‘Topic 1.1: Electric Charge and Basic Properties of Electric Charge 1 Study following statements about electric charge. (A) Charge i a point (B) Charge is a property of matter (C) The SI unit of charge is coulomb, (D) ‘Two types of changes exist in nature. Choose the correct statements, (1) Only (A), (B) and (C) @) Only (A), (C) and (D) ) Only (B), (C) and (D) (4) Only (A), (B) and (D) 2. Choose the correct statement about electric charges. (1) Charges always exist in equal and opposite pars. (2) Charges can exist without mater. (3) Anneutral body contains no charge. (4) An isolated charge can exist. 3. Definition of one coulomb is (A) ‘Two charges of one coulomb each separated by cone metre distance repel each other with a force of 9x 10°N. (B) One coulomb is the charge transferred in one second through the section of wire carrying a current of one ampere (©) Inone coulomb there are 6.25 x 10" electrons ‘Choose the correct statements. (1) Only (A) (2) Only (B) (3) Only (A) and (C) (4) (A), B) and (©) Topicwise Questions zal | 4, Which of the following properties explain that charg | dacs a cai | (1) Charge quantization | (2) Charge conservation 6) Charge invariance (@) Charge is camed by mar $. When a plastic comb is pased trough dry bai, del Charge eured by the eo (1) veya negate (3) somatimes negative (2) always postive @) none ofthe above 6. What will happen when we rub a glass rod with sik cloth? (1) Some of the electrons from the glass rod are transferred to the silk cloth. (@) The glass rod gets positive charge and silk cloth gets negative charge (G) New charges are created inthe process of rubbing (4) Both (1) and (2) are correct. 7. Following statements are given about the electri charge (A) Like charges repel and unlike charges attract each other. (B) Unlike charges repel and like charges attract exch | other. | (C) Stationary charges interact only eletrically. (D) Moving charges interact electromagneticlly “The correct statements are (1) Only (A), (B) and (C) (2) Only (A), (C) and (D) {@) Only (B), (©) and (D) (4) All statements are correctelec Charged and Pa Xo SN 9. 10. ML 2, 1. M4 According to charge quantization (A) charge eannot have any value (B) charge ean have only discrete values (©) the basic mit of electricity is e= 1,6 10°C, (D) the charge q mst be an integral multiple of ei qztne ‘The correct statements are (1) Only (A), (B) and (©) @) Only (A), ©) and (D) @) Only (B), (©) and (D) (4) Allstatements are correct In accordance with charge conservation (A) charge eannot be destroyed but can be created (B) charge can neither be created nor be destroyed (©) charge can be converted into energy. ‘The correc statements are (1) Only (A) and (C) (2) Only (A) and (B) ) Only (B) and (C) (4) Only (B) Ifa body is charged by rubbing it. is weight, (1) always decreases slightly (2) always inereases slightly (3) may increase slightly or may decrease slightly (@) remains precisely the same There are two metallic spheres of same radii but one is solid and the other is hollow, then (1) Solid sphere can be given more charge (2) Hotow sphere can be given more charge (@) They ean be charged equally (maximum) (@) None ofthe above When a body is earth connected, electrons from the earth flow into the body. This means the body is, (1) Uncharged (2) Charged posi ©) Charged negatively (4) An insulator [A positively charged insulator is brought near (but does not touch) two metalic spheres that are in contact. The tetallc spheres are then separated. The sphere which ‘as initially farthest fom the insulator will have (1) nonet charge 2) anegatve charge ) positive charge (4) either a negative or a positive charge ly Five balls numbered 1 to $ are suspended using separate threads. Pais (1, 2), (2, 4) and (4, 1) show electrostatic attraction, while pairs (2, 3) and (4, 5) show repulsion ‘Therefore ball 1 must be (1) Positively charged (@) Negatively charged 8) Neutral (4) Made of metal 15, In two cases, two identical conducting spheres are given ‘equal charges, in one case of the same type whereas in another case of opposite type. The distance between the spheres is not large compared to the diameter. Let F, and FF, be the magnitude of the force of interaction between the spheres, as shown, then Fr OQO-oh 20 A Fer Q har @A1>m>1V (Q) 1> >> IV @) M>I>1v> I (4) > IV>1> 0 22, An electrically isolated hollow (initially uncharged), conducting sphere has a small positively charged ball suspended by an insulating rod from its inside surface, ‘see diagram. " ve causes the inner surface of the sphere to becom, negatively charged. When the ball is centred inthe sph | Ineelectrc field outside the conducting sphere is (1) 2010 (2) the same as ifthe sphere wasn’t there {G) twice what it would be ifthe sphere wasn’t there | (4) equal in magnitude but opposite in direction to wh it would be ifthe sphere wasn't there 23, What is the amount of charge possessed by | ke of | electrons? Given that mass of an electron is 9.1% 107%. | (1) 6.25 x 10°C Q) 1.76% 10"'C (@) 1.76 10!%C (4) 125% 10" 24, A polythene pices rubbed with wool is found to hae | negative charge of 3.6 x 10” C, [fan electron has a mas, 9,1 x 10 kg, find the mass transferred to the polythene (1) 2.25 x 10!” kg, 2) 6.25x10"% kg | (3) 2.05 x 107 kg. (4) 4.15« 10" kg) 25. A copper sphere of mass 2.0 g contains about | 2 x 10 atoms. The charge on the nucleus of each atom | is 29e (e = electronic charge). The mass of an electron s | 9.11 « 10! kg, How much mass will the sphere lose or gain ifitis a given a charge of +2 uC? (1) Loss of 1.13 x 10" g (2) Gain of 1.13 x 10g (3) Neither gain nor loss of any mass. (4) Change in mass will depend upon the kinetic energy of the electrons 26. Assume that each of copper atom has one free electron. ‘Given that atomie weight of copper = 63.5 and Avogadro number = 6.02 x 10%, What is the charge possessed by 1 mg of eopper free electrons? () 152 @) L76C @) 476¢ (@) 125¢ 27, Estimate the negative charge possessed by fiee electrons in | g of water. Given that Avogadro number =6.02 x 10" and molecular weight of water = 18. (1) 625 x108C @) $35x10°C @) 1.76 x10'C ( 125x108¢ Topic 1. Coulomb's Law and Forces Between Multiple Charges 28, Which of the following statements is incorrect about Coulomb's law? (1) It obeys Newton's third law. (2) Itis a central force. ) It obeys the superposition principle. (4) Coulomb force is constant with respect tothe medium,29. 30. 31. 32. 3 4 There are two charges 9, = + 1 WC and g, =+5 UC. The ratio of the forees acting on them will be a 4s Qu @) 5: (4) Las ‘A charge 4, exerts some force on a second charge gy. If third charge q3 is brought in the neighbourhood of the first tvo charges, then the force of g, exerted on gy (1) decreases (2) increases (3) remains unchanged (4) increases iq is of same sign as 9, 493 is of opposite sign ‘Two charges qy, 92 are placed in vacuum at a distance d and the force acting between them is F. If the charges are immersed in a medium of dielectric constant ‘and decreases if =9, the force of interaction becomes () oF 2) 3F FE F OF a> ‘Two points charges +3 UC and +8 {WC repel each other with a force of 40 N. Ifa charge of -5 jC is added to each of them, then the force between them will become (@) -10N Q) HON @) #20N (4) 20N ‘Two identical simple pendulums, 4 and B, are suspended from the same point. The bobs ae given positive charges, with d having more charge than B. They diverge and reach quilibrium, with and B making angles 8, and 0, withthe vertical respectively. Which of the following is correct? (> 8, @) <8 @) 4-6, (4) The tension in A is greater than that in B. ‘Two identical conducting spheres having unequal positive charges 9, and g, separated by distance r. They are made {touch each other and then separated again to the same distance, The electrostatic force between the spheres in this case will be (neglect induction of charges) (1) Jess than before (2) same as before 3) more than before (4) zero ‘Wo point charges placed at a distance rin air experience ® certain force. Then the distance at which they will experience the same force in a medium of dielectric constant K is ok @) & 8 ¥ @ NK 36. 