Einstein Classes, Unit No. 102, 103, Vardhman Ring Road Plaza, Vikas Puri Extn., Outer Ring Road New Delhi , Ph. : ,

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1 PE ELECTOSTATICS C Popeties of chges : (i) (ii) (iii) (iv) (v) (vi) Two kinds of chges eist in ntue, positive nd negtive with the popety tht unlike chges ttct ech othe nd like chges epel ech othe. Ecess 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. Pctice Poblems : On chging neutl body, the mss of the body will chnge.. Conside neutl body A nd chged body B on which µc chge eists. Fom the body B 6.5 electons e etcted nd supplied to the body A. Then the chge on body A will become µc the chge on body B will become 9 µc the mss of body A will incese the mss of body B will be moe thn the mss when it is neutl Answes : [(), b, c, d] C Electic field : It is vecto untity. The mgnitude of electic field due to point chge t the distnce is given by k. It is defined fo point chge s follows : Due to positive chge k (OP) E OP OP, OP ( )î (y y)ĵ (z z)kˆ OP ( Due to negtive chge ) (y y) (z z) k E (OP) PO PO, PO OP Hee k whee 4 is known s bsolute pemittivity constnt nd is known s eltive pemittivity o dielectic constnt of the medium. The vlue of = 8.85 C /Nm nd k = 9 9 Nm /C Pinciple of supeposition : 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 E... Einstein Clsses, Unit No.,, Vdhmn ing od Plz, Viks Pui Etn., Oute ing od New Delhi 8, Ph. : 9695, 857

2 Pctice Poblems : PE. 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 +, e plced on five vetices of egul hegon of side L metes. The mgnitude of the foce on point chge of vlue plced t the cente of the hegon is 5k /L k /L k /L. (n ) numbe of eul chges, ech of chge, e plced t the cones of egul polygon of side length. The net electic field t the cente of the polygon is 4k sin n 4kcos n 4ktn n 4kcot 4. Two chges of eul vlues (ech hs the vlue ) e plced distnce d pt. The mimum vlue of electic field on the pependicul bisecto of the line joining them is n 6k / d [Answes : () d () c () (4) ] 8k / d 4k / d k / d C Electic field fo continuous chge distibution. Apply the following steps to clculte the electic field t the concened point due to continuous chge distibution. Tke the diffeentil element nd clculte the chge on this element. Fo line chge distibution, d = dl, whee is the chge pe unit length. Fo sufce chged distibution = da, whee is the chge pe unit e. Fo volume chge distibution d = dv, whee is the chge pe unit volume. Clculte the electic field t the concened point due to diffeentil element ( de ) Tke the components of de, if possible Pctice Poblem : Integte with pope limits.. Find the electic field due to following configution : (i) due to unifomly chged od of chged pe unit length nd length L t distnce fom one of the end of the od long the length of the od (ii) due to unifomly chged od of chged pe unit length nd length L t distnce fom mid-point of the od long the pependicul bisecto (iii) due to ing of dius with unifom chge distibution on the is t the distnce fom the cente (iv) due to unifomly chged disc of dius with sufce chge density on the is of the disc t the distnce fom the cente (v) due to long thin wie of unifom line chge density t pependicul bisecto t the distnce fom the wie. Einstein Clsses, Unit No.,, Vdhmn ing od Plz, Viks Pui Etn., Oute ing od New Delhi 8, Ph. : 9695, 857

3 PE C4 Coulomb Foce : E, whee is the test chge plced in the etenl electic field E. Column C5 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. 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 whee is the m 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 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 downwd, ne mg upwd, ne downwd, mg ne. Which of the following pth of chge pticle is possible in unifom electic field? Stight pth Pbolic pth Cicul pth Hypebolic pth [Answes : () b (), b] C6 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. Pctice Poblems :. Dw the ptten of electic lines of foces fo the following : positively chged spheicl conducto negtive chge plced t the cente of spheicl conducting shell positive chge plced t ny point inside hollow conducting sphee C7 Electic flu : Electic flu is popotionl to the numbe of electic field lines tht penette sufce. The electic flu though sufce is defined by the epession 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. Einstein Clsses, Unit No.,, Vdhmn ing od Plz, Viks Pui Etn., Oute ing od New Delhi 8, Ph. : 9695, 857

4 PE 4 C8 Guss s Lw : Guss s Lw sys tht the net electic flu though ny closed gussin sufce is eul E C9 to the net chge inside the sufce divided by : E E.dA clculte the electic field due to vious symmetic chge distibutions. Appliction of Guss s Lw to symmetic chge distibutions in. Using Guss s lw, one cn Guss s Lw is useful in detemining electic fields when the chge distibution hs high degee of symmety. The sufce should lwys be chosen to tke dvntge of the symmety of the chge distibution, so tht we cn emove E fom the integl nd solve fo it. The gol in this type of clcultion is to detemine sufce tht stisfies one o moe of the following conditions :. The vlue of the electic field cn be gued by symmety to be constnt ove the sufce.. The dot poduct cn be epessed s simple lgebic poduct E da becuse E nd da e pllel.. The dot poduct is zeo becuse E nd da e pependicul. 4. The field cn be gued to be zeo eveywhee on the sufce. Pctice Poblems :. The electic chge is plced t the cente of cube of side. The electic flu though one of its fces will be 6 4. Electic chge is plced t the cone of cube. The electic flu though the opposite fce of the cube is [Answes : () () d] C Electic Field due to specil type of configution :. A ing of Chge E 4 E y =, / ( ). At the Cente due to secto of ing E sin 4 4, E ( cos) y Einstein Clsses, Unit No.,, Vdhmn ing od Plz, Viks Pui Etn., Oute ing od New Delhi 8, Ph. : 9695, 857

5 . A Disc of Chge PE 5 E 4. Infinite Sheet of Chge 5. Infinitely Long Line of Chge E density, whee is the sufce chge 6. Finite Line of Chge E,E, whee is the line chge density E 4 [cos cos], E 4 sin sin 7. A Spheicl Volume Chge Distibution (non-conducting solid sphee) 8. Spheicl Conducto (Hollow o Solid) E,E 4 is volume chge density 4 4 E = <, E Einstein Clsses, Unit No.,, Vdhmn ing od Plz, Viks Pui Etn., Oute ing od New Delhi 8, Ph. : 9695, 857

6 Pctice Poblems : PE 6. A sphee of dius hs unifom volume chge distibution. At distnce fom its cente, fo <, the electic field is diectly popotionl to / /. Conside two non-conducting solid sphees of unifom volume chge distibution with some pt ovelped with ech othe. One of the sphee hs positive chge nd nothe hs negtive chge but the mgnitude of volume chge density e eul. The electic field in the ovelped pt is unifom eveywhee non-unifom diected fom cente to cente of the sphees none. The electic field inside the cylindeicl cvity of non-conducting unifom volume cylindeicl chged distibution is zeo eveywhee unifom eveywhee non-unifom eveywhee none 4. A thin tunnel is mde long the dimete of unifom spheicl volume negtive chged distibution of chged density. A positive chge nd mss m is elesed inside the tunnel. If the chge pefomes SHM then the time peiod of this chge pticle is m m m m [Answes : () c (), c (), b (4) ] C 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 C4 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 4 k Einstein Clsses, Unit No.,, Vdhmn ing od Plz, Viks Pui Etn., Oute ing od New Delhi 8, Ph. : 9695, 857

7 PE 7. A positive chge is plced t the cente of the cicle of dius. Anothe negtive chge nd mss m is moving with cetin speed ound this cicul pth. Then the speed of the chged pticle is k m the totl enegy of the chged pticle is k the line momentum of chged pticle is vible the ngul momentum of chged pticle bout the cente of the cicle emins constnt. The closest distnce of ppoch of n -pticle (elesed fom vey lge distnce) of enegy E fom fied nucleus of tomic numbe Z. kze E kze E kze E 4kZe E [Answes : () (), b, c, d () ] C5 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 eists nd it is found tht the enegy stoed in the field pe unit volume is given by E. Pctice Poblems :. Conside spheicl chged conducto of totl chge nd dius. Then the enegy contined inside the conducto is zeo the totl enegy stoed in the spce is k fction of the enegy stoed in the spheicl shell of inne dius nd oute dius is.5 ll the bove. Conside spheicl unifom volume chged distibution of totl chge nd dius. Then the enegy contined inside the sphee is k the fction of enegy stoed outside the sphee is 6 5 fction of the enegy stoed in the spheicl shell of inne dius nd oute dius is.5 ll the bove [Answes : () d (), b] C6 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 etenl 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. Einstein Clsses, Unit No.,, Vdhmn ing od Plz, Viks Pui Etn., Oute ing od New Delhi 8, Ph. : 9695, 857

8 PE 8 C7 The potentil V due to point chge t distnce, C8 Potentil due to collection of point chges, V k C9 whee potentil will be clculted. Potentil due to continuous chge distibution i k V i i, whee i is the distnce of chge i t the point Fo given continuous chge distibution, define diffeentil element of chge, find its potentil t the concened point, nd by using the following eution find the potentil of ll the chge elements, kd V. Cy out integtion, using ppopite limits to include the entie chge distibution. In the integl be ceful bout which geometic untities vy nd which e constnt. Electic potentil due to specil type of chge distibution. A ing of Chge V 4. A Disc of Chge V. A sphee of Chge V 8 8, V 4 4. Conducting Sphee (Hollow o Solid) V, V 4 4 Einstein Clsses, Unit No.,, Vdhmn ing od Plz, Viks Pui Etn., Oute ing od New Delhi 8, Ph. : 9695, 857

9 Pctice Poblems : PE 9. An -pticle nd poton e cceleted though the sme potentil diffeence. The tio of speed cuied by the two pticles. : : : :. Two point chges +4µC nd 6µC e septed by distnce of cm in i. The numbe of points on the line joining the two chges t which the electic potentil zeo 4. The wok done to cy chge pticle of +nc fom infinity to the cente of the sue of side m, which cies t its fou cones chges of + nc, + nc, nc nd nc espectively. 6 nj nj 8 nj nj 4. A cube of side b hs chge t ech of its vetices. The potentil due to this chge y t the cente of the cube.is 4/ b / b / b 6/ b [Answes : () () b () c (4) C 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 dv potentils t nd b. In diffeentil fom, we hve E ˆ d Pctice Poblems :. Find the electosttic potentil due to : b b E.d unifomly chged hollow sphee of dius inside nd outside spheicl conducto of dius inside nd outside whee V nd V b e the non-conducting sphee of dius with unifom volume chge distibution inside nd outside In ech cse the totl chge is. Also dw the vition of potentil with distnce in ech cse.. Conside points A, B nd C in unifom electosttic field s shown. Then the potentil is minimum t A B C none. In spce the electic potentil is chnging with distnce ccoding to V = k. The electic field hs the vition with distnce s line constnt pbolic hypebolic Einstein Clsses, Unit No.,, Vdhmn ing od Plz, Viks Pui Etn., Oute ing od New Delhi 8, Ph. : 9695, 857

10 PE 4. The electosttic potentil V is chnging with distnce ccoding to the following gph. Then The electic field with distnce emins constnt The electic field with distnce continuously incesing Fo some distnce the electic field will be constnt, fo some distnce it will be zeo nd then it will become constnt The electic field will chnge its diection 5. A metl sphee with chge is suounded by n unchged concentic thin spheicl shell. The potentil diffeence between them is V. If the shell is now given n dditionl chge, wht is the new potentil diffeence between them? V V/ zeo V [Answes : () c () (4) c, d (5) ] C 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 A B C eul t ll points [Answes : () b] 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 fied 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 eist inside conducto Einstein Clsses, Unit No.,, Vdhmn ing od Plz, Viks Pui Etn., Oute ing od New Delhi 8, Ph. : 9695, 857

11 PE. 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 V k,. k V k k 9. Foce cting on conducting sufe : The foce df cting on smll element of e ds of the conducto whee the locl chge density is, is given by df = Pctice Poblems :. Two chged conducting sphees of dii nd b e connected to ech othe by wie. Wht is the tio of electic fields t the sufces of the two sphees? Use the esult obtined to eplin why chge density on the shp nd pointed ends of conducto is highe thn on its fltte potions.. Conside two concentic sphees of dii nd with sme sufce chged density. Find (e) (f) (g) totl chge on ech sphee potentil t the common cente potentil t ny point inside the fist sphee potentil of fist sphee potentil t ny point between the two sphees t the distnce fom the cente potentil of oute sphee potentil t ny point outside t the distnce fom the cente. How the chge cn be tnsfeed fom one sphee to nothe sphee completely? 4. A spheicl conducting shell of inne dius nd oute dius hs chge. A chge is plced t the cente of the shell. Wht is the sufce chge density on the inne nd oute sufce of the shell? Is the electic field inside cvity (with no chge) zeo, even if the shell is not spheicl, but hs ny iegul shpe? Eplin. ds [Answes : () b/ () 4, 6 k k k (e) 4k 8k (f) k (g) k (4) /(4 ), ( + )/(4 )] Einstein Clsses, Unit No.,, Vdhmn ing od Plz, Viks Pui Etn., Oute ing od New Delhi 8, Ph. : 9695, 857

12 C PE 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 cones of n isoseceles ight ngle tingle of totl peimete ( + )l. Eul chges e plced t the cones of lgest length. The mgnitude of the electic dipole moment of the system is l l l 4 l [Answes : () b] C4 C5 Electic field due to dipole (i) Along the Ais : The electic field intensity long the is lwys point in the diection of the kp dipole. It mgnitude is given by E. (ii) Along the Bisecto : The diection of electic field long the bisecto is lwys opposite to the kp y dipole moment. Mth emeticlly, Electic potentil due to dipole E (i) (ii) kp Along the Ais : The electic potentil long the -is is given by V Pctice Poblems : Along the Bisecto : The electic potentil long the bisecto is lwys zeo.. A given chge situted t cetin distnce fom shot electic dipole in the end-on position epeiences 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 is nd E be tht on the ight bisecto t the sme distnce fom the dipole, then E E = E E = E E = E. A negtive chge nd mss m is elesed t the cetin distnce d fom shot dipole of dipole moment p on the is. Find initil cceletion speed when the distnce will become hlf 4. A chged pticle of chge nd mss m is pojected with cetin speed u fom point on the pependicul bisecto of the dipole of dipole moment p. Afte cetin time it psses though the point lying on the is of the dipole t the distnce fom the dipole. Find the speed t this moment. E kp [Answes : () d () b () md 6kp md kp (4) u ] m C6 Dipole in n etenl electic field :. The net foce epeienced by dipole in n etenl unifom electic field is zeo.. When n electic dipole of dipole moment p is plced in n electic field E, the field eets toue on the dipole : p E. Einstein Clsses, Unit No.,, Vdhmn ing od Plz, Viks Pui Etn., Oute ing od New Delhi 8, Ph. : 9695, 857

13 PE. 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 d. Pctice Poblems :. 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 mimum 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. A shot dipole is plced long the is of cicul unifomly chged ing vey ne to the cente. Then the foce cting on the dipole is constnt diectly popotionl to distnce of the dipole fom cente zeo invesely popotionl to distnce of the dipole fom cente [Answes : () () () ] Einstein Clsses, Unit No.,, Vdhmn ing od Plz, Viks Pui Etn., Oute ing od New Delhi 8, Ph. : 9695, 857

