CHECK YOUR GRASP. +q +2q A B. D 2q +q

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1 J-Physics XCIS 1 CHCK YOU GASP SLCT TH COCT ALTNATIV (ONLY ON COCT ANSW) 1. Using mass (M), length (L), time (T) and cuent as fundamental uantities, the dimension of pemittivity is : ML T A M 1 L T 4 A MLT A (D) ML T 1 A. Two point chages 9e and e ae kept 16 cm. apat fom each othe. Whee should a thid chage be placed between them so that the system is in euilibium state : 4 cm fom 9e 1 cm fom 9e 4 cm fom e (D) 1 cm fom e. Fou chages ae aanged at the cones of a suae ABCD as shown in the figue. The foce on the chage kept at the cente O will be : A B D C pependicula to side AB along the diagonal AC along the diagonal BD (D) zeo 4. When chage is given to a soap bubble, it shows : an incease in size sometimes an incease and sometimes a decease in size no change in size (D) none of these 5. Two eual negative chages ae fixed at point (, a) and (, a) on y axis. A positive chage is eleased fom est at the point (a, ) on the x axis. The chage will : execute simple hamonic motion about the oigin move to the oigin and emain at est move to infinity (D) execute oscillatoy but not simple hamonic motion 6. Figues below show egula hexagon, the chages ae placed at the vetices. In which of the following cases the electic field at the cente is zeo I II 5 III IV III I (D) II 7. Two infinite linea chages ae placed paallel to each othe at a distance.1 m fom each othe. If the linea chage density on each is 5 C/m, then the foce acting on a unit length of each linea chage will be :.5 N/m.5 N/m 4.5 N/m (D) 7.5 N/m 8. An electon of mass m e, initially at est, moves though a cetain distance in a unifom electic field in time t 1. A poton of mass m p, also, initially at est, takes time t to move though an eual distance in this unifom electic field. Neglecting the effect of gavity, the atio t /t 1 is nealy eual to : 1 (m p /m e ) 1/ (m e /m p ) 1/ (D) An electon is pojected as in figue with kinetic enegy K, at an angle = 45 between two chaged plates. The magnitude of the electic field so that the electon just fails to stike the uppe plate, should be geate than: IV NOD6 ()\Data\14\Kota\J-Advanced\SMP\Phy\Unit-7\lectostatics\nglish\xecise.p65

2 J-Physics K d 45 K d K d K d (D) Infinite 1. A point chage 5 C is located in the XY plane at the point of position vecto ˆi ˆj is the electic field at the point of position vecto 8 ˆ i 5ˆj mete: 1 V/m.4 V/m 9 V/m (D) 45 V/m mete. What 1 1. Thee point chages 1C, C and C ae placed at the cones of an euilateal tiangle of side 1m. The wok euied to move these chages to the cones of a smalle euilateal tiangle of side.5m in two diffeent ways as in fig. and fig. ae W a and W b then: A 1C A 1C A' B' C' C B B' C' C C B C C C W a > W b W a < W b W a = W b (D) W a = and W b = 1. As pe this diagam a point chage is placed at the oigin O. Wok done in taking anothe point chage fom the point A (, a) to anothe point B (a,) along the staight path AB is : A y O B x ( 1 4 a ) a zeo ( 1 4 a ) 1 (D) ( 1 4 a ) a NOD6 ()\Data\14\Kota\J-Advanced\SMP\Phy\Unit-7\lectostatics\nglish\xecise.p65 1. Two identical thin ings, each of adius mete ae coaxially placed at distance mete apat. If 1 and coulomb ae espectively the chages unifomly spead on the two ings, the wok done in moving a chage fom the cente of one ing to that of the othe is : zeo (D) Two identical paticles of mass m cay a chage each. Initially one is at est on a smooth hoizontal plane and the othe is pojected along the plane diectly towads fist paticle fom a lage distance with speed v. The closest distance of appoach be : 1 4 mv mv 1 4 mv (D) 1 4 mv

3 J-Physics 1 5. In a egula polygon of n sides, each cone is at a distance fom the cente. Identical chages ae placed at (n 1) cones. At the cente, the intensity is and the potential is V. The atio V/ has magnitude : n (n 1) (n 1) / (D) (n 1)/n 1 6. An alpha paticle of enegy 5 MeV is scatteed though 18 by a fixed uanium nucleus. The distance of closest appoach is of the ode : 1 Å 1 1 cm 1 1 cm (D) 1 15 cm 1 7. A chage coulomb expeiences a foce N when placed in a unifom electic field. The potential diffeence between two points sepaated by a distance of 1 cm along the field line is : 1 V 9 V 1 V (D) 9 V 1 8. Unifom electic field of magnitude 1 V/m in space is diected along the line y= x. Find the potential diffeence between point A (,1) & B(1,) : 1 V V V (D) 1 9. The euation of an euipotential line in an electic field is y=x, then the electic field stength vecto at (1, ) may be : 4i ˆ ˆj 4i ˆ 8ˆj 8i ˆ 4ˆj (D) 8i ˆ 4ˆj. In a cetain egion of space, the potential is given by V=k (x y z ). The electic field at the point (1, 1, 1) has magnitude : k 6 k 6 k (D) 4k 1. The figue below shows two euipotential lines in XY plane fo an electic field. The scales ae maked. The X component x and Y component y of the electic field in the space between these euipotential lines ae espectively : Y (in cm) Volt 4 Volt X (in cm) 1 V/m, V/m 1 V/m, V/m V/m, 1 V/m (D) V/m, 1 V/m. A non conducting ing of adius.5 m caies a total chage C distibuted non unifomly on its cicumfeence poducing an electic field evey whee in space. The value of the integal being cente of the ing) in volt is : 1 (D) zeo 5 d (=. Two point chages and ae held fixed at ( d, ) and (d, ) espectively of a x y co odinate system. Then which of the following statement is incoect : The electic field at all points on the x axis has the same diection No wok has to be done in binging a test chage fom to the oigin lectic field at all point on y axis is paallel to x axis (D) The dipole moment is d along the ve x axis NOD6 ()\Data\14\Kota\J-Advanced\SMP\Phy\Unit-7\lectostatics\nglish\xecise.p65

4 { J-Physics 4. The wok done in otating an electic dipole of dipole moment p in an electic field though an angle fom the diection of electic field, is : p (1 cos) p zeo (D) p cos 5. Which one of the following patten of electic line of foce can't possible : (D) 6. A sphee of adius and chage is placed inside an imaginay sphee of adius whose cente coincides with the given sphee. The flux elated to imaginay sphee is : 7. Due to a chage inside a cube the electic field is x = 6 x 1/, y =, z =. The chage inside the cube is (appoximately) : 4 (D) Y.1m O X Z.1 m 6 C 6 C 7 C (D) 6 C 8. lectic flux though a suface of aea 1 m lying in the xy plane is (in V m) if ˆi ˆj kˆ : (D) 9. Two spheical, nonconducting, and vey thin shells of unifomly distibuted positive chage and adius d ae located at a distance 1d fom each othe. A positive point chage is placed inside one of the shells at a distance d/ fom the cente, on the line connecting the centes of the two shells, as shown in the figue. What is the net foce on the chage? d d/ NOD6 ()\Data\14\Kota\J-Advanced\SMP\Phy\Unit-7\lectostatics\nglish\xecise.p65 61 d to the left 61 d 6 61 d 6 to the left (D) 61 d 1d 5 to the ight to the ight. A solid metallic sphee has a chage. Concentic with this sphee is a conducting spheical shell having chage. The adius of the sphee is a and that of the spheical shell is b (b > a). What is the electic field at a distance (a < < b) fom the cente? 4 4 (D)

5 J-Physics 1. A hollow metal sphee of adius 5 cm is chaged such that the potential on its suface is 1V. The potential at the distance cm fom the cente of the sphee is : zeo 1 V same as at a point 5 cm away fom the suface (D) same as at a point 5 cm away fom the suface. A solid conducting sphee having a chage is suounded by an unchaged concentic conducting hollow spheical shell. Let the potential diffeence between the suface of the solid sphee and that of the oute suface of the hollow shell be V. If the shell is now given a chage of, the new potential diffeence between the same two sufaces is : V V 4V (D) V. A cube of metal is given a chage ( ), which of the following statements is tue : Potential at the suface of cube is zeo Potential within the cube is zeo lectic field is nomal to the suface of the cube (D) lectic field vaies within the cube 4. A metallic solid sphee is placed in a unifom electic field. The lines of foce follow the path(s) shown in figue as : (D) 4 CHCK YOU GASP ANSW KY XCIS -1 u e A n s. B B B A D B C B C D C B B B B C A D D u e A n s. B C A A A C A C C A B B A C D 54 NOD6 ()\Data\14\Kota\J-Advanced\SMP\Phy\Unit-7\lectostatics\nglish\xecise.p65

6 J-Physics XCIS BAIN TASUS Select the coect altenatives (one o moe than one coect answes) 1. A chaged cok of mass m suspended by a light sting is placed in unifom electic field of stength = ˆ 5 i ˆj 1 NC 1 as shown in the figue. If in euilibium position tension in the sting is with the vetical is : mg 1 then angle \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\ 6 45 (D) 18. A chaged paticle having some mass is esting in euilibium at a height H above the cente of a unifomly chaged non conducting hoizontal ing of adius. The foce of gavity acts downwads.; The euilibium of the paticle will be stable : fo all values of H only if H > only if H < (D) only if H =. The chage pe unit length of the fou uadant of the ing is, and espectively. The electic field at the cente is : - y x î ĵ î 4 (D) None 4. The figue shows a nonconducting ing which has positive and negative chage non unifomly distibuted on it such that the total chage is zeo. Which of the following statements is tue? NOD6 ()\Data\14\Kota\J-Advanced\SMP\Phy\Unit-7\lectostatics\nglish\xecise.p65 O The potential at all the points on the axis will be zeo. The electic field at all the points on the axis will be zeo. The diection of electic field at all points on the axis will be along the axis. (D) If the ing is placed inside a unifom extenal electic field then net toue and foce acting on the ing would be zeo. 55 axis

7 J-Physics 5. A cicula ing caies a unifomly distibuted positive chage. The electic field () and potential (V) vaies with distance () fom the cente of the ing along its axis as : V V (D) 6. Find the foce expeienced by the semicicula od chaged with a chage, placed as shown in figue. adius of the wie is and the infinite line of chage with linea chage density is passing though its cente and pependicula to the plane of od. 4 (D) 4 7. Which of the following is tue fo the figue showing electic lines of foce? ( is electical field, V is potential) A > B B > A V A > V B (D) V B > V A 8. An electic chage 1 8 C is placed at the point (4m, 7m, m). At the point (1m, m, m), the electic : potential will be 18 V field has no Y component field will be along Z axis (D) potential will be 1.8 V 9. Two point chages and /4 ae sepaated by a distance x. Then : x /4 potential is zeo at a point on the axis which is at a distance x/ on the ight side of the chage /4 potential is zeo at a point on the axis which is at a distance x/5 on the left side of the chage /4 electic field is zeo at a point on the axis which is at a distance x on the ight side of the chage /4 (D) thee exist two points on the axis whee electic field is zeo 1. Two positively chaged paticles X and Y ae initially fa away fom each othe and at est. X begins to move towads Y with some initial velocity. The total momentum and enegy of the system ae p and : If Y is fixed, both p and ae conseved If Y is fixed, is conseved, but not p If both ae fee to move, p is conseved but not (D) If both ae fee, is conseved, but not p 56 NOD6 ()\Data\14\Kota\J-Advanced\SMP\Phy\Unit-7\lectostatics\nglish\xecise.p65

8 J-Physics 1 1. Two paticles X and Y, of eual mass and with uneual positive chages, ae fee to move and ae initially fa away fom each othe. With Y at est, X begins to move towads it with initial velocity u. Afte a long time, finally : X will stop, Y will move with velocity u X and Y will both move with velocities u/ each X will stop, Y will move with velocity < u (D) both will move with velocities < u/ 1. In a unifom electic field, the potential is 1V at the oigin of coodinates, and 8V at each of the points (1,, ), (, 1, ) and (,, 1). The potential at the point (1, 1, 1) will be : 4V 8V (D) 1V 1. Fou chages of 1 C, C, C, and 6 C ae placed one at each cone of the suae of side 1m. The suae lies in the x y plane with its cente at the oigin. The electic potential is zeo at the oigin. The electic potential is zeo eveywhee along the x axis only if the sides of the saue ae paallel to x and y axis. The electic potential is zeo eveywhee along the z axis fo any oientation of the suae in the x y plane. (D) The electic potential is not zeo along the z axis except at the oigin Potential at a point A is volt and at a point B is 7 volt, an electon is moving towads A fom B : It must have some K.. at B to each A It need not have any K.. at B to each A To each A it must have moe than o eual to 4 ev K at B (D) When it will each A, it will have K.. moe than o at least eual to 4 ev if it was eleased fom est at B 1 5. A paticle of chage 1C & mass 1 gm moving with a velocity of 4 m/s is subjected to a unifom electic field of magnitude V/m fo 1 sec. Then it's final speed cannot be :.5 m/s 4 m/s m/s (D) 6 m/s 1 6. A paticle of mass m and chage is thown in a egion whee unifom gavitational field and electic field ae pesent. The path of paticle : may be a staight line may be a cicle may be a paabola (D) may be a hypebola 1 7. A hoizontal electic feild ( = (mg)/) exists as shown in figue and a mass m attached at the end of a light od. If mass m is eleased fom the position shown in figue find the angula velocity of the od when it passes though the bottom most position : NOD6 ()\Data\14\Kota\J-Advanced\SMP\Phy\Unit-7\lectostatics\nglish\xecise.p65 g g m =45 57 mg = 1 8. The diagam shows a small bead of mass m caying chage. The bead can feely move on the smooth fixed ing placed on a smooth hoizontal plane. In the same plane a chage has also been fixed as shown. The potential at the point A due to is V. The velocity with which the bead should poejcted fom the point A so that it can complete a cicle should be geate than : 6V m V m m g V m (D) 5g B a (D) None of these 4a g A

9 J-Physics 1 9. The diagam shows thee infinitely long unifom line chages placed on the X,Y and Z axis. The wok done in moving a unit positive chage fom (1, 1, 1) to (, 1, 1) is eual to: Y Z X n n n (D) None. The electic potential deceases unifomly fom V to V along X axis in a coodinate system as we moves fom a point ( x, ) to (x, ), then the electic field at the oigin : must be eual to V x may be eual to V x must be geate than V x (D) may be less than V x 1. A poton and a deuteon ae initially at est and ae acceleated though the same potential diffeence which of the following is false concening the final popeties of the two paticles? They have diffeent speeds They have same momentum They have same kinetic enegy (D) They have been subjected to same foce. Thee points chages ae placed at the cones of an euilateal tiangle of side L as shown in the figue: The potential at the centoid of the tiangle is zeo. The electic field at the centoid of the tiangle is zeo. L The dipole moment of the system is L L (D) The dipole moment of the system is L L. The dipole moment of a system of chage distibuted unifomly on an ac of adius subtending an angle / at its cente whee anothe chage is placed is (D) 4. An electic dipole is kept on the axis of a unifomly chaged ing at distance / fom the cente of the ing. The diection of the dipole moment is along the axis. The dipole moment is P, chage of the ing is and adius of the ing is. The foce on the dipole is nealy : 4kP 4kP 58 kp (D) zeo 5. Point P lies on the axis of a dipole. If the dipole is otated by 9 anticlock wise, the electic field vecto at P will otate by : 9 clockwise 18 clockwise 9 anticlock wise (D) 18 anticlockwise NOD6 ()\Data\14\Kota\J-Advanced\SMP\Phy\Unit-7\lectostatics\nglish\xecise.p65

10 J-Physics 6. Two shot electic dipoles ae placed as shown. The enegy of electic inteaction between these dipoles will be p 1 p Kp p cos 1 Kp p cos 1 Kp p sin 1 (D) 4Kp p cos 7. Chages 1 and lies inside and outside espectively of a closed suface S. Let be the field at any point on S and be the flux of ove S. 1 If 1 changes, both and will change. If 1 = and then but = If changes, will change but will not change. (D) If 1 and = then = but 8. An electic dipole is placed at the cente of a sphee. Mak the coect answe : The flux of the electic field passing though the sphee is zeo The electic field is zeo at evey point of the sphee The electic potential is zeo eveywhee on the sphee (D) The electic potential is zeo on a cicle on the suface 9. An infinite, unifomly chaged sheet with suface chage denisty cuts though a spheical Gaussian suface of adius at a distance x fom its cente, as shown in the figue. The electic flux though the Gaussian suface is : x x x (D) x NOD6 ()\Data\14\Kota\J-Advanced\SMP\Phy\Unit-7\lectostatics\nglish\xecise.p65. At distance of 5 cm and 1 cm outwads fom the suface of a unifomly chaged solid sphee, the potentials ae 1 V and 75 V espectively. Then : potential at its suface is 15 V the electic field on the suface is 15 V/m 59 the chage on the sphee is (5/) x 1 1 C (D) the electic potential at its cente is 5 V 1. An electic field conveges at the oigin whose magnitude is given by the expession = 1 N/C, whee is the distance measued fom the oigin. Total chage contained in any spheical volume with its cente at oigin is negative. Total chage contained at any spheical volume, iespective of the location of its cente, is negative. Total chage contained in a spheical volume of adius cm with its cente at oigin euals 1 1 C. (D) Total chage contained in a spheical volume of adius cm with its cente at oigin has magnitude 1 9 C.

11 J-Physics. A bullet of mass m and chage is fied towads a solid unifomly chaged sphee of adius and total chage. If it stikes the suface of sphee with speed u, find the minimum value of u so that it can penetate though the sphee. (Neglect all esistnace foces o fiction acting on bullet except electostatic foces) m u m 4 m 8 m (D) 4 m. A unit positive point chage of mass m is pojected with a velocity v inside the tunnel as shown. The tunnel has been made inside a unifomly chaged non conducting sphee. The minimum velocity with which the point chage should be pojected such that it can it each the opposite end of the tunnel, is eual to : / 1 / 4m 4m 6m (D) zeo because the initial and the final points ae at same potential 1 / 4. Thee concentic conducting spheical shells have adius, and and 1, and ae final chages espectively. Innemost and outemost shells ae aleady eathed as shown in figue. choose the wong statement. 1 / 1 1 = 1 = 4 1 (D) 1 5. Shown in the figue a spheical shell with an inne adius 'a' and an oute adius 'b' is made of conducting mateial. A point chage is placed at the cente of the spheical shell and a total chage is placed on the shell. Chage is distibuted on the sufaces as : on the inne suface,, on oute suface on the inne suface, on the oute suface on the inne suface, on the oute suface (D) The chage is spead unifomly between the inne and oute suface 6. In the pevious uestion assume that the electostatic potential is zeo at an infinite distance fom the spheical 1 shell. The electostatic potential at a distance (a < < b) fom the cente of the shell is whee K 4 K a 6 K (D) K b a b NOD6 ()\Data\14\Kota\J-Advanced\SMP\Phy\Unit-7\lectostatics\nglish\xecise.p65

12 J-Physics 7. Thee ae fou concentic shells A, B, C and D of adii a, a, a and 4a espectively. Shells B and D ae given chages and espectively. Shell C is now eathed. The potential diffeence V A V C is : K a K a K 4a (D) K 6a 8. X and Y ae lage, paallel conducting plates closed to each othe. ach face has an aea A. X is given a chage. Y is without any chage. Points A, B and C ae as shown in figue : The field at B is The field at B is A A The fields at A, B and C ae of the same magnitude (D) The field at A and C ae of the same magnitude, but in opposite diections 9. Plates A and B constitutes an isolated, chage paallel plate capacito. The inne sufaces ( I and IV) of A and B have chages and espectively. A thid plate C with chage is now intoduced midway between A and B. Which of the following statements is not coect? The suface I and II will have eual and opposite chages The sufaces III and IV will have eual and opposite chages The chage on suace III will be geate than A (D) The potential diffeence between A and C will be eual to the potential diffeence between C and B 4. A wheel having mass m has chages and on diametically opposite points. It emains in euilibium on a ough inclined plane in the pesence of unifom vetical electic field. The value of is : - I II A C X III B Y B - IV C mg mg mg tan (D) None NOD6 ()\Data\14\Kota\J-Advanced\SMP\Phy\Unit-7\lectostatics\nglish\xecise.p65 BAIN TASS ANSW KY XCIS - u e Ans. A,B B A A B B AD A ABC B A B AC AC A u e Ans. AC B A B B B AD A D A B ABC AD D ACD u e Ans. ABC B A C B D D ACD D B 61

13 J-Physics XCIS MISCLLANOUS TYP USTIONS TU / FALS 1. The wok done in caying a point chage fom one point to anothe in an electostatic field depends on the path along which the point chage is caied.. An electic line of foces in the x y plane is given by the euation x y = 1. A paticle with unit positive chage, initially at est at the point x = 1, y = in the x y plane, will move along the cicula line of foce.. A small metal ball is suspended in a unifom electic field with the help of an insulated thead. If high enegy X ay beam falls on the ball, the ball will be deflected in the diection of the field. 4. A ing of adius caies a unifomly distibuted chage. A point chage is placed in the axis of the ing at a distance fom the cente of the ing eleased fom est. The paticle executes a simple hamonic motion along the axis of the ing. 5. Two identical metallic sphees of exactly eual masses ae taken. One is given a positive chage coulomb and the othe an eual negative chage. Thei masses afte chaging ae diffeent. FILL IN TH BLANKS 1. lectic lines... (can/can not) have sudden beaks.. Figue shows line of constant potential in a egion in which an electic field A B is pesent. The values of the potential ae witten in backets. Of the point A, B and C, the magnitude of the electic field is geatest at the point.... (5V) (4V) (V) (V) C (1V). Two small balls having eual positive chage (coulamb) on each ae suspended by two insulating stings of eual length L (mete) fom a hook fixed to a stand. The whole set up is taken in a satellite into space whee thee is no gavity (state of weightlessness). The angle between the sting is... and the tension in each sting is... newtons. 4. A point chage moves fom point P to point S along the path PS (fig.) Y in a unifom electic field pointing paallel to the positive diection of the X axis. The coodiantes of points P,, and S (a, b, ), (a,, ) (a, b, S P X ) (,, ) espectively. The wok done by electic field is The electic potential V at any point x, y, z (all in metes) in space is given by V = 4x volt. The electic field at the point (1m,. m) is... V/m. 6. Five point chages, each of value coulomb, ae placed on five vetices of a egula hexagon of side L mete. The magnitude of the foce on the point chage of value coulomb placed at the cente of the hexagon is... newton. 6 - NOD6 ()\Data\14\Kota\J-Advanced\SMP\Phy\Unit-7\lectostatics\nglish\xecise.p65

14 J-Physics M ATCH TH COLUMN 1. Two paallel metallic plates have suface chage densities 1 and as shown in figue. 1 I II III Column I Column II If 1 = (p) lectic field in egion III is towads ight If 1 > () lectic field in egion I is zeo If 1 < () lectic field in egion I is towads ight (s) Nothing can be said. Column I shows gaphs of electic potential V vesus x and y in a cetain egion fo fou situations. Column II shows the ange of angle which the electic field vecto makes with poisitive x diection Column I : V vesus x, V vesus y Column II : ange of angle 45 (p) () 45 9 NOD6 ()\Data\14\Kota\J-Advanced\SMP\Phy\Unit-7\lectostatics\nglish\xecise.p65 (D) 45 6 () (s)

15 J-Physics. In each situation of column I, two electic dipoles having dipole moments p 1 and p of same magnitude (that is, p 1 = p ) ae placed on x axis symmetically about oigin in diffeent oientations as shown. In column II cetain infeences ae dawn fo these two dipoles. Then match the diffeent oientations of dipole in column I with the coesponding esults in column II. Column I Column II y p 1 p x ( a,) (a,) ( p 1 and p ae (p) The toue on one dipole due to pependicula to x axis as shown) othe is zeo y p 1 p x ( a,) (a,) ( p 1 and p ae () The potential enegy of one dipole in pependicula to x axis as shown) electic field of othe dipole is negative y p 1 p x ( a,) (a,) ( p 1 and p ae () Thee is one staight line in x-y plane (not paallel to x axis as shown) at infinity) which is euipotential (D) y p 1 p x ( a,) (a,) ( p 1 and p ae (s) lectic field at oigin is zeo. paallel to x axis as shown) 4. In the figue shown P is a point on the suface of an imaginay sphee. Column I Column II lectic field at point P (p) due to 1 only lectic flux though a small aea at P () due to only lectic flux though whole sphee () due to both 1 and 64 1 P NOD6 ()\Data\14\Kota\J-Advanced\SMP\Phy\Unit-7\lectostatics\nglish\xecise.p65

16 J-Physics 5. Column I gives cetain situations involving two thin conducting shells connected by a conducting wie via a key K. In all situations one sphee has net chage and othe sphee has no net chage. Afte the key K is pessed, column II gives some esulting effect. Column I Column II shell I K initially no net chage shell II (p) Chage flows though connecting wie initially no net chage K () Potential enegy of system of sphees deceases shell I shell II initially no net chage shell I shell II K () No heat is poduced (D) initially no net chage (s) The sphee I has no chage afte euilibium is eached K shell I shell II NOD6 ()\Data\14\Kota\J-Advanced\SMP\Phy\Unit-7\lectostatics\nglish\xecise.p65 6. A spheical metallic conducto has a spheical cavity. A positive chage is placed inside the cavity at its cente. Anothe positive chage is placed outside it. The conducto is initially electically neutal. Column I (Cause) 65 Column II ( ffect) If outside chage is shifted to othe position (p) Distibution of chage on inne suface of cavity changes If inside chage is shifted to othe position () Distibution of chage on oute suface of within cavity conducto changes If magnitude of chage inside cavity is () lectic potential at the cente of conducto inceased changes due to chages pesent on oute suface of conducto (D) If conducto is eathed (s) Foce on the chage placed inside cavity changes

17 J-Physics 7. In each situation of column I, some chage distibutions ae given with all details explained. The electostatic potential enegy and its natue is given situation in column II. Column I Column II A thin shell of adius a and having 1 (p) 8 a in magnitude a chage unifomly distibuted ove its suface as shown A thin shell of adius 5a a chage unifomly distibuted ove its suface and a point chage a and having 5a placed at its cente as shown A solid sphee of adius a and having () a chage unifomly distibuted thoughout its volume as shown () a 5 a (D) A solid sphee of adius a and having (s) Positive in sign a chage unifomly distibuted thoughout its volume. The solid sphee is suounded by a a concentic thin unifomly chaged spheical shell of adius a and caying chage as shown a in magnitude in magnitude ASSTION & ASON These uestions contains, Statement 1 (assetion) and Statement (eason). 1. Statem ent 1 : Chage is invaiant. a n d Statem ent : Chage does not depends on speed o fame of efeence. Statement 1 is Tue, Statement is Tue ; Statement is not a coect explanation fo Statement 1 Statement 1 is Tue, Statement is False. Statement 1 is False, Statement is Tue. (D) Statement 1 is Tue, Statement is Tue ; Statement is a coect explanation fo Statement 1 a. Statem ent 1 : Mass of ion is slightly diffeed fom its element. a n d Statem ent : Ion is fomed, when some electons ae emoved o added so the mass changes Statement 1 is Tue, Statement is Tue ; Statement is not a coect explanation fo Statement 1 Statement 1 is Tue, Statement is False. Statement 1 is Tue, Statement is Tue ; Statement is a coect explanation fo Statement 1 (D) Statement 1 is False, Statement is Tue.. Statem ent 1 : Chage is uantized a n d Statem ent : Chage, which is less than 1 C is not possible Statement 1 is Tue, Statement is Tue ; Statement is a coect explanation fo Statement 1 Statement 1 is Tue, Statement is Tue ; Statement is not a coect explanation fo Statement 1 Statement 1 is Tue, Statement is False. (D) Statement 1 is False, Statement is Tue. 66 NOD6 ()\Data\14\Kota\J-Advanced\SMP\Phy\Unit-7\lectostatics\nglish\xecise.p65

18 J-Physics 4. Statem ent 1 : In electostatic electic lines of foce can neve be closed loops, as a line can neve stat and end on the same chage. a n d Statem ent : The numbe of electic lines of foce oiginating o teminating on a chage is popotional to the magnitude of chage. Statement 1 is Tue, Statement is Tue ; Statement is a coect explanation fo Statement 1 Statement 1 is Tue, Statement is Tue ; Statement is not a coect explanation fo Statement 1 Statement 1 is Tue, Statement is False. (D) Statement 1 is False, Statement is Tue. 5. Statement 1 : If a point chage is placed in font of an infinite gounded conducting plane suface, the point chage will expeience a foce. a n d Statem ent : This foce is due to the induced chage on the conducting suface which is at zeo potential Statement 1 is Tue, Statement is Tue ; Statement is a coect explanation fo Statement 1 Statement 1 is Tue, Statement is Tue ; Statement is not a coect explanation fo Statement 1 Statement 1 is Tue, Statement is False. (D) Statement 1 is False, Statement is Tue. 6. Statem ent 1 : When two chaged sphees ae touched, then total chage is always devides eually. a n d Statem ent : Flow of chage take place untill potential euals. Statement 1 is Tue, Statement is Tue ; Statement is a coect explanation fo Statement 1 Statement 1 is Tue, Statement is Tue ; Statement is not a coect explanation fo Statement 1 Statement 1 is False, Statement is Tue. (D) Statement 1 is Tue, Statement is False. NOD6 ()\Data\14\Kota\J-Advanced\SMP\Phy\Unit-7\lectostatics\nglish\xecise.p65 7. Statem ent 1 : The paticles such as photon o neutino which have no (est) mass can neve have a chage. a n d Statem ent : Chage can not exist without mass. Statement 1 is Tue, Statement is Tue ; Statement is not a coect explanation fo Statement 1 Statement 1 is Tue, Statement is Tue ; Statement is a coect explanation fo Statement 1 Statement 1 is Tue, Statement is False. (D) Statement 1 is False, Statement is Tue. 8. Statem ent 1 : When chages ae shaed between two bodies, thee occus no loss of chage, but thee does occu a loss of enegy. a n d Statem ent : In case of shaing of chages consevation of enegy fails. Statement 1 is Tue, Statement is Tue ; Statement is a coect explanation fo Statement 1 Statement 1 is Tue, Statement is Tue ; Statement is not a coect explanation fo Statement 1 Statement 1 is Tue, Statement is False. (D) Statement 1 is False, Statement is Tue. 9. Statem ent 1 : Induced chage does not contibute to electic field o potential at a given point. a n d Statem ent : A point chage is kept outside a solid metallic sphee, the electic field inside the sphee is zeo. Statement 1 is Tue, Statement is Tue ; Statement is a coect explanation fo Statement 1 Statement 1 is Tue, Statement is Tue ; Statement is not a coect explanation fo Statement 1 Statement 1 is Tue, Statement is False. (D) Statement 1 is False, Statement is Tue. 67

19 J-Physics 1. Statem ent 1 : A conducting sphee chaged upto 5V is placed at the cente of a conducting shell chaged upto 1V and connected by a wie. All the chage of the shell flows to the sphee. a n d Statem ent : The positive chage always flows fom highe to lowe potential. Statement 1 is Tue, Statement is False. Statement 1 is False, Statement is Tue. Statement 1 is Tue, Statement is Tue ; Statement is a coect explanation fo Statement 1 (D) Statement 1 is Tue, Statement is Tue ; Statement is not a coect explanation fo Statement Statem ent 1 : When a chaged paticle is placed in the cavity in a conducting sphee, the induced chage on the oute suface of the sphee is found to be unifomly distibuted. a n d Statem ent : Conducting suface is euipotential suface. Statement 1 is Tue, Statement is Tue ; Statement is not a coect explanation fo Statement 1 Statement 1 is Tue, Statement is Tue ; Statement is a coect explanation fo Statement 1 Statement 1 is Tue, Statement is False. (D) Statement 1 is False, Statement is Tue. 1. Statem ent 1 : lectic field intensity at suface of unifomly chage spheical shell is. If shell is puncheed at a point then intensity at puncheed point become /. a n d S t a t e m e n t : lectic field intensity due to spheical chage distibution can be found out by using Gauss law. Statement 1 is Tue, Statement is Tue ; Statement is a coect explanation fo Statement 1 Statement 1 is Tue, Statement is Tue ; Statement is not a coect explanation fo Statement 1 Statement 1 is Tue, Statement is False. (D) Statement 1 is False, Statement is Tue. 1. Statem ent 1 : If two concentic conducting sphee which ae connected by a conducting wie. No chage can exist on inne sphee. a n d Statem ent : When chage on oute sphee will exist then potential of inne shell and oute shell will be same. Statement 1 is Tue, Statement is Tue ; Statement is a coect explanation fo Statement 1 Statement 1 is Tue, Statement is False. Statement 1 is False, Statement is Tue. (D) Statement 1 is Tue, Statement is Tue ; Statement is not a coect explanation fo Statement Statem ent 1 : A metallic shield in fom of a hollow shell may be built to block an electic field. a n d Statem ent : In a hollow spheical shield, the electic field inside it is zeo at evey point. Statement 1 is Tue, Statement is Tue ; Statement is a coect explanation fo Statement 1 Statement 1 is Tue, Statement is Tue ; Statement is not a coect explanation fo Statement 1 Statement 1 is Tue, Statement is False. (D) Statement 1 is False, Statement is Tue Statement 1 : A hollow metallic sphee of inne adius a and oute adius b has chage at the cente. A negatively chaged paticle moves fom inne suface to oute suface. Then total wok done will be zeo. a n d Statem ent : Potential is constant inside the metallic sphee. Statement 1 is Tue, Statement is Tue ; Statement is not a coect explanation fo Statement 1 Statement 1 is Tue, Statement is False. Statement 1 is False, Statement is Tue. (D) Statement 1 is Tue, Statement is Tue ; Statement is a coect explanation fo Statement 1 68 NOD6 ()\Data\14\Kota\J-Advanced\SMP\Phy\Unit-7\lectostatics\nglish\xecise.p65

20 J-Physics 1 6. S t a t em e nt 1 : lectic field at a point P is zeo if potential at that point is zeo. a n d S t a t em e nt : Potential diffeence between two points in space is zeo if electic field at all points in space is zeo. Statement 1 is Tue, Statement is Tue ; Statement is a coect explanation fo Statement 1 Statement 1 is Tue, Statement is Tue ; Statement is not a coect explanation fo Statement 1 Statement 1 is Tue, Statement is False. (D) Statement 1 is False, Statement is Tue. COMPHNSION BASD USTIONS Compehension # 1 lectostatic foce on a chaged paticle is given by F. If is positive F and if negative F. In the figue m A = m B = 1kg. Block A is neutal while B = 1C. Sizes of A and B ae negligible. B is eleased fom est at a distance 1.8 m fom A. Initially sping is neithe compessed no elongated. K=18N/m A smooth x= =1 N C B x=1.8m x-axis 1. If collision between A and B is pefectly inelastic, what is velocity of combined mass just afte collision? 6m/s m/s 9m/s (D) 1m/s. uilibium position of the combined mass is at x =...m The amplitude of oscillation of the combined mass will be : 5 9 (D) 7 9 m 14 m 7 m 9 (D) 16 m 9 NOD6 ()\Data\14\Kota\J-Advanced\SMP\Phy\Unit-7\lectostatics\nglish\xecise.p65 Compehension # A vey lage, chaged plate floats in deep space. Due to the chage on the plate, a constant electic field exists eveywhee above the plate. An object with mass m and chage is shot upwad fom the plate with a velocity v and at an angle. It follows the path shown eaching a height h and a ange. Assume the effects of gavity to be negligible. 1. Which of the following must be tue concening the object? v must be positive must be negative m must be lage (D) m must be small. Which of the following is tue concening all objects that follow the path shown when popelled with a velocity v at an angle? They must have the same mass 69 h They must have the same chage They must have the same mass and the same chage(d) Thei mass to chage atios must be the same

21 J-Physics. Suppose is 1N/C, m is 1kg, is 1C, v is 1 m/s and is. What is h? 5m 45m 8m (D) 15m 4. Which of the following will esult in an incease in? Inceasing both and m by a facto of Deceasing both and m by a facto of Inceasing by a facto of while deceasing m by a facto of (D) Deceasing by a facto of while inceasing m by a facto of 5. Which of the following is tue concening the flight of the pojectile shown? Inceasing the mass m deceases the maximum height h Inceasing the chage inceases the maximum height h Inceasing the mass m deceases the downwad acceleation (D) Inceasing the chage deceases the downwad acceleation Compehension # In a cetain expeiment to measue the atio of chage and mass of elementay chaged paticles, a supising esult was obtained in which two paticles moved in such a way that the distance between them emained constant always. It was also noticed that, this two paticle system was isolated fom all othe paticles and no foce was acting on this system except the foce between these two masses. Afte caeful obsevation followed by intensive calculation it was deduced that velocity of these two paticles was always opposite in diection and magnitude of velocity was 1 m/s and 1 m/s fo fist and second paticle espectively and masses of these paticles wee 1 kg and 1 kg espectively. Distance between them came out to be 1 Å. (1 Å = 1 1 m) 1. Acceleation of the fist paticle was zeo m/s 1 16 m/s (D) m/s. Acceleation of second paticle was m/s m/s 1 16 m/s (D) Zeo. If the fist paticle is stopped fo a moment and then eleased. The velocity of cente of mass of the system just afte the elease will be 1 1 m/s 1 1 m/s 1 m/s (D) None of these 4. Path of the two paticles was Intesecting staight lines Paabolic Cicula (D) Staight line w..t. each othe 5. Angula velocity of the fist paticle was ad/s ad/s ad/s (D) zeo Compehension # 4 lectic potential is a scala uantity. Due to a point chage at distance, the potential is given by V = A point chage is placed at (a, ) and anothe chage is placed at ( a ). 1. At how many points on the x axis, (at finite distance) electic potential will be zeo? 1 (D) NOD6 ()\Data\14\Kota\J-Advanced\SMP\Phy\Unit-7\lectostatics\nglish\xecise.p65

22 J-Physics. If we plot a gaph of potential (V) on x axis it will be like : a x= a x-axis a x= a x-axis a x= a x-axis (D) a x= a x-axis Compehension # 5 lectic potential on the axis of a chaged ing of adius at distance x is given by : 1 V =. ( = chage on the ing) 4 x lectic potential is a physical uantity measued fo unit positive chage and the potential enegy is the uantity measued fo whole chage. If only consevative foces (e.g., electostatic) act on a system, mechanical enegy emains conseved. An insulated ing having a chage 1 = 1 5 C is unifomly distibuted ove it has adius 4m. Anothe paticle having chage = C is eleased fom est along its axis at distance x = m fom its cente. Mass of both ing and the paticle is 1kg each. Neglect gavitational effects. ing is fee to move. 1. Maximum speed of paticle will be : 4.4 m/s.1 m/s 5. m/s (D) 6.1 m/s. If ing is not fee to move then maximum speed of paticle will be 5 ms ms 1 Compehension # 6 5 ms 1 (D) None of these When two concentic shells ae connected by a thin conducting wie, whole of the chage of inne shell tansfes to the oute shell and potential diffeence between them becomes zeo. Suface chage densities of two thin concentic spheical shells ae and espectively. Thei adii ae and. Now they ae connected by a thin wie. NOD6 ()\Data\14\Kota\J-Advanced\SMP\Phy\Unit-7\lectostatics\nglish\xecise.p65 1. Potential on eithe of the shells will be : (D) zeo. Suppose electic field at a distance (> ) was 1 befoe connecting the two shells and afte connecting the two shells, then 1 is : zeo 1 (D) ½. Suppose electic field at a distance was 1 befoe connecting the two shells and afte connecting the two shells, then 1 is : zeo 1 9/8 8/9 71

23 J-Physics Compehension # 7 Van-de gaff geneato is a man made high voltage geneato used to geneate a potential diffeence of ode of 1 6 V. Which can be futhe utilised to acceleate the chaged paticles fo executing nuclea eaction. Fo example we can acceleate -paticles to make bombadment on N to convet it into O. The maximum chage which can be held by a conducto depends on dielectic stength of the suounding medium. Fo example : The dielectic stength of ai is MV/m i.e. It is the maximum value of electic field, above which the suounding ai get ionsided & become conducting. 1. What maximum chage can be built on suface of dome having adius cm, if it is suounded by ai. 1 C 1 C 1 C (D) 1.5 C. The 66V ails on a subway can kill a peson upon contact. A 1 V Van de Gaaff geneto, howeve, will only give a mild shock. Which of the following best explains this paadox? The geneato povides moe enegy pe chage, but since it has few chages it tansfes a lesse amount of enegy The geneato povides moe enegy, but since thee is little enegy pe chage the cuent is small Most of the enegy povided by the geneato is dissipated in the ai because ai pesents a smalle esistance then the human body (D) Most of the enegy flows diectly to the gound without going though the human body since the geneato is gounded. Why is the potential of the dome limited by the dielectic stength of the ai? Once the potential of the dome eaches the dielectic stength of the ai, chage fom the belt is epelled by the chage on the dome Once the potential of the dome eaches the dielectic stength of the ai, the ai heats the metal of the dome, and it is no longe a good conducto Once the ai molecules become ionized, chaged on the dome can leak into the ai (D) Once the ai molecules become ionized, they no longe conduct electicity Compehension # 8 An acceleato poduces a naow beam of potons, each having an initial speed of v. The beam is diected towads an initially unchaged distant metal sphee of adius and centeed at point O. The initial path of the beam is paallel to the axis of the sphee at a distance of (/) fom the axis, as indicated in the diagam. Acceleato Poton Beam / Axis of sphee O The potons in the beam that collide with the sphee will cause it to become chaged. The subseuent potential field at the acceleato due to the sphee can be neglected. The angula momentum of a paticle is defined in a simila way to the moment of a foce. It is defined as the moment of its linea momentum; linea momentum eplacing the foce. We may assume the angula momentum of a poton about point O to be conseved. Assume the mass of the poton as m P and the chage on it as e. Given that the potential of the sphee inceases with time and eventually eaches a constant value. 1. The total enegy () of a poton in the beam tavelling with speed v at a distance of Assuming that the sphee has acuied an electostatic chage is e 4 less than e 4 7 geate than e 4 (D) zeo fom point O. NOD6 ()\Data\14\Kota\J-Advanced\SMP\Phy\Unit-7\lectostatics\nglish\xecise.p65

24 J-Physics. Afte a long time, when the potential of the sphee eaches a constant value, the tajectoy of poton is coectly sketched as / 1 4 O 1 (D) 4. Once the potential of the sphee has eached its final, constant value, the minimum speed v of a poton along its tajectoy path is given by v v / v (D) None of these 4. The limiting electic potential of the sphee is m Pv 8e m Pv 4e m Pv e (D) None of these 5. If the initial kinetic enegy of a poton is.56 kev, then the final potential of the sphee is.56 kv 1.9 kv geate than.56 kv (D) needs moe infomation Compehensi on # 9 The sketch below shows coss sections of euipotential sufaces between two chaged conductos that ae shown in solid black. Some points one the euipotential sufaces nea the conductos ae maked as A, B, C,... The aangement lies in ai. [Take = C /N m ].m Lage conducting plate Solid conducting sphee A B C D V V 1V 1VVV4V NOD6 ()\Data\14\Kota\J-Advanced\SMP\Phy\Unit-7\lectostatics\nglish\xecise.p65 1. Suface chage density of the plate is eual to C/m C/m C/m (D) C/m. A positive chage is placed at B. When it is eleased no foce will be exeted on it it will move towads A it will move towads C (D) it will move towads. How much wok is euied to slowly move a 1 µc chage fom to D? 1 5 J 1 5 J J (D) J 7

25 J-Physics Compehension # 1 ( Method of electical images ) The method of electical images is used to solve the electostatic poblems, whee chage distibution is not specified completely. The method consists of eplacement of given chage distibution by a simplified chage distibution o a single point chage o a numbe of point chages povided the oiginal bounday conditions ae still satisfied. Fo example conside a system containing a point chage placed at a distance d of fom an infinite eathed conducting plane. The bounday conditions ae : d (i) Potential is zeo at infinity (ii) Potential is zeo at each point on the conducting plane d - If we eplaced the conducting plane by a point chage ( ) placed at a distance 'd' opposite to conducting plane. The chage ( ) is called the electical image. Now system consists of two chages an at sepaation d. If chage moves to a distance 'y' fom the bounday of conducting plane (now absent), the electical image also moves to the same distance 'y' fom the bounday of conducting plane, so that the new distance between and is y. 1. The foce between point chage and eathed conducting plane is d (epulsive) d (attactive) 1 4 4d (epulsive) (D) 1 4 4d (attactive). The potential enegy of system of chage placed at a distance d fom the eathed conducting plane is 1 4 d 1 4 d 1 4 d (D) d. The wok done in caying chage fom distance d to distance y fom eathed conducting plane is zeo 4 y d d y (D) y d MISCLLANOUS TYP USTION ANSW KY XCIS - T ue / False 1. F. F. T 4. F 5. T Fill in the Blanks 1. cannot. B. 18, 16 L 4. a 5. 8i ˆ 6. Match the Column 1.,, p. s, p, (D). p, p,,s p, (D) p, 4. p 5. p, p, p,,s (D),s 6., p,s p,, (D), 7. p,s,s,s (D) s L Assetion - eason 1. D. C. C 4. B 5. A 6. C 7. B 8. C 9. D 1. B 11. A 1. B 1. D 14. A 15. D 16. D Compehension Based Comp. # 1 : 1. B. C. D Comp. # : 1. B. D. D 4. D 5. C Comp. # : 1. D. A. C 4. C 5. A Comp. # 4 : 1. B. D Comp. # 5 : 1. B. A Comp. # 6 : 1. A. B. A Comp. # 7 : 1. A. B. C Comp. # 8 : 1. C. D. B 4. A 5. B Comp. # 9 : 1. A. B. D Comp. # 1 : 1. D. D. C NOD6 ()\Data\14\Kota\J-Advanced\SMP\Phy\Unit-7\lectostatics\nglish\xecise.p65

26 J-Physics XCIS 4 [A] CONCPTUAL SUBJCTIV XCIS 1. Thee paticles, each of mass 1 g and caying a chage, ae suspended fom a common point by insulated massless stings, each 1 cm long. If the paticles ae in euilibium and ae located at the cones of an euilateal tiangle of side length cm, calculate the chage on each paticle. (Take g = 1 m/s ).. Two eual point chages = µc ae placed at each of the two opposite cones of a suae and eual point chages at each of the othe two cones. What must be the value of so that the esultant foce on is zeo?. A point chage is situated at a distance d fom one end of a thin non conducting od of length L having a chage (unifomly distibuted along its length) as shown in figue. Find the magnitude of electic foce between the two. 4. A thin cicula wie of adius has a chage. If a point chage is placed at the cente of the ing, then find the incease in tension in the wie. 5. An infinite numbe of chages, each eual to =1 C ae placed along the x axis at x = 1,, 9...m. Calculate the magnitude of electic field at x = if the consecutive chages have opposite signs. 6. The figue shows thee infinite non conducting plates of chage pependicula to the plane of the pape with chage pe unit aea, and. Find the atio of the net electic field at that point A to that at point B. A B.5m.5m 5m 5m 7. Find the electic field at cente of semicicula ing shown in figue. Y X NOD6 ()\Data\14\Kota\J-Advanced\SMP\Phy\Unit-7\lectostatics\nglish\xecise.p65 8. A clock face has negative chages,,,..., 1 fixed at the position of the coesponding numeals on the dial. The clock hands do not distub the net field due to point chages. At what time does the hou hand, point in the same diection of electic field at the cente of the dial. 9. Two concentic ings, one of adius 'a' and the othe of adius 'b' have the chages and (/5) / espectively as shown in the figue. Find the atio b/a if a chage paticle placed on the axis at z=a is in euilibium. = A 75

27 J-Physics 1. In the figue shown S is a lage nonconducting sheet of unifom chage density. A od of length and mass 'm' is paallel to the sheet and hinged at its mid point. The linea chage densities on the uppe and lowe half of the od ae shown in the figue. Find the angula acceleation of the od just afte it is eleased. S 1 1. Conside thee identical metal sphees A, B and C. Sphees A caies chage 6 and sphee B caies chage. Sphee C caies no chage. Sphees A and B ae touched togethe and then sepaated. Sphee C is then touched to sphee A and sepaated fom it. Finally the sphee C is touched to sphee B and sepaated fom it. Find the final chage on the sphee C. 1. Conside the configuation of a system of fou chages each of value. Find the wok done by extenal agent in changing the configuation of the system fom figue (i) to figue. (ii). a a a (i) (ii) 1. Two identical paticles of mass m cay chage each. Initially one is at est on a smooth hoizontal plane and the othe is pojected along the plane diectly towads the fist fom a lage distance with an initial speed v. Find the closest distance of appoach Thee chages.1 coulomb each ae placed on the cones of an euilateal tiangle of side 1m. If the enegy is supplied to this system at the ate of 1kW, how much time would be euied to move one of the chages onto the midpoint of the line joining the othe two? 1 5. Thee point chages, and 8 ae to be placed on a 9cm long staight line. Find the positions whee the chages should be placed such that the potential enegy of this system is minimum. In this situation, what is the electic field at the position of the chage due to the othe two chages? 1 6. A chage is unifomly distibuted ove a thin ing with adius. A negative point chage and mass m stats fom est at a point fa away fom the cente of the ing and moves towads the cente. Find the velocity of this paticle at the moment it passes though the cente of the ing A simple pendulum of length and bob mass m is hanging in font of a lage nonconducting sheet having suface chage density. If suddenly a chage is given to the bob & it is eleased fom the position shown in figue. Find the maximum angle though which the sting is deflected fom vetical Two fixed, eual, positive chages, each of magnitude = C ae located at points A and B sepaated by a distance of 6 m. An eual and opposite chage moves towads them along the line COD, the pependicula bisecto of the line AB. The moving chage, when it eaches the point C at a distance of 4 m fom O, has a kinetic enegy of 4 J. Calculate the distance of the fathest point D which the negative chage will each befoe etuning towads C. 76 NOD6 ()\Data\14\Kota\J-Advanced\SMP\Phy\Unit-7\lectostatics\nglish\xecise.p65

28 J-Physics D 1 9. Positive and negative chages of 1C each ae placed at two points as shown in the figue. Find the potential diffeence between A and B- A O B C 1 C A B 1 C m 1m m. Two fixed chages and ae located at the points with coodinates ( a, ) and (a, ) espectively in the x y plane.(i) Show that all points in the x y plane whee the electic potential due to the two chages is zeo, lie on a cicle. Find its adius and the location of its cente (ii) Give the expession V(x) at a geneal point on the x axis and sketch the function V(x) on the whole x axis. (iii) If a paticle of chage stats fom est at the cente of the cicle, show by a shot uantitative agument that the paticle eventually cosses the cicle. Find its speed when it does so. 1. A point chage & mass 1 g expeiences a foce of 1 N at a point at a distance cm fom a long infinite unifomly chaged wie. If it is eleased find its speed when it is at a distance 4 cm fom wie.. A dipole is placed at oigin of coodinate system as shown in figue,find the electic field at point P (, y). y P (,y) O 45 P X. Two point dipoles pk ˆ and P ˆk ae located at (,, ) and (1m,, m) espectively. Find the esultant electic field due to the two dipoles at the point (1m,, ). 4. Show that, fo a given dipole, V & cannot have the same magnitude at distances less than m fom the dipole. Suppose that the distance is magnitude. 5 m, detemine the diections along which V & ae eual in 5. The length of each side of a cubical closed suface is. If chage is situated on one of the vetices of the cube, then find the flux passing though shaded face of the cube. NOD6 ()\Data\14\Kota\J-Advanced\SMP\Phy\Unit-7\lectostatics\nglish\xecise.p65 6. A point chage is located on the axis of a disc of adius at a distance a fom the plane of the disc. If one fouth (1/4th) of the flux fom the chage passes though the disc, then find the elation between a &. a 7. A chage is unifomly distibuted ove a od of length. Conside a hypothetical cube of edge with the cente of the cube at one end of the od. Find the minimum possible flux of the electic field though the entie suface of the cube. 8. A paticle of mass m and chage moves along a diamete of a unifomly chaged sphee of adius and caying a total chage. Find the feuency of S.H.M. of the paticle if the amplitude does not exceed. 77

29 J-Physics 9. A chage is distibuted ove two concentic hollow sphees of adii and (> ) such that the suface densities ae eual. Find the potential at the common cente.. Thee concentic spheical metallic shells, A, B and C of adii a, b and c (a < b < c) have suface chage densities, and espectively. (i) Find the potential of the thee shells A, B and C. (ii) If the shells A and C ae at the same potential, obtain the elation between the adii a, b and c. 1. Thee ae 7 dops of a conducting fluid. ach has a adius and they ae chaged to a potential V. They ae then combined to fom a bigge dop. Find its potential.. Two thin conducting shells of adii and ae shown in figue. The oute shell caies a chage and the inne shell is neutal. The inne shell is eathed with the help of switch S. Find the chage attained by the inne shell. S. A spheical balloon of adius chaged unifomly on its suface with suface density. Find wok done against electic foces in expanding it upto adius. CONCPTUAL SUBJCTIV XCIS ANSW KY X C IS - 4 ( A ) C.. 1 C 1 4 d d L zeo 7. 4k î m K a m V 4 1 N / C sec 1 5. cm 6cm 8, = 1 6. K m 1 7. tan -1 mg m fom O 1 9. volt. (i) 4a, (5a, ) (ii) V= 4 fo x a 4 1 x a a x (iii) 1. n 8 ma. KP ˆ i ˆ j y a x a x fo x > a. 7 kpkˆ , 15, 5, a= m 4. (i) V A = V B = V C = (ii) ab=c 1. 9V.. (a bc), a b c b, a c b c c NOD6 ()\Data\14\Kota\J-Advanced\SMP\Phy\Unit-7\lectostatics\nglish\xecise.p65

30 J-Physics XCIS 4 [B] BAIN STOMING SUBJCTIV XCIS 1. small balls having the same mass & chage & located on the same vetical at heights h 1 & h ae thown in the same diection along the hoizontal at the same velocity v. The 1 st ball touches the gound at a distance fom the initial vetical. At what height will the nd ball be at this instant? The ai dag & the chages induced should be neglected.. Two wies AB & CD, each 1m length, cay a total chage of. micocoulomb each and ae placed as shown in figue. The ends B & C ae sepaated 1m distance. Detemine the value of electic intensity at the point P in the vecto fom. Note that P is the mid point of BC. A y B P C O x D. Two identical balls of chages 1 & initially have eual velocity of the same magnitude and diection. Afte a unifom electic field is applied fo some time, the diection of the velocity of the fist ball changes by 6 and the magnitude is educed by half. The diection of the velocity of the second ball changes thee by 9. In what popotion will the velocity of the second ball changes? 4. A cicula ing of adius with unifom positive chage density pe unit length is fixed in the Y Z plane with its cente at the oigin O. A paticle of mass m and positive chage is pojected fom the point P,, on the positive X axis diectly towads O, with initial velocity v. Find the smallest value of the speed v such that the paticle does not etun to P. 5. Two concentic ings of adii and ae placed with cente at oigin. Two chages each ae fixed at the diametically opposite points of the ings as shown in figue. Smalle ing is now otated by an angle 9 about Z axis then it is again otated by 9 about Y axis. Find the wok done by electostatic foces in each step. If finally lage ing is otated by 9 about X axis, find the total wok euied to pefom all thee steps. y x z NOD6 ()\Data\14\Kota\J-Advanced\SMP\Phy\Unit-7\lectostatics\nglish\xecise.p65 6. An infinite dielectic sheet having chage density has a hole of adius in it. An electon is eleased on the axis of the hole at a distance fom the cente. What will be the velocity which it cosses the plane of sheet. (e = chage on electon and m= mass of electon). 7. Small identical balls with eual chages ae fixed at vetices of egula 9 gon with side a. At a cetain instant, one of the balls is eleased & a sufficiently long time inteval late, the ball adjacent to the fist eleased ball is feed. The kinetic enegies of the eleased balls ae found to diffe by K at a sufficiently long distance fom the polygon. Detemine the chage of each pat. 79 e

31 J-Physics 8. A nonconducting ing of mass m and adius is chaged as shown. The chaged density i.e. chaged pe unit length is. It is then placed on a ough nonconducting hoizontal suface plane. At time t =, a unifom electic field ˆ i is switched on and the ing stat olling without sliding. Detemine the fiction foce (magnitude and diection) acting on the ing, when it stat moving. x y 9. The electic field in a egion is given by = x i. Find the chage contained inside a cubical volume bounded by the sufaces x =, x =a, y=, y=a, z= and z=a. [Take = 5 1 N/C, = cm and a = 1cm] 1. Figue shown a section though two long thin concentic cylindes of adii a & b with a>b. The cylindes have eual and opposite chages pe unit length. Find the electic field at a distance fom the axis fo (i) < a (ii) a < < b (iii) >b b a 1 1. A solid non conducting sphee of adius has a non unifom chage distibution of volume chage density,, whee is a constant and is the distance fom the cente of the sphee. Show that : (i) The total chage on the sphee is = and (ii) The electic field inside the sphee has a magnitude given by, = K A cavity of adius is pesent inside a solid dielectic sphee of adius, having a volume chage density of. The distance between the centes of the sphee and the cavity is a. An electon e is kept inside the cavity at angle =45 as shown. How long will it take to touch the sphee again? a 1. Two small metallic balls of adii 1 & ae kept in vacuum at a lage distance compaed to the adii. Find the atio between the chages on the two balls at which electostatic enegy of the system is minimum. What is the potential diffeence between the two balls? Total chage of balls is constant A positive chage is unifomly distibuted thoughout the volume of dielectic sphee of adius. A point mass having chage and mass m is fied towads the cente of the sphee with velocity v fom a point a distance (>) fom the cente of the sphee. Find the minimum velocity v so that it can penetate / distance of the sphee. Neglect any esistance othe than electic inteaction. Chage on the small mass emains constant thoughout the motion. 8 e NOD6 ()\Data\14\Kota\J-Advanced\SMP\Phy\Unit-7\lectostatics\nglish\xecise.p65

32 J-Physics 1 5. lectically chaged dops of mecuy fall fom altitude h into a spheical metal vessel of adius in the uppe pat of which thee is a small opening. The mass of each dop is m & chage is. What is the numbe 'n' of last dop that can still ente the sphee. h 1 7. Two chages 1 & ae placed at A and B espectively. A line of foce emeges fom 1 at angle with line AB. At what angle will it teminate at? A 1 B NOD6 ()\Data\14\Kota\J-Advanced\SMP\Phy\Unit-7\lectostatics\nglish\xecise.p65 BAIN STOMING SUBJCTIV XCIS ANSW KY X C I S - 4 ( B ) 1. H = h 1 h g. 5. v W fist step v 8 4 K i ˆ 199ˆj 4., W second step =, W total = 6. v= m e m 7. 4 Ka 8. ˆ i C 1. K,, 1. 6 m 1 1. ea = K m sin sin 1 5. n = V m 4 mg h

33 J-Physics XCIS 5 PVIOUS YA USTIONS 1. On moving a chage of C by cm, J of wok is done, then the potential diffeence between the points is- [AI - ] (1).1 V () 8 V () V (4).5 V. A chaged paticle is placed at the cente O of cube of length L (ABCDFGH). Anothe same chage is placed at a distance L fom O. Then the electic flux though ABCD is- [ A I - ] H G F C O (1) /4 L () zeo () / L (4) / L. A thin spheical conducting shell of adius has a chage. Anothe chage is placed at the cente of the shell. The electostatic potential at a point P at a distance / fom the cente of the shell is- (1) () B L () (4) D A 4 ( ) 4 4 [ A I - ] 4. Two spheical conductos B and C having eual adii and caying eual chages in them, epel each othe with a foce F when kept apat at some distance. A thid spheical conducto having same adius as that of B but unchaged, is bought in contact with B, then bought in contact with C and finally emoved away fom both. The new foce of epulsion between B and C is- [ AI-4] (1) F () F () F (4) F A chaged paticle is shot towads anothe chaged paticle which is fixed, with a speed v. It appoaches upto a closest distance and then etuns. If was given a speed v, the closest distance of appoach would be- [ AI-4] v (1) () () / (4) /4 6. Fou chages eual to ae placed at the fou cones of a suae and a chage is at its cente. If the system is in euilibium, the value of is- [ A I - 4 ] (1) 4 (1 ) () 4 (1 ) () (1 ) (4) (1 ) 7. A chaged ball B hangs fom a silk thead S, which makes an angle with a lage chaged conducting sheet P, as shown in the figue. The suface chagedensity of the sheet is popotional to- [ A I - 5 ] P (1) cos () cot () sin (4) tan S B NOD6 ()\Data\14\Kota\J-Advanced\SMP\Phy\Unit-7\lectostatics\nglish\xecise.p65

34 J-Physics 8. Two point chages 8 and ae located at x = and x = L espectively. The location of a point on the x-axis at which the net electic field due to these two point chages is zeo is- [ A I - 5 ] (1) L () L 4 () 8L (4) 4L 9. Two thin wie ings each having a adius ae placed at a distance d apat with thei axes coinciding. The chages on the two ings ae and. The potential diffeence between the centes of the two ings is- [ A I - 5 ] (1) 4 d () 1 1 d () zeo (4) d 1. An electic dipole is placed at an angle of to a non-unifom electic field. The dipole will expeience- (1) a tanslational foce only in the diection of the field [ A I - 6 ] () a tanslational foce only in a diection nomal to the diection of the field () a toue as well as a tanslational foce (4) a toue only 1 1. Two spheical conductos A and B of adii 1 mm and mm ae sepaated by a distance of 5 cm and ae unifomly chaged. If the sphees ae connected by a conducting wie then in euilibium condition, the atio of the magnitude of the electic fields at the sufaces of sphees A and B is- [ AI - 6] (1) 4 : 1 () 1 : () : 1 (4) 1 : 4 1. An electic chage 1 µc is placed at the oigin (, ) of X-Y coodinate system. Two points A and B ae situated at (, ) and (, ) espectively. The potential diffeence between the points A and B will be - [AI - 7] (1) 9 V () zeo () V (4) 4.5 V 1. Chages ae placed on the vetices of a suae as shown. Let be the electic field and V the potential at the cente. If the chages on A and B ae intechanged with those on D and C espectively, then- A B D C NOD6 ()\Data\14\Kota\J-Advanced\SMP\Phy\Unit-7\lectostatics\nglish\xecise.p65 (1) emains unchanged, V changes () both and V change [ A I - 7 ] () and V emain unchanged (4) changes and V emains unchanged 1 4. The potential at a point x (measued in µm) due to some chages situated on the x-axis is given by : V(x) = /(x 4) volt. The electic field at x = 4 µm is given by : [AI-7] (1) 5 V/µm and in the ve x diection () 5 V/µm and in the ve x diection () 1 V/µm and in the ve x diection (4) 1 V/µm and in the ve x diection A thin spehical shell of adius has a chage spead unifomly ove its suface. Which of the following gaphs most closely epesents the electic field () poduced by the shell in the ange, whee is the distance fom the cente of the shell? [ AI - 8] (1) O () () O () 8 () O () (4) O ()

35 J-Physics 1 6. A chage is placed at each of the opposite cones of a suae. A chage is placed at each of the othe two cones. If the net electical foce on is zeo, then euals :- [AI - 9] (1) 1 () 1 () (4) 1 This uestion contains Statement 1 and Statement. Of the fou choices given afte the statements, choose the one that best descibes the two statements Statement 1 : Fo a chaged paticle moving fom point P to point the net wok done by an electostatic field on the paticle is independent of the path connecting point P to point. Statement : The net wok done by a consevative foce on an object moving along closed loop is zeo. [ AI - 9] (1) Statement 1 is tue, Statement is tue; Statement is not the coect explanation of Statement 1 () Statement 1 is false, Statement is tue () Statement 1 is tue, Statement is false (4)Statement 1 is tue, Statement is tue; Statement is the coect explanation of Statement Two points P and ae maintained at the potential of 1V and 4V, espectively. The wok done in moving 1 electons fom P to is :- [AI - 9] (1) J () J () J (4) J 1 9. Let () = 4 be the chage density distibution fo a solid sphee of adius and total chage. Fo a point 'p' inside the sphee at distance 1 fom the cente of the sphee, the magnitude of electic field is [AI - 9] (1) () () (4) 4. A thin semi-cicula ing of adius has a positive chage distibuted unifomly ove it. The net field at the cente O is :- [AI - 1] (1) ĵ () 4 ĵ () ˆj 4 (4) 1 ˆj 1. Let thee be a spheically symmetic chage distibution with chage density vaying as 5 () = 4 upto =, and () = fo >, whee is the distance fom the oigin. The electic field at a distance ( < ) fom the oigion is given by : [AI - 1] (1) 5 4 () 4 5 () 5 4 (4) Two identical chaged sphees ae suspended by stings of eual lengths. The stings make an angle of with each othe. When suspended in a liuid of density.8 g cm, the angle emains the same. If density of the mateial of the sphee is 1.6 g cm, the dielectic constant of the liuid is : [AI - 1] (1) 1 () 4 () (4). Two identical chaged sphees suspended fom a common point by two massless sting of length ae initially a distance d(d << ) apat because of thei mutual epulsion. The chage begins to leak fom both the sphees at a constant ate. As a esult the chages appoach each othe with a velocity v. Then as a function of distance x between them :- [ AI - 11] (1) v x 1/ () v x () v x 1/ (4) v x 1 4. The electostatic potential inside a chaged spheical ball is given by = a b whee is the distance fom the cente; a, b ae constant. Then the chage density inside the ball is :- [AI - 11] (1) 4 a () 6 a () 4 a (4) 6 a NOD6 ()\Data\14\Kota\J-Advanced\SMP\Phy\Unit-7\lectostatics\nglish\xecise.p65

36 J-Physics 5. Two positive chages of magnitude '' ae placed at the ends of a side (side 1) of a suae of side 'a'. Two negative chages of the same magnitude ae kept at the othe cones. Stating fom est, if a chage moves fom the middle of side 1 to the cente of suae, its kinetic enegy at the cente of suae is :-[AI - 11] (1) a () zeo () 1 4 a 5 1 (4) 1 4 a 5 6. This uestion has Statement- 1 and Statement-. Of the fou choices given afte the statements, choose the one that best descibes the two statements. An insulating solid sphee of adius has a unifomaly positive chage density. As a esult of this unifom chage distibution thee is a finite value of electic potential at the cente of the sphee, at the suface of the sphe and also at a point out side the sphee. The electic potential at infinity is zeo. [ AI - 1] Statement-1: When a chage '' is taken fom the cente to the suface of the sphee, its potential enegy changes by Statement-: The electic field at a distance ( < ) fom the cente of the sphee is. (1) Statement-1 is tue, Statement- is tue and Statement- is the coect explanation of Statement-1. () Statement-1 is tue, Statement- is tue and Statement- is not the coect explanation of statement-1. () Statement-1 is tue, Statement- is false (4) Statement-1 is false, Statement- is tue. 7. In a unifomly chaged sphee of total chage and adius, the electic field is plotted as a function of distance fom the cente. The gaph which would coespond to the above will be :- [ AI - 1] (1) () () (4) 8. Two chages, each eual to, ae kept at x = a and x = a on the x-axis. A paticle of mass m and chage is placed at the oigin. If chage is given a small displacement (y << a) along the y-axis, the net foce acting on the paticle is popotional to [ AI - 1] (1) y () y () 1 y (4) 1 y 9. A chage is unifomly distibuted ove a long od AB of length L as shown in the figue. The electic potential at the point O lying at a distance L fom the end A is :- [AI - 1] NOD6 ()\Data\14\Kota\J-Advanced\SMP\Phy\Unit-7\lectostatics\nglish\xecise.p65 (1) 8 L () 4 L 85 () ANSW-KY 4 L ln (4) ln 4 L ue Ans ue Ans

37 J-Physics XCIS 5 PVIOUS YA USTIONS MC' S WITH ON COCT ANSWS 1. A chage is fixed at each of the points x = x, x = x, x = 5x... on the x axis and a chage is fixed at each of the points x = x, x = 4x, x = 6x... Hee x is a positive constant. Take the electic potential at a point due to a chage at a distance fom it to be /4. Then the potential at the oigin to the above system of chages is : [IIT-J 1998] zeo 8 x n infinite (D) n () 4 x. Thee chages, and ae placed at the vetices of a ight angle tiangle (isoscles tiangle) as shown. The net electostatic enegy of the configuation is zeo, if is eual to : [IIT-J ] a 1 (D). Thee positive chages of eual value ae placed at the vetices of an euilateal tiangle. The esulting line of foce should be sketched as in : [IIT-J 1] (D) 4. A unifom electic field pointing in positive x diection exists in a egion. Let A be the oigin, B be the point on the x axis at x = 1 cm and C be on the point on the y axis at y = 1cm. Then the potentials at the A, B and C satisfy : [IIT-J 1] V A < V B V A > V B V A < V C (D) V A > V C 5. Two eual point chages ae fixed at x = a and x = a on the x axis. Anothe point chage is placed at the oigin. The change in the electical potential enegy of, when it is displaced by a small distance x along the x axis, is appoximately popotional to : [IIT-J ] x x x (D) 1/x 6. A metallic shell has a point chage kept inside its cavity. Which one of the following diagams coectly epesents the electic lines of foces? [IIT-J ] (D) 86 NOD6 ()\Data\14\Kota\J-Advanced\SMP\Phy\Unit-7\lectostatics\nglish\xecise.p65