37. 38, 39, 40, a. a Sis chivas re 1] SY ‘Two copper balls, each weighing 10g are kept nai em ‘apart, If one electron from every 10° atoms, is transferred from one tall tothe othe, the coulomb fore ees them is (atomie weight of copper is 63.3) (1) 2.0% 10! N (2) 20x 10¢N 3) 2.0x 10°N (4) 2.0% 10°N What is the Coulomb's force between two ceparicles ‘separated by a distance of 3,2 x 10"! m? (1) 90N (2) 45N (3) 60N (4) 7SN Force of ataction between two point elec charges placed ata distance din a medium is What dita Apart should these be kep inthe same medium se ta foree between them becomes 3? () wa (Q) 3a @) 94 (6 Wa Two pot charges +9¢ and +e are kept 16cm apart from cach other: Where should a thicd charge q be placed between them so thatthe system sin quit Sate? (0) 6em from 9e @) 12cm from 490 @) 6emom +e @) 12cm fom +e ‘Two spherical conductors B and C having equal radi and eanying equal charges in them repel exch othe wih a force F when kept apart at some diatance A td spherical conductor having same radius as that of Bot “uncharged is brought in contact with B, then ‘brought in contact with Cand finally removed ava from bute The now force of repulsion between Band Cis ( Aa @) 374 6) Fs 378 Two equally charged, identical metal spheres A and B repel each other wih a force‘. The spheres ar kept fixed witha distance between them. A thid ident, bur uncharged sphere is brought in contact with f nd then placed atthe mid-point ofthe line joining 4 and Bh. ‘The magnitude ofthe et let ore on Cis MF @ 3F4 om @ FA ‘Two small balls having equal postive charge (coin) on each are suspended by two insulated sting of equal length Z meter, from a hook fixed to a stand. The woe Set up is taken in satelite into space where there is no sraviy (state of weightlessness). Then the angle between the sting and tension in he string is(a) 180" (3) 180" xs ant she a Be g ‘acts between the (Wo is ers 43, TWo similar spheres I at a certain distance, The foree Fin the mide of two spheres, anothe having +0 change is keply then it ewperienes magnitude andl direction as @) SF towards +0 chanee G) SF towards -O shorge {G) AP towars 40 cage 44. Do identical balls having ar certain distance apart repel eae force, They are brought is contaet charges and placed at Jy other with a certain. ‘and then moved apart mn. The increases 4.5 times tial value. The ratio of the initial comparison with the iit charges ofthe balls is 12 @)3 Bs 6 tance x apart. At what 45, Two charges +e and +e are at a dist distance, a charge q must be placed from cl that it is in equilibrium? () x2 (2) 2813 @) x3 (@) 06 46. Two small spherical balls each carrying a charge Q = 10 nC (10 micro-coulomb) are suspended by two insulating threads of equal lengths Im each, from a point fixed in the ceiling, Its found that in equilibrium threads are separated by an angle 60° between them, as shown in the figure, What is the tension in the threads? yharge +e SO (Given: 10° Nm/C? ) ‘eo ‘a a (1) 18N @ 18N 3) 0.18N (4) 180N, 47. A charge q is placed at the center of the line joining two equal charges Q. The system of three charges will be in cquilibrium ifq is equal to @ el @ -2 era @ +2 48. 49. 