14 PE 4 SINGLE COECT CHOICE TYPE. The distnce between two fied positive chges 4e nd e is l. A chge is plced long the line joining the two fied chges. It hs been found tht this chge is in stble euilibium fo longitudnl displcements. The position nd sign of this chge is l/ fom e nd negtive sign l/ fom 4e nd negtive sign l/ fom e nd positive sign l/ fom 4e nd positive sign. A chge is divided into two pts nd the two pts e septed by cetin distnce d. Then the mimum foce between them will be k 4d k d k d k d. 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 4. 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 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 6. 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 t m E t m E t 4m 7. 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 8. 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 9. 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 / Einstein Clsses, Unit No.,, Vdhmn ing od Plz, Viks Pui Etn., Oute ing od New Delhi 8, Ph. : 9695, 857

15 . Two identicl thin ings, ech of dius metes, e coilly 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 ). 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. 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 4. 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 5. An electic dipole is plced t the oigin long the -is. The electic field t ny point in the -y plne is long the y-is fo which position vecto mkes n ngle with the -is. Then tn euls to / ½ 6. 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 7. 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 PE 5 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 is vies s /, whee is the distnce fom the is. 9. A metllic sphee is plced in unifom electic field. The lines of foce follow the pth(s) shown in the figue s 4. Two smll blls hving eul positive chges coulombs on ech e suspended by insulting stings of eul length L metes fom hook fied 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 6, /,, 8 L L 6 /, 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-is. 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 L L Einstein Clsses, Unit No.,, Vdhmn ing od Plz, Viks Pui Etn., Oute ing od New Delhi 8, Ph. : 9695, 857

16 PE 6 E 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. A dop of wte of mss 8 g flls wy fom the bottom of chged conducting sphee of dius cm, cying with it chge of 9 C nd leving on the sphee unifomly distibuted chge of.5 6 C. The speed of the dop fte it hs fllen cm is..66 m/s.66 m/s.66 m/s 4.66 m/s 4. Foce between two identicl chges plced t distnce of in vcuum is F. Now slb 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 5. 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 6. If n electon entes into spce between the pltes of pllel plte cpcito t n ngle with the pltes nd leves t n ngle to the pltes. The tio of its kinetic enegy while enteing the cpcito to tht while leving will be F F cos cos sin sin cos cos sin sin 7. A chge + is fied t ech of the points =, =, = 5,...d inf. on the -is nd chge is fied t ech of the points =, = 4, = 6,...d inf. Hee is positive constnt. Tke the electic potentil t point due to chge t distnce fom it to be /(4 ). Then, the potentil t the oigin due to the bove system of chges is 8 ln 4 ln 8. One end of cm long silk thed is fied 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 n ngle of 6 with the veticl. The sufce chge density on the plte in µc/m is A point chge is plced t distnce of fom the cente of n unchged conducting sphee of dius (< ). The potentil t ny point on the sphee is zeo 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 Einstein Clsses, Unit No.,, Vdhmn ing od Plz, Viks Pui Etn., Oute ing od New Delhi 8, Ph. : 9695, 857

17 . 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. A block of mss m nd hving chge is plced on smooth hoizontl tble nd is connected to wll though n unstessed 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. 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 sufce of oute sphee is b/ 4. In the bove poblem, let the potentil diffeence between the inne sphee nd oute sphee befoe ething is V nd fte ething is V. Then PE 7 ANSWES (SINGLE COECT CHOICE TYPE). c.. b b 6. c 7. b c. d. b.. d 4. d c 7. d 8. c 9. d.. d. d. c 4. b b 7. d b.. b.. 4. V = V V > V V > V V V Einstein Clsses, Unit No.,, Vdhmn ing od Plz, Viks Pui Etn., Oute ing od New Delhi 8, Ph. : 9695, 857

18 PE 8 EXCECISE BASED ON NEW PATTEN COMPEHENSION TYPE Compehension- A pticle of mss 5 6 g is kept ove lge hoizontl sheet of positive chge of density 4. 6 C/m.. The ntue of chge on this pticle so tht if elesed, it does not fll down positive negtive my be positive o negtive none. The numbe of electons on this pticle.4 6 in ecess.4 6 in less.4 4 in ecess.4 4 in less. The chnge in mss of this pticle is. 4 kg. 4 kg.9 4 kg.9 4 kg Compehension- A positive chge of 4 8 C is distibuted unifomly on the sufce of sphee of dius cm. It is coveed by concentic, hollow conducting sphee of dius 5 cm. 4. The electic field t point cm wy fom the cente is 9 4 N/C 9 6 N/C 9 N/C 9 5 N/C 5. A negtive chge of 6 8 C is plced on the hollow sphee. The sufce chge density on the oute sufce of the hollow sphee is the electic field outside the hollow sphee will chnge. ll e coect Compehension- Afte the powe souce is cut-off, sphee A with dius of cm chged to potentil of kv is connected by mens of wie fist to emote unchged sphee B nd then, fte it is disconnected fom B, to emote unchged sphee C. The dii of the sphee C nd B e cm. 7. The initil enegy of sphee A is 5 5 J J.5 5 J.5 5 J 8. The wok of dischge duing connection of A nd B is 5 5 J J.5 5 J.5 5 J 9. The wok of dischge duing connection of A nd C is 5 5 J J.5 5 J.5 5 J Compehension-4 A chge is unifomly distibuted on the sufce of n nnul disc of inne dius nd oute dius. A chge pticle of mss m nd chge is elesed fom est t point on the is of the disc f fom the cente of the disc.. The vition of electic field due to this disc on the is ne the cente is constnt line eponentil none of these. The speed with which the pticle will ech the cente of the disc is 6 C/ m 4 6 C/ m m( ) 6 6 C/ m 8 6 C/ m 6. Now the oute sufce is gounded then choose the coect sttement : the sufce chge density on the inne sphee will emin sme. the potentil diffeence between the ` inne nd oute sphee will emin sme. 4 m( m( m( ) ) ) Einstein Clsses, Unit No.,, Vdhmn ing od Plz, Viks Pui Etn., Oute ing od New Delhi 8, Ph. : 9695, 857

19 . The peiod of smll oscilltions if the chged pticle is elesed ne the cente of the ing PE 9 m ( ) 4 m ( ) none of these 4 Compehension-5 m ( ) m ( ) Two fied chges nd e locted t the points with co-odinte (, ) nd (, ) espectively in the -y plne.. The locus of the points in the -y plne whee the electic potentil due to the two chges is zeo A line A cicle An ellipse Hypebol 4. Let the potentil V () t genel point on the -is then which of the following gph will epesent the vition of V () on the whole -is? 5. If pticle of chge + stts fom est fom the point (5, ). Afte cetin time it hs been found tht the pticle is cossing though the point (9, ). At this point the pticle hs the kinetic enegy K nd potentil enegy U then K =, U K, U = K, U K =, U = MATIX-MATCH TYPE Mtching- Column - A Column - B (A) Electosttic Field (P) zeo (B) Wok done by the electic () non-zeo (C) field fo closed pth The electic potentil t the cente of the chged () cnnot be ing detemined (D) The electic field t the (S) consevtive cente of the unifom spheicl volume chge distibution (T) mechnicl enegy is conseved Mtching- Column A Column B (A) Electic lines of foces (P) cnnot intesect (B) Euipotentil sufces () cnnot closed cuves (C) Gvittionl lines of () cn intesect foces (D) Stem line cuves (S) cn closed in fluids cuves (T) none of these Einstein Clsses, Unit No.,, Vdhmn ing od Plz, Viks Pui Etn., Oute ing od New Delhi 8, Ph. : 9695, 857

20 Mtching- Column A Column B (A) (P) vition of electic field due to unifom volume chge distibution (B) () vition of potentil due to unifom volume chge distibution (C) () vition of potentil due to spheicl conducto (D) (S) vition of (T) field due to spheicl conducto vition of field due to infinite line chged. Mtching-4 PE Fou identicl chges ech of chge e plced t (,, ), (,, ), (,, ) nd (,, ) Column A Column B (A) Electic potentil t the (P) oigin (B) Electic field t the () 4 oigin k 4k (C) Mimum electic field () (D) Mimum electic (S) none potentil MULTIPLE COECT CHOICE TYPE. An infinite numbe of chges, ech eul to coulomb, e plced long the -is t (in metes) =,, 4, 8,...nd so on. Let the potentil nd field in SI units t = due to this set of chges e espectively y nd 4 4. Then = y = 4/ = 4/ y =. Thee chges,, e locted t the vetices of n euiltel tingle. At the cicumcente of the tingle field is zeo potentil is non-zeo potentil is zeo field is non-zeo. Two point chges + nd e held fied t ( d, ) nd (d, ) espectively of (, y) co-odintes system, then : The electic field E t ll points on the -is hs the sme diection. E t ll points on the Y-is is long i No wok hs to be done in binging test chge fom infinity to the oigin The dipole moment is d diected long negtive -is Einstein Clsses, Unit No.,, Vdhmn ing od Plz, Viks Pui Etn., Oute ing od New Delhi 8, Ph. : 9695, 857

21 4. In which cse the pticle my pefom Simple Hmonic Motion PE foce epeienced by one coulomb chge t = m will be N negtive chge plced, vey ne to the cente nd on the is of unifomly positive chged ing. A shot dipole plced in unifom electic field with ny oienttion. positive chge plced, vey ne to the cente nd on the is of unifomly positive chged ing. A negtive chge plced inside the positive unifom volume chge distibution 5. A positively chged thin metl ing of dius is fied in the y-plne with its cente t the oigin O. A negtively chged pticle P is elesed fom est t the point (,, z ) whee z >. Then the motion of P is. peiodic, fo ll vlues of z stisfying < z < simple hmonic, fo ll vlues of z stisfying < z ppoimtely simple hmonic, povided z < < such tht P cosses O nd continues to move long the negtive z-is towds z =. 6. An ellipsodil cvity is cuved within pefect conducto. A positive chge is plced t the cente of the cvity. The points A nd B e on the cvity sufce s shown in the figue. Then : the foce epeienced by the bove chge will be towds + is unifom electic field eists in this egion long the -is. 8. A pticle of mss m, chge is f wy fom nothe fied pticle of chge. If the fist pticle stts moving towds the fied pticle with speed v, the minimum seption between the two pticles is popotionl to m v 9. A conducting sphee of dius, cying chge, lies inside unchged conducting shell of dius. If they e joined by metl wie, v / chge will flow fom the sphee to the shell / chge will fom fom the sphee to the shell chge will flow fom the sphee to the shell k mount of het will be poduced 4. A simple pendulum of length L hs bob of mss m, with chge on it. A long veticl sheet of chge, with chge pe unit e, psses though the point of suspension of the pendulum. At euilibium, the sting mkes n ngle with the veticl. Its time peiod of oscilltion is T in this position. Then tn mg tn mg electic field ne A in the cvity = electic field ne B in the cvity T L / g T L / g chge density t A = chge density t B potentil t A = potentil t B totl electic field flu though the sufce of the cvity is / 7. The electic potentil in egion long the X-is vies with ccoding to the eltion V() = Then potentil diffeence between the points = nd = is 5 volt. Fou identil chges e plced t the point (,, ), (,, ), (,, ) nd (,, ). The potentil t the oigin is zeo The field t the oigin is zeo The potentil t ll points on the z-is, othe thn the oigin, is zeo The field t ll points on the z-is, othe thn the oigin, cts long the z-is. Einstein Clsses, Unit No.,, Vdhmn ing od Plz, Viks Pui Etn., Oute ing od New Delhi 8, Ph. : 9695, 857

22 . Fou chges, ll the sme mgnitude, e plced t the fou cones of sue. At the cente of the sue, the potentil is V nd the field is E. By suitble choices of the signs of the fou chges, which of the following cn be obtined? V =, E = V =, E V, E = V, E. A deuteon nd n -pticle e plced in n electic field. The foces cting on them e F nd F, nd thei cceletions e nd espectively. F = F F F = 4. Two identicl chges + e kept fied some distnce pt. A smll pticle P with chge is plced midwy between them. If P is given smll displcement, it will undego simple hmonic motion if is positive nd is long the line joining the chges. is positive nd is pependicul to the line joining the chges. is negtive nd is pependicul to the line joining the chges. is positive nd is long the line joining the chges. 5. A ing with unifom chge nd dius, is plced in the yz plne with its cente t the oigin. The field t the oigin is zeo The potentil t the oigin is k The field t the point (,, ) is The field t the point (,, ) is k. k 6. Let V nd E be the potentil nd the field espectively t point. Which of the following ssetions e incoect? If V =, E must be zeo If V, E cnnot be zeo If E, V cnnot be zeo None of these 7. Two lge, pllel conducting pltes e plced close to ech othe. The inne sufces of the two pltes hve sufce chge densities + nd. The PE oute sufce e without chge. The electic field hs mgnitude of / in the egion between the pltes / in the egion between the pltes / in the egion outside the pltes zeo in the egion outside the pltes 8. A conducting sphee A of dius, with chge, is plced concenticlly inside conducting shell B of dius b. B is ethed. C is the common cente of A nd B. The field t distnce fom C, whee b, is k The potentil t distnce fom C, whee b, is k The potentil diffeence between A nd B is k b The potentil t distnce fom C, whee b, is k b Assetion-eson Type Ech uestion contins STATEMENT- (Assetion) nd STATEMENT- (eson). Ech uestion hs 4 choices (A), (B), (C) nd (D) out of which ONLY ONE is coect. (A) (B) (C) (D) Sttement- is Tue, Sttement- is Tue; Sttement- is coect eplntion fo Sttement- Sttement- is Tue, Sttement- is Tue; Sttement- is NOT coect eplntion fo Sttement- Sttement- is Tue, Sttement- is Flse Sttement- is Flse, Sttement- is Tue. STATEMENT- : In unifom electic field pis of points septed by the sme distnce must hve the sme potentil diffeence STATEMENT- : Electic lines of foces e othogonl to the euipotentil sufces. STATEMENT- : Wok done by the electosttic field is independent of the pth tken STATEMENT- : Electosttic field is consevtive in ntue Einstein Clsses, Unit No.,, Vdhmn ing od Plz, Viks Pui Etn., Oute ing od New Delhi 8, Ph. : 9695, 857

23 . STATEMENT- : Guss lw is not vlid fo the moving chge to clculte the electic flu STATEMENT- : Guss lw is deived fom the coulombs lw 4. STATEMENT- : A bigge positive chged sphee cn ttct neutl sphee plced outside the bigge sphee STATEMENT- : Like point chges lwys epel ech othe 5. STATEMENT- : A smll metl bll is suspended in unifom electic field with the help of insulted thed. If electomgnetic wves of high enegy incident on the bll then it will be deflected long the diection of the electic field. The ngle of deflection with the veticl will initilly chnge nd fte some time it will become constnt. STATEMENT- : The bll becomes positive chged due to the incidence of electomgnetic wves nd fte some time this chge will become constnt. 6. STATEMENT- : The tjectoy of the chged pticle lwys coincides with the lines of the foces. STATEMENT- : A sttiony chged pticle hs the line motion in unifom electic field PE 7. STATEMENT- : In the conducting mteil the electic field is lwys zeo STATEMENT- : The electic field due to conducto is noml to the conducting sufce t electosttic euilibium. 8. STATEMENT- : The electic flu due to electic dipole enclosed by ny type of gussin sufce is lwys zeo STATEMENT- : The electic flu depends only on the lgebic sum of the chges contined in the gussin sufce. 9. STATEMENT- : In unifom electic field point chge cn hve stight pth o pbolic pth STATEMENT- : The electic foce in unifom electic field is lwys pependicul to the diection of motion of the chged pticle. STATEMENT- : A point chge is plced outside the unchged conducting sphee t distnce. Thee is no electic field due to chged distibution on the sphee t the cente. STATEMENT- : The net electic field t ny point inside the sphee is zeo. (Answes) EXCECISE BASED ON NEW PATTEN COMPEHENSION TYPE.. b. b 4. d d c 9. d. b.. d. b b MATIX-MATCH TYPE. [A-S, T ; B-P ; C- ; D-P]. [A-P, ; B-P, S ; C-P, ; D-P, ]. [A- ; B-P ; C-S ; D-T] 4. [A- ; B-P ; C-S ; D-] MULTIPLE COECT CHOICE TYPE., b. c, d. b, c, d 4., d 5., c 6. c, d 7., b, c 8., b, d 9. c, d. b, d. b, d., b, c, d. b, c 4., c 5., b 6., b, c 7. b, d 8., c, d ASSETION-EASON TYPE. D. A. D 4. B 5. A 6. D 7. D 8. A 9. C. D Einstein Clsses, Unit No.,, Vdhmn ing od Plz, Viks Pui Etn., Oute ing od New Delhi 8, Ph. : 9695, 857

24 PE 4 INITIAL STEP EXECISE (SUBJECTIVE). Two coppe sphees of dii = cm nd = cm e connected to souce of emf E =, V. Clculte the foce cting between them if thei centes e = m pt.. A chged thin unifom non-conducting wie bcd with chge pe unit length is bent into the fom shown in figue. The wie b nd cd e vey long. Find out the intensity of the electic field t the point O.. Thee identicl metl pltes with lge sufce es e kept pllel to ech othe s shown in figue. The leftmost plte is given chge, the ightmost chge nd the middle one emins neutl. Find the chge ppeing on the oute sufce of the ightmost plte. 4. One end of cm long silk thed is fied 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. (i) Find the tension in the sting in euilibium. (ii) Suppose the bll is slightly pushed side nd elesed. Find the time peiod of the smll oscilltions. 5. A long cylindicl wie cies positive chge of line density. An electon of chge e evolves ound it in cicul pth unde the influence of the ttctive electosttic foce. Pove tht kinetic enegy of the electon is independent of the dius? 6. A long cylindicl volume contins unifomly distibuted chge of density. Find the electic field t point P inside nd outside the cylindicl volume t distnce fom its is. The dius of the cylinde is. Also dw the vition of E with espect to. 7. A chge is plced t the cente of n unchged, hollow metllic sphee of dius. Find the sufce chge density on the inne sufce nd on the oute sufce. If chge is put on the sphee, wht would be the sufce chge densities on the inne nd the oute sufces? Find the electic field inside the sphee t distnce fom the cente in the situtions nd. E 8. The electic field in egion is given by E i. l Find the chge contined inside cubicl volume bounded by the sufce =, =, y =, y =, z = nd z =. Tke E = 5 N/C, l = cm nd = cm. 9. The dipoles of dipole moments p nd p pllel to ech othe e plced t distnce pt. (i) will they ttct o epel? (ii) wht is the foce of intection? Detemine the electic potentil nd electic intensity t distnce nd t n ngle fom the is of the dipole. The dipole moment of the dipole is p. Find the wok euied to tun n electic dipole end fo end in unifom electic field E, in tems of the mgnitude p of the dipole moment, the mgnitude E of the field, nd the initil ngle between p nd E. Einstein Clsses, Unit No.,, Vdhmn ing od Plz, Viks Pui Etn., Oute ing od New Delhi 8, Ph. : 9695, 857

25 . A dipole of electic moment p is locted t distnce fom long thed chged with line density. Find the foce on the dipole if it is plced pllel to the thed pependicul to the thed.. A thin conducting ing of dius hs n electic chge +. A point chge + is plced t the cente of the ing. Assume tht the chge distibution on the ing is unifom. Find the intection foce between the chged pticle nd the ing? Find the incese in tension of the wie?. A thin fied ing of dius m hs positive chge of µc unifomly distibuted ove it. A pticle of mss.9 gm nd hving negtive chge of µc is plced on the is t distnce of cm fom the cente of the ing. Pove tht the motion of the pticle is simple hmonic? Find the mimum speed of the pticle?. Two-point chges +4 nd + e plced t distnce L pt. A thid chge is so plced tht ll the thee chges e in euilibium. Find the loction mgnitude nd ntue of thid chge. Discuss lso, whethe the euilibium of the system is stble, unstble o neutl? 4. A pticle of chge nd mss m moves ectilinely unde the ction of n electic field E = A B whee B is positive constnt nd is distnce fom the point whee the pticles ws initilly t est. Find distnce tveled by the pticle befoe it comes to est nd cceletion t tht moment. pove tht the pticle is pefoming SHM nd find its time peiod. Find the mimum speed? 5. An electic field E ĵn / C eists in the spce. A chge pticle of specific chge C/kg is pojected fom (, ) m with velocity ( î ĵ) m/s. Does the pticle etce its pth nywhee long Y-is. If yes, find the coodinte of tht point? Also find the dius of cuvtue of the pth of pticle t this instnt? Neglect the effect of gvity. Conside the effect of gvity (g = m/s ) nd the bove electic field is E ĵn / C, then wht is the eution of tjectoy of the pticle? PE 5 6. Two eul point chges + e plced distnce pt t points A nd B. In the electic field of these chges, pticle of mss m nd chge moves with constnt speed in cicle of dius with cente t point O midwy between A nd B. The plne of the cicul pth is noml to the line joining A nd B. Find the totl enegy of the pticle? Neglect the gvittionl foce. 7. A conducting sphee of dius hs chge on it. A thin ing of dius ( > ) held concentic with the sphee cies totl enegy on it. Find the finl chge on the sphee if it is gounded. 8. Two pllel non-conducting ings nged with thei centl es long common line. ing hs unifom chge nd dius ;ing hs unifom chge nd the sme dius. The ings e septed by distnce. The net electic field t point P on the common line, t distnce fom ing, is zeo. Wht is the tio /? 9. A block contining net positive chge is plced on smooth hoizontl tble which temintes in veticl wll s shown in figue. The distnce of the block fom the wll is d. A hoizontl electic field E towds ight is switched on. Assuming elstic collision (if ny) find the time peiod of the esulting oscilltoy motion. Is it simple hmonic motion? Now conside the collision is inelstic (coefficient of estitution is e). Find the totl distnce tvelled by the block nd totl time of motion.. Figue shows five point chges long stight line. The seption between the chges is cm. Find fo wht vlues of nd would be net foce on ech of the othe thee chges be zeo?. Thee point chges,, nd lie t the cones of n euiltel tingle of side cm. The foces between them e F = 5.4 N (ttctive), F = 5 N (epulsive), nd F = 9N (ttctive). Given thn is negtive, wht e, nd. Einstein Clsses, Unit No.,, Vdhmn ing od Plz, Viks Pui Etn., Oute ing od New Delhi 8, Ph. : 9695, 857

26 . The figue shows combintion of chges clled n electic udupole. Find the electic field stength t point A t (, ) nd t point B t (, ) Show tht in eithe cse E 4 fo >>, whee is the distnce fom the oigin. PE 6 6. Figue shows long, non-conducting, mssless od of length L, pivoted t its cente nd blnced with block of weight W t distnce fom the left end. At the left nd ight ends of the od e ttched smll conducting sphees with positive chges nd, espectively.. A dipole whose dipole moment is p lies long the -is p pî is plced in nonunifom field C E î. Wht is the foce on the dipole? 4. A cone mde of insulting mteil hs totl chge sped unifomly ove its sloping sufce. Clculte the enegy euied to bing up smll test chge fom infinity to the pe of the cone. The cone hs slope length L. 5. The electicl potentil function fo n electic field diected pllel to the -is is shown in the given gph Dw gph of the electic field stength. If the -is psses though conducto, whee is the conducto locted A distnce h diectly beneth ech of these sphees is fied sphee with positive chge Find the distnce when the od is hoizontl nd blnced. Wht vlue should h hve so tht the od eets no veticl foce on the being when the od is hoizontl nd blnced? 7. A non-conducting spheicl shell, of inne dius nd oute dius b, hs positive volume chge density = A/ (within its thickness), whee A is constnt nd is the distnce fom the cente of the shell. In ddition, positive point chge is locted t tht cente. Wht vlue should A hve if the electic field in the shell ( b) is to be unifom? 8. Conside unifom spheicl volume chged distibution with totl chge in dius. Wht is the totl enegy inside the sphee? Wht fction of totl enegy is outside the sphee? Wht is the totl enegy due to this volume chged distibution? 9. A thin, spheicl, conducting shell of dius is mounted on n isolting suppot nd chged to potentil of V. An electon is then fied fom point P t distnce fom the cente of the shell ( >> ) with initil speed v nd diectly towd the shell s cente. Wht vlue of v is needed fo the electon to just ech the shell befoe evesing diection?. Conside conducting sphee of dius with spheicl cvity inside the sphee t the distnce d fom the cente of the sphee. A chge is plced inside the cvity. Tke the point P outside the sphee t distnce fom the cente nd t the distnce b fom the point chge. Wht is the electic field t P. Wht is the electic potentil t P. Einstein Clsses, Unit No.,, Vdhmn ing od Plz, Viks Pui Etn., Oute ing od New Delhi 8, Ph. : 9695, 857