7. A pllel plte cpcito is chged to cetin p.d. A slb of thickness mm is inseted between the pltes nd it becomes necessy to incese the distnce between the pltes by.4 mm to mintin the sme p.d. The dielectic constnt of the slb is b. b 4. b 5. c ANSWES b 8. c 9. d. b Einstein Clsses, Unit No.,, Vdhmn ing od Plz, Viks Pui Extn., Oute ing od