50. si. 52, 53. arranged at the comers of @ square) Four charges are figure. The force on the charge kept at TUCD as shown in the center O's (1 2210 {Q) along the diagonal AC (3) along the diagonal BD @) perpendicular to side AB | ‘Tivee equal charges are placed on the three comers of ta aquare. If the force between 4 and gz is F,z and that! fetween gy and q3 i8 Fy, then the ratio of magnitudes Fal Fi) oy @2 oF ou Charges 4Q, 4 are Q are placed along x-axis at posit thea 12 and x= | respectively. Fed the vale of 0 that force on charge Q is zero. Me @) o2 @) -92 @-0 ‘Two equal negative charges ~g are fixed at points (0, a Bi Orn a)on tyne Apative carpe Oise fom rest at the point (2a, 0) on the x-axis The chargd will (1) Execute simple harmonic motion about the origin (Q) Move to the origin and remains at rest @) Move to infinity (8) Execute osillatry but ot simple barmoni mation Electric charges of 1 j1C, -1 tC and 2 C are placed i air at the comers 4, B and Crespectively ofan equ triangle ABC having length of each side 10 em. Th resultant force on the charge at Cis () 09N @ 18N @) 27N (@ 36N Three charges each of magnitude g are placed at th comers of an equilateral triangle, the electrostatic Frey on the charge placed at the centre is (each side of triangle isl) (1) Zero 13? gy 13 © are F56. Equal charges g are placed atthe four comets 4, B, C, D, ofa square of length a. The magnitude ofthe force on the charge at B will be ie @ reget wn) @ . oe olde Charges Q, -4, Q, -g are placed at the comers 4, B, C, D of a square respectively. If the resultant force on the charge Q is zero due to other charges, what isthe relation between Q and g? () = 2%iq @) 9-2 @0-% © O- see ‘An infinite number of charges, each of charge 1 [C, are placed on the x-axis with co-ordinates x= 1,2, 4, 8, 2. Ifa charge of 1 Cis kept atthe origin, then what isthe net force acting on 1 C charge? (1) 9000 N @) 12000 @) 24000 (4) 36000 Four charges are arranged at the comers of a square ABCD, as shown in the figure. The force on a positive ‘charge kept atthe centre O is () Zero (2) Along the diagonal AC ) Along the diagonal BD (4) Perpendicular to side AD ‘Three charges are placed at the vertices of an equilateral triangle of side ‘a’ as shown in the following figure, The force experienced by the charge placed atthe vertex A in ‘ direction normal to BC is -@ “¢ (©) OKareya) (3) Zero 2) BO" /(4neya*) () O* /2neqa) '59, Four charges equal to~Q are placed at the four comers of 1 square and a charge q is at its centre. Ifthe system is in equilibrium the value of gis a ~Sa+2v3) @ Las) @ -Sa+aa) ) S042) Topic 1.3: Electric Field 60. Choose the correct statement about the electric field (1) Itis produced by positive charges only. (2) It can exist only in the material medium, (3) An electron moves in the direction of field, (4) Itis a conservative fel. 1, Identify the incorrect statement about the electric field (1) Charge is the source of electric field (2) Electric field exerts force on every charge. 3) Energy is stored in electric field. (4) Electric field isthe zone of influence of a charge. 62, ABC is an equilateral triangle, Charges +g are placed at each comer. The electric intensity at O will be ta,d ae pale! © ae Oh amr x0 tw! oy ® ae ‘The insulation property of sir breaks down at E=3x 10° Vm", The maximum charge that can be given toa sphere of diameter $ m is approximately. () 2x10? @) 8x107C @) 2x10 (@) 8x10%C 64, Figures given below show regular hexagons and charges are arranged at the vertices. oa! ‘g-@ we pe ‘ 1O--Oe65. 66. 6. 68, 0. 70. ow oe DW In which ofthe given cases the eleettio ild at the e 2) Only (A), (C) ana (Dy (4) Only (B) and (©) ‘Two point charges (+Q) and (20) are fixed on the X-axis at positions a and 2a from origin respectively, At what positions on the axis, the resultant electric field is zero? () Only x= 2a (2) Only x=-V2a € Bath se Only rot Two charges +5 WC and +10 WC are placed 20 em apart, The net elect Feld at the mid-point between the two charges is (1) 45 x 10° NIC directed towards +5 wc (2) 45x 10°NIC directed towards +10 nC () 13.5 10° N/C directed towards +5 1C (4) 13.5 x 10° NIC directed towards +10 uC ‘The distance between the two charges 25 WC and 36 uC is 11 em. At what point onthe line joining the two, the intensity wil be zero (i) Ata distance of Sem fom 25 we @) Ata distance of 5 em fiom 36 uC (G) Ata distance of 10cm ffom 25 iC (4) Ata distance of 10 em from 36 4 “wo pont charges #8 and 2g are located at x = 0 and x= L respectively. The location ofa point on the x-axis at Which the net electri field due to these wo point charges iszerois ay se @ aL @2L ws ‘Two point charges Q and -39 are placed at some distance apart. If the electric field at the location of Q is E then at the locality of -30, itis () -E (2) EI3 G) -3E (4) £16 ‘wo point charges ~q and +9/2 are situated atthe origin and athe point (a0, 0 respectively The point along the axis where the elect field vanishes is (Only (A)(B) and (C) (3) Only (B) and (D) a ca @) x=V2a a bi 8) x28 Ba Oa Oo Ea i THe Baul ehartes gare placed atthe vertices and c an equilateral wlngle ine of side sees electric field atthe point Cig TH Mid | a 2a j rege! | 4 —L_ 2Kega 72 Ths Mecl point charges, as shown ate plac ihe ‘vertices of an isosceles right angled triangle. Wh a of the numbered vectors coincides in direction with p* electric field at the mid-point ‘M of the hypotenuse? “ 4 3 a ‘ ¢ 4 1 @2 @)3 @4 7B. In the following four stuations, charged fk ons, charged pants ae qu distance fom te origin Arrange them scone | the magnitude ofthe nt elec held st ong ene first ug i) ©} 29 Si Gi) -@—3} Ox 4a 24 ) ~~} -0-« ” EI (1) @> GH> Gi)>)—_@ >> G>G) @) @> Gi) > G)> (iv) ——-@) Gv) > Git) > >. 74, Five point charges each having magnitude ‘g’ are placed at the comer of hexagon as shown in fig. Net electric field) atthe centre “O"is To getnet electric field at ‘O"be 6E, charge placed on the remaining sixth comer should be 1®—@a Da a©—Oa () 6q Q) 69 @Q)5q @) 3975. Charges q,2g, 39 and 4g are placed atthe comers A, B, C and D of @ square as shown in the following figure, The direction of electric field atthe centre ofthe square is slong () 4B @) ce @) BD @ ac ‘The bob of a pendulum of mass 8 x 10° kg carries an clecrie charge of 39.2 x 107" coulomb in an electric eld of 20 x 10 volumeter in horizontal direction and itis at rest. The angle made by the pendulum with the vertical will be (p27 @) 48° @ sr ® pr ‘A proton and an electron are placed in @ uniform electric field. Which of the following is corect? (1) The electric forces acting on them will be equal @) The magnitudes of the forces will be equal ) Their accelerations will be equal (4) The magnitudes of their accelerations will be equal The intensity of electric field required to balance a proton cof mass 1.7 x 10” kg and chargel.6 x 10"! Cis nearly () 1x10 Vin Q) 1x108 Vim @) 1x10" Vim (@ 1x:10° Vim The intensity ofthe electric field required to keep a water 4zop of radius 10° em just suspended in air when charged with one electron is approximately (1) 260 volvem @) 260 newton/coulomb ©) 130 volvem () 130 newton/eoulomb How many electrons should be removed from a coin ‘of mass 1.6 g, so that it may float in an electric field of intensity 10? N C™ directed upward? (take g = 10 ms?) @ @ 10 @B) 10 4) 10° Conduction electrons are almost uniformly distributed within a conducting plate. When placed in an electrostatic field E, the electric field within the plate (1) Is2er0 (2) Depends upon m, (3) Depends upon £ (@) Depends upon the atomic numberof the conducting element 16. n. 8 a1. 82. A positively charged particle moving along, x-axis with A certain velocity enters a uniform electric field directed. along positive y-axis. ts I velocity changes but horizontal velocity ins consta (2) Horizontal velocity changes but vertical velocity femains constant 3) Both vertical and horizontal velocities change (4) Neither vertical nor horizontal velocity changes. ‘A charged particle of mass m and charge 4 is released from rest in an electric field of constant magnitude E. The kinetic energy of the particle after time. Fam 2 ‘There is a uniform electric field of strength 10? Vim slong Jeaxis. A body of mass 1g and charge 10“C is projected into the field from origin along the positive x-axis with velocity 10 mvs. Its speed in mis after 10 sis (Neglect gravitation) (10 @ sv (3) 10/2 (4) 20 ‘An electron of mass m initially at rest moves through 4 certain distance in a uniform electric field in time, ‘A proton of mass m, also intially at rest takes time fs 0 ‘move through an equal distance in this uniform electric field. Neglecting the effect of gravity, the ratio of tis nearly equal to ai (2) (jm)? B) (mim,)'” (4) 1836 ‘An electron moving wit the speed 5X 10° m/s is shot parallel to the electric field of intensity 1 x 10° NIC. Field is responsible for the retardation of motion of electron. Now evaluate the distance travelled by the electron before ‘coming to rest for an instant (mass of e = 9 x 107" kg charge = 1.6 x 107C) 1m @) 0.7mm @) Tem @) 07cm ‘The figure shows the path ofa positively charged particle 1 through a rectangular region of uniform electric eld as shown in the figure, What is the direction of deflection of pariles 2,3 and 4? o 84, 85, 86. 87, Bown ) down, top, down (2) down, down, top ) top, top, down, @) top, down, down __Electrle Charges and Fields = CS |Kitd> Physics |: Electric Field Lines = Topic 88, Study following statements about the electric foe. (A) Two field lines eannotinterseet each other. (B) The path trace by a positive change is a fel line (©) Field tines are eontinuous (D) A field ine cannot Choose the eorreet statements (Only (A), (B) and (C) (@) Only (B) and (D) 89. Electric lines of force around a negative point char (1) circular, anticlockwise (2) eirular, clockwise (3) radial, inward (4) radial, outwards 90. Figure shows the el chharged body. Ifthe elect Iy and ifthe displacement (2) Only (A),(C)and (D) (4) Only (B) and (C) ge are ctr lines of force emerging from & field at Aand Bare E, and Ey {between A and Bisr, Q) Ey 91, The field ee which is not possible is given by ® amen o> wo ® Se ® =— 92. The field = which is/are not possible: © -sS oes : = < Q) Only (A), (C)and (D) (4) Only (B) and (C) (1) Only (A), (B) and (©) (3) Only (B) and (D) 94, 1 95. 96. re charge is brought near an isolated at positive e he electric field lines are best L A co Fiveting sphere. Th | ‘sqrvenY | (i) EQ OS Bie 2) Figure (ii) (4) Figure (iv) ven figure gives electric lines of force due to two charges q, and dt ‘What are the signs of the two charges? (1) Both are negative (2) Both are positive (3) 41 is positive but gis negative (4) 4, is negative but gis positive Consider the four field pattems shown. Assuming there are no charges in the regions shown, which of the pattems represents a possible electrostatic field? i AS @ Q) SES Which of the following figures correctly shows the top view sketch of the electric field Lines for « uniformly charged hollow cylinder as shown in figure? a Ox 3 3_ Steele Shae 97. Which of the following figure represents the electric eld lines due toa single positive charge? 98. Which of the following figure represents the electric fcld lines due toa single negative charge? ®™-o- 103. ® Figure shows the electric field lines around three point charges 4, B and C. Which ofthe following charges are positive? 4B. YY @ Sy Le yy TRS a () Only (2) Only c ©) Both A and c 4) Both B and c 100, Which of the following represents the electric field lines due to a combinations of two negative charges? w Which of the following figure represents the electric field lines due to a combination of one positive and one negative charge? a sex 8 Iw aK @) @ | 101, @) 108, 102. A charge @ is fixed ata distance d infront of an infinite ‘etal plate. The lines of force are represented by 7 i ay [a ©) Qisnegatve snd |O|>| a] ©) gis positive and |Q| By> Ee Q) y= By= Be @) 32x10” (4) 3210” QB) Ey=Ec> Ep (A) Ey Bo< En 112, ‘Three charges of (+24), (~ q) and (— 4) are placed at the comers A, B and C of an equilateral triangle of side aay 107. In a region with uniform electric field, lines of force per unit area is E. Ifa sp conductor is placed in this region, the num! this combination is force per unit ara inside the conductor willbe ME (2) more than E (les than £ @ 2200. y 108, charge particles eto move nan electric eld Iwill ; travel / 2 (a) Always along ine of free é afin of force it ini velocity i 210 ine () qa (2) Zero some initial velocity in longa line foe,ithas ere the line of force 7 i iy 2 @) qa ¢ 5” the direction of an acute angle wit (4) None of the above 109, Inthe elec field shown in figure, theclectricfeld lines 44, prectic charges 4,4,-29 ae placed at the comers of ne eft have wie the separation as that between those : ae ame I the magnitude of the field at pont is ‘an equilateral triangle ABC of side I. The magnitude of 40 NC" ealelate the force experienced by a proton electri dipole moment ofthe system is placed at point 4, Also find the magnitude of electri field Og (2) 2ql at the point B. @) V3qt @ aq SPP Ea EEE nam eee erEe 114, An electric dipole is kept in non-uniform electric field. PRN rr eid ata at experiences: a (1) A force and a torque (2) A force but nota torque [— ae eae eee (3) A torque but not a force (4) Nether force nor torque ‘What is the angle between the electric dipole moment and (1) 64x10 N, 15NCt 115, (2) 64x 10" N, 20NC™ the electric field strength due to it on the equatorial line @) 64x 10" N, 25 NC (1) 0° (2) 90° (@) 64x10" N, 30NC (3) 180° (4) 120° 116, An electric dipole in a uniform electric field experiences ‘Topic 1.5: Electric Dipole and Dipole in (When itis placed at an angle @ with the field) (1) Force and torque both Uniform External Field (2) Force but no torque 110. Study following statements about dipole moment . G) Torque but no force (8) The dines of ite monet i 27 aero _—_ ipole moment is Cm. electric dipole is placed in an electri eld genes (© Dipole moment is »vexorquntiy and dirested Ea teteetieio placed in an electric fel 1 negative to postive charge. ©) Die moneat is acer (a) The net electric force on the dipole must be 2270 a siaief aa se oeiee aiee (2) The net electric force onthe dipole may be 220 eee eal potential energy of the {@) The torque on the dipole due tothe field must be 22) (4) The torque on the dipole due to the field may be 22419. 120. m1. 1m, 123. 14, ns, 126, ‘The distance between tho two charges +y and -7 of a dipole is r. On the axial line at @ distance o from the centre of dipole, the intensity is proportional to field E” then at what angle between P” and F” the value of orque willbe maxirnum (i) 90° @) 180° (4) 45° ‘The elect field at a point on equatorial ine ofa dipole and direction ofthe dipole moment (D Will be paatet (2) Will be in opposite direction (3) Will be perpendicular @) Are not related ILE, be the electric field strength ofa short dipole at a point on its exal ine and that onthe equatorial line at the same distance, then s @) £,= 28, (4) None of the sbove The ratio of electric feds onthe axis and at equator of an clectie dipole willbe (tet (2) 2:1 3) 4:1 @ 1:2 Iftne magnitude of intensity of electric fed ata distance on axial line and ata distance yon equatorial line on given dipole are equal, then x:yis mist @ ty @ 12 © Ba A tiven charge is situated at a certain distance ffom an clesrc dipole in the end-on positon experiences a force F Ifthe distance ofthe charge is doubled, the force ating on the charge will be () 2F @ Fa (3) Fla (4) FI8 An electric dipole consisting of two opposite charges of 2x 10° C each separated by a distance of 3 cm is ‘placed in an electric field of 2x 10" NIC. The maximum forque on the dipole wil be (1) 12x10¢°Nm Q) 12x10°Nm G) 24x10'Nm (4) 24x10°Nm The elect intensity dito dipole of length 10 om and having a charge of 500 KC, at a point on the axis at a distance 20 em from one of the charges as shown in the figure in air, is Qo @) B,-E. 127. 128, 129, 130. a1, 132, 20 em—> (1) 625% 107 NIC (2) 9.28 107 NIC @) Idx tN (4) 20.5 x 107 NIC For a dipole g=2x10%C and d=0.01m. Calculate the maximum torque for this dipole if £ = 5x10 NIC. () 1x 107 Nev (2) 10% 10° Nm G) 10x 107 Nm (4) 1 10? Nm? ‘The electric field due to an electric dipole at a distance 1 from its centre in axial position is E. Ifthe dipole is rotated through an angle of 90° about its perpendicular axis, the electric field atthe same point will be ME @ E14 @) £/2 (2B A neutral water molecule (HO) in its vapour state has an electric dipole moment of magnitude 6.4 x 10 C-m, How far apart are the molecules ceatres of positive and negative charge (1) 4m Q4a @) 44m @) 4pm An electric dipole consists of two equal and opposite charges placed 2 cm apart. When the dipole is placed in a ‘uniform electri field of strength 10° NC“ it experiences ‘a maximum torque of 0.2 » 10° N m. Find the magnitude of each charge. (1) 20 nc. Q) 01 nc @) 1spc @) lon Two electric dipoles of moment P and 64 P are placed in opposite direction on a line at a distance of 25 em. The electric field will be zero at point between the dipoles whose distance from the dipole of moment P is () Sem @ Bom (3) 10em @® + om 4 3 ‘Two short dipoles pk and 2 are located at (0,0,0) and (Am, 0, 2 m) respectively. The resultant electric field due to the two dipoles atthe point (1 m, 0,0) is -1p a =1P. Ree © are pep. none of th Sak ® ese13, aaa 3s pelaeey Ie is situated in an electric field of uniform imeasty € whose dipole momen isp an tome of pee aa aes dlisplaced slightly from the muilibrium pos frequency of itt oscillations is Ten oy ye (a) An electric dipole is plac line of charge at some Identify the correct statement: sed perpendicular to an infinite 134, distance as shown in figure: z i (1) The dipole is attracted towards the line chara ©) The dipole is repelled away from the line charBe {G) The dipole does not experience a force {@) The dipole experiences a force as well as a torque opie 16: Electric Flux, Gauss's Law and “Applications of Gauss’s Law 135. ‘Study the statements related to flux. (a) Flux is defined forthe eletrc and magnetic fields. {B) Flux is defined for any vector field (©) Flax is a vector quantity. (D) Flu is defined for gravitational fed also. Choose the correct statements (1) Only (A), (B) and (D) ) Only (B) and (C) (2) Only (A), (C)and (D) (4) Only (A) and (C) 136. The SI (1) NC? @) NC?m? (4) NC* a 137. The dimensional formula of electric flux is @ Mir?) @) (MILAT?AT) @) META] @ MLPA) Choose the correct statement about the Gauss Law. (1) The quantity ¢ \B-d5 is affected by the charges 138. lying outside the gaussian surface. @ The quantity Za depends on the charge distibution inside the gaussian surface. (3) The quantity $ EB. is independent of the charge distribution inside the gaussian surface. (8) The quantity gd depends on the shape of the ‘gaussian surface 139. 140. a1. 142. [ below is a distribution of charges. The flux of shown eld due to these charges through the surface Sig (1) 34fo (2) 2aley @) gito (4) Zero Consider te charge configuration and spherical Gausian cots shown inthe figure. When calculating the fax se clecrie eld over the spherical surface the electric field will be due to +a (1) a (2) Only the positive charges G) Allie charges (@) #4, and -4 ‘The electric fux through the surface Hood > ® @® o) (1) in figure (iv) is the largest (2) in figure (ii) is the least (3) in figure (ji) is same as in figure (ii) but is smaller than figure (iv) (4) is the same for all the figures. ‘The electric flux for Gaussian surface A that charged particles in free space is (given q) 8.85 nC, g3=— 56 nC) 85 x 10-2C2/Nm*) &D (1) 10° Nm? ct (3) 6.32 10° Nm? C* enclose the = -14 26, Gaussian surface A Gaussian surfice B | @ 10° CN“ mi? Bs (4) 63210 CN a143. 144. 48, Electric charge is uniformly distributed slong a long straight wire of radius 1 mm, Tho charge per centimetre Tength of the wire is Q coulomb, Another cylindrical surface of radius 50 cm and length 1 m symmetrically encloses the wