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moving a chargc of 20 coulomb by 2 cm, 2 J of work is, done, then the potential difference between the points is, On, , 2, , (a), , 0.1 V, , (c), , 2V, , If there, , are n, , then the energy stored is equal to, (a), , c), , CV, , CV, , (b), (d), , 1, 2, , b), , 12002, , (b), (d), , capacitors in, , 8V, 0.5 V., parallel connected, , (a) q/4T EgL, zero, , (c) q/2 EL, to, , V volt, , source,, , 2002, , nCV, , C, , 2n, , A charged particle q is placed at the centre O of cube of, length L (A BCDEFGH). Another same chargeq is placed, at a distance L from O. Then the electrie flux through ABCD, , 2002), , H, , O, , G, , L, , (d) q/3 menL, A., , If a charge q is placed at the centre of the line joining two, equal charges Q such that the system is in equilibrium then, 2002, the value of q is, , (a) 02, (b)-02, (d) -04, (c) 94, Capacitance (in F) of a spherical conductor with radius I m, 20021, is, (a), , 1.11010, , (C) 9x10, , (b) 10, (d) 103

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6, , brought in contact with B, then brought in contact, with c, finally removed away from both. The new force, of, , If the electric flux entering and leaving an enclosed surface, , and, , respectivelyis oy and d2.the electric charge inside the surface, (b) (01+¢2)E%, , (a)(02-1Eo, , (c)(2-1)/t, (d) (01+02E, A sheet of aluminium foil of negligible thickness, introduced, , 8., , repulsion between B and C is, , 2003, , will be, , 13., , is, between the plates of a capacitor. The, , capacitance of the capacitor, 2003, (b), remains, unchanged, (a) decreases, (d) increases, (c) becomes infinite, A thin spherical conducting shell ofradius R has a charge q., Another charge Q is placed at the centre of the shell. The, , 4TtER, , C), , 20, 47TER, , 14., , 4TtE,R, , (c) 4x10- joule, , (d), , Four, , 2004, , 2r, r4, , charges equal to -Q are placed at the four corners afa, a charge q is at its centre. If the, system is in, , 2004, , (a), , 12/2), , b)+2), , (C), , 2/, , d-2), , A charged oil drop is suspended in a uniform field of 3x10*, so that it neither falls nor rises. The charge on the, drop, , v/m, , g= 10m/s), , coulombon, , a condenser of capacity 100 micro-farad is, , 16x10joule, , (b), , r2, , will be (Take the mass of the charge = 9.9x10-15 kg and, , The work done in placing a charge of 8x10, , (a), , charge particle q' is shot towards another charged narm, 'which is fixed, with a speed v.lt approaches o, a closest distance r and then returns., Ifq were givenuptoa, speed of 2v' the closest distances of approach would he, , A, , equilibrium the value of q is, , 15, , (d) 4TteR, , (d) 3 F78, , 2.004, , square and, , 20, 2, (b) 4TER 4TE,R, , g+0)2, , (b) 3 F/4, , F/4, , (c)r, , (2003, , 20, , (a), , F/8, , (c), , (a), , electrostatic potential at a point P a distance from the, centre of the shell is, , (a), , (a), (c), , 12003, , 2004, , (b) 3.2x10-18C, , 1.6x10-18C, 3.3x10-18C, , (d), , 4.8x10-18C, , b) 3.1x100 joule, , 16. Two point charges + 8q and -2q are located atr =0 and, , (d) 32x10-2joule, , =L respectively. The location of a point on the r axis at, which the net electrie field due to these two point charges is, , Three charges 4 , t4, and -q, are place as shown in the, , 2005, , zero is, , figure. Thex - component of the force on-4, is proportional, , 12003, , to, , 17, , (a), , 4, , (b), , 2L, , (c), , 4 L, , (d), , 8 L, , Two thin wire rings each having a radius R are placed at a, , distance d apart with their axes coinciding. The charges on, , the two rings are +q and -q. The potential difference, a, , 2, , -q, , (a), , cos, , (b), , X, , (a), , 2T E, , sin, , os, , (d), , R, , R+d, , R, , R, , qR, , b) 477, , (c), , 2005, , between the centres of the two rings is, , b, , d, , sin 6, , a, 11, , Due to the consequent decrease in diameter thechangein, the resistance ofthe wire will be, 2003, (a) 200%, (b) 100%%, (c), , 12., , 41Tt E, , The length ofa given cylindrical wire is increased by 100%., , 50%, , (d) 300P, , Two spherical conductors B and C having equal radii and, carrying equal charges on them repel each other with a force, F when kept apart at some distance. A third spherical, conductor having same radiusas that B but n, , hargedis, , +d", , (d) zero, 18., , quall, , A paralle! plate capacitor is made by stacking R, spaced plates connected alternatively. If the capaet, , c, , Detween any two adjacent plates is C" then the res, , capacitance is, (a) (n 1)C, , (c) 7C, , b, (d, , (7)C, C, , tanee

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19., , A charged ball B hangs froma silk thread S, which makes an, , angle, in the, , 25., , Charges are placed on the vertices of a, , with a large charged conducting sheet P, as shown, , figure. The surface charge density, , cot 0, , (b), , cos 0, , of the sheetis, , [2005, , (a), , sin e, , mCAT, S, , 26., , (d), , C, , E and Vremain unchanged, , charges situated on the x-axis is given by, , Vo)-20/(r-4) volt, The electric field E atx=4 umis given by, , (c), , (5/3) volt/ u m and in the +ve x direction, , (d) (10/9) volt/ u mand in the-vex direction, , C, , 27., , A parallel plate condenser with a dielectric of dielectric, , constant kK between the plates has a capacity C andis, charged to a potential V volt. The dielectric slab is slowly, removed from between the plates and then reinserted. The, net work done by the system in this process is, [2007], , a translational force only in the direction ofthe field, , (b) a translational force only in a direction normal to the, direction of the field, a torque as well as a translational force, , (a), , (b)K-1)cv?, , zero, , (d) a torque only, , 22., , Two insulating plates are both uniformly charged in such a, , (c) CV (K-1), , way that the potential difference between them is, , V-V= 20V. (i.e., plate 2 is at a higher potential). The, , 28., , surfaces of the earth and the moon respectively and if, Millikan's oil drop experiment could be performed on the, two surfaces, one will find the ratio, 20071, , infinitely large. An electron is released from rest on the inner, surface of plate 1. What is its speed when it hits plate 2?, (a), , 2.65 x 10 m/s, , (b), , 7.02 x 1012 m/s, , (c), , 1.87 x 10 m/s, , 2006, , electronic charge, , (a), , X, , 29., , (a) 4:1, (c) 2:1, , 1:2, , =, , 2006, , 0) respectively., , The potential difference, , between the points A and B will be, , (a) 4.5 volts, (c) Zero, , (d) 8E EM, , A parallel plate capacitor with air between the plates has, , 3 and thickness, , the surfaces of spheres A and B is, b), , (b), , 9 volts, , (d), , 2 volt, , 20071, , 1, , dielectrics. One ofthe dielectries has dielectric constant k,, , constant k, =, , d, , while the other, , 6 and thickness, , (a) 1.8pF, (c) 40.5pF, 30., , one, , has dielectric, , Capacitance of the, , capacitor is now, , -Yco-ordinate system. Two points A and B are situated at, and (2,, , (b), , a. The space between the plates is now filled with two, , (d) 1:4, An clectric charge 103u C is placed at the origin (0, 0) of, , V2,2, , 8M8E, , capacitance of 9 pF. The separation between its plates is, , then in equilibrium condition, the ratio ofthe magnitude of, at, , on, , (c)0, , 3. Two spherical conductors A and B ofradii I mm and 2 mm, are separated, by a distance of 5 cm and are uniformly, Charged. Ifthe spheres are connected by a conducting wire, , the electric fields, , the, , moont o be, electronic charge on the earth, , K-0.1 m, , (d) 32x 10-m/s, , d) K-1) cv?, , K, If 8g and gM are the accelerations due to gravity on the, , plates are separated by d = 0.1 m and can be treated as, , (e=1.6x 10-19 C,m,=9.11 x 10-3l kg), , 20071, , (10/9) volt/ u m and in the +ver direction, , (b) (5/3) volt/ u m and in the -vex direction, , msAT, , An electric dipole is placed at an angle of 30° to a nonuniform electric field. The dipole will experience, 2006, , (c), , (d), , The potential at a point x (measured in u m) due to some, , [2005], , S, , 2msAT, , both E and V change, , (a), , 2mCAT, , (b), , (a), , (c), , D, , s'and mass m'. If the temperature of the block is raised by, AT', the potential diffèrenceV' across the capacitance is, , (a), , E changes, Vremains unchanged, , (b)E remains unchanged, V changes, , discharged through a small coil of resistance wire embedded in a thermally insulated block of specific heat capacity, , 21., , D, , 20071, , and C respectively, then, , 20. A fully charged capacitor has a capacitance C'. It is, , (C), , shown., , Ifthe charges on A and B are interchanged with those on, , (c) tan, (d), , as, , Let E be the electric field and Vthe potential at the centre., a, , proportional to, , (a), , square, , (b) 45 pF, , 2008, , (d) 20.25pF, , A thin, , spherical shell of radus R has charge Q spread, uniformly over its surface. Which of the following graphs, most closely represents the electric field, E(n produced by, the shell in the range 0<r<o, wherer is, the distance from, the centre of the shell?, 2098

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36., , Let there be, , a, , chargedensity varying as, (a), , (b), , and, , o, , origin., , E), , (c), 31., , Iwo, , P and, , O, , 10 V and, , are, , maintained the potentials, The work done in moving, , 32, , 37., , Ifthenet electrical force on Qis zero, then Qq equals: 20091, 33., , This, , question, , c), , 38, , 39., , Statement-l is true, Statement-2 is true: Statement-2 is, the correct explanation of, , electrostatic potential inside a charged spherical ball i, , given by = ar, are, , +b where r is the distance, from the centre, constants. Then the charge, , density inside the, , In, , a, , 201, , (b)-24Ta, (d)-24TtaEo, , uniformly charged sphere of total charge Qand radius, , R, the electric field E is plotted as function of, distance from, the centre, The graph which would correspond to the above, , Statement-1., , (b) Statement-I is true, Statement-2 is true; Statement-2 is, not the correet, , elocty, 201, , (b) vocr, (d) vc -, , (a) baeo, (c) 6aEo, , Statement-2: Ihe net work done by a conservative force, , (a), , The, , and a, b, ball is:, , particle is independent of the path connecting point P to, , object moving along a closed loop is zero., , 3e03 R, , result charges approach each other, constant, with a velo, of, Then as a function distance x between them., , (c) v, , point ., on an, , 2010, , a, , (a) vox, , Of, , thefour choices given afier the statements, choose the one, that best describes the two statements., Statement-1: For a charged particle moving from 2009, point Pto, point Q, the net work done by an electrostatic field on the, , b), , identical charged spheres suspended from a, comn, two massless strings of, length 1 are inisi, distance d(d<< ) apart oecause of their, mutual ally, The charge begins to leak from both the spheres at repulsion, a, rate. As, , (d)-2/2, , V., , contains Statement-l and Statement-2., , om the ongnm, , Two, , ., , (b) 1, , , where r is the distance, tance from the, a distance, rtr< R) fro, , point by, , charge Q is placed at each of the opposite corners of a, Square. A charge q is placed at each of the other two corners., (a)-1, , R, , Pola R)upto rsp, , (d PorS, 3E4 R), , (c), , 2009, , (d)-9.60x10-17J, , A, , R, , of, , at, , (b)-2.24x10-16J, , (c) 2.24x 1016J, , r, , Plr)=, , The electric fielda, , Por5, 43, , a), , - 4 V. respectively., 100 electrons from, Pto Qis:, , (a) 9.60 x 10 J, , for, , 1S given by, , (d), , points, , pr)=0, , NSICS, ribution vit, , spherically symmetrie charge distrih, , will be:, , 2012, , explanation of Statement-1., , (c) Statement-l is false. Statement-2 is true., (d) Statement-l is true. Statement-2 is false., 34., , Let P(r)=, , (b, , (a), , be the charge density distribution fora, TR*, , Rr, , solid sphere of radius R and total charge . For a point p, inside the sphere at distance r from the centre, ofthe sphere., the magnitude of electric field is, , (a), , 4TT E, , (b), , On, , Rr, , E, , 2009, (c), , (d), , 4T E R", , Rr, , (c), 35,, , 3t Ey R, , 40., , (d) 0, , R, , Of the tour, , This questions has statement-I and statement-2., , choices given after the statements, choose the one that, , A thin semi-circular ring of radius r has a positive chargeq, , best describe the two statements., , distributed uniformly over it. The net field E at the centre O, , An insulating solid sphere of radius R has a uniformiy, , 1S, , positive charge density p. As a resuit ofthis uniform charg, , (a, , 2010, AT" E, , distribution there is a finite value of electricpotential at tn, , centre, a, , (b), , 4T, , 2012, , ofthe sphere, at the surface ofthe sphere, , and also, , point out side the sphere. The electric potential, , at, , in finite, , is zero., , Statement -i: When a charge q is take from the centre, C, , the surface of the, , 3t0, , sphere its potential, , oy, energy changes

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Statement-2:The electric field at a distance r(r<R) from, the, , (a), , (b), , centre of the, , sphere is PL, , 3E0, , Statement I 1s true, Statement 2 is true; Statement 2 is, , a) 6x10' C/m, , b) 3x10 C/m, , (c) 3x10' C/m, , (d) 6x10* C/m, , not the correct explanation of statement 1., , In the given circuit, charge Q, on the 2uF capacitor changes, function of'C' is given, as C is varied from 1uF to 3uF. Q, as a, , Statement I 1s true Statement 2 is false., , properly by: (figures, , are, , drawn, , are no, schematically, JEEand, Main 2015), , to scale), , (c)Statement I is false Statement 2 is true., , (d) Statement I is true, Statement 2 is true, Statement 2 is, , the correct explanation of Statement 1, 41. Two capacitors C, and C, are charged to 120 V and 200 V, , 2uF, , respectively. It is found that connecting them together the, , potential on each, , one can, , be made, , Then, , zero., , JEE Main 2013], , (b) 3C =5C2, , (a) 5C =3C2, (c) 3C1, , +, , 5C2, , E, , =, , Charge, , (d) 9C = 4C2, , 0, , 42 Two charges, cach equal to q, are kept at x= - a and x = a on, , (a), thex-axis. A particle ofmass m and charge qo=is placed, , 3uF, , at the origin. If charge 9o is given a small displacement, , Charge, , (y&<a) along the y-axis, the net force actingon theparticle, JEE Main 2013], , IS proportional to, , (a), , b)-y, , (c), , (d), , Q2, (b), , 1uF, Charge, , 43. A, charge Q is uniformly distributed over a long, length L as shown in the figure. The electric potential at the, point O lying at distance L from the end A is, JEE Main 2013], , rod AB of, , 3uF, , Q2, (C), , A, , C, , 3uF, (a), , 30, (b) 4TtE, , 8TtEL, , Charge, , Qln 2, , (d) 4Te0, , 4TtEL In 2, , (d), , 44 ASSume that an electric field, tne, , potential difference V, , at the origin and V, , =, , -, , 30xi, , Vo., , exists in space. Then, , where, , Vo, , is the potential, , the potential at x=2 mis:, , JEE Main 2014), , (a) 120 J/C, , (c) -80J/C, , 45., , 3uF, , theequipotential surfaces with potentials, , (b) -120.J/C, , (d) 80 J/C, made of, , 1uF, , 47-A uniformly charged solid sphere of radius R has potential, Va (measured with respect to ) on its surface. For this sphere, , two circular, , plates, , ediiel plate capacitor is, with a diclectric of dielectric, e d by a distance 5 mm and, the, When the electric field in, ant22 between them., of the positive, dielectric is 3x10 V/nm the charge densityJEE, Main 2014), plate will be close to:, , 3Vo SVo 3V, 4, , 4, , Vo have radius R,, Ra. R3 and R, respectively. Then, , and 4, , JEE Main 2015), , (a) R0and R, (R, R,), (b) 2R R, (c) R0and R,(R,-R), d) R0 and (R. - R)(R, , R

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48. A long cylindrical shell carries positive surface charge d in, , (a), , 420NC, , half and negative surface charge a in the lower, half. The electric field lines around the cylinder will look like, , (c), , 240 NNC, , the upper, , figure given, , in, , (figures, , are, , schematic and not, , drawn, , to, , JEE Main 2015], , scale), , 50., , A, , P = , where A is, , constant and, , is the, , distance froma, from the, of the spheres is a point charge (, of A such that the electric, r, , value, the spheres will be constant, is:, , eld in the region, , A combination ofcapacitors is set up as shown in the figure., , The magnitude ofthe electric field, due to a point charge Q, 4, (having a charge equal to the sum of the charges on the, F and 9 u F capacitors), at a point distance 30 m from it., u, , 2Q, , 1JEE Main 2016], , would equal, , (a) ( a-b*), , b), , 2Q, Ta, , 3 uF, 4F, 9uF, , 2uF, 8V, , (c), , Q, 27t a, , Q, , (d), , Q.The, , een, (JEE Mainbetw2016, , (d), , (c), 49., , a, , nd, , density, , entre. At the centre, , (b), , SICS, , iSI, , The region between two concentric spheres of radi, respectively (see figure), have volume charge d, , b,, , r, , (a), , (b) 480NNC, (d) 360NIC, , 2m(b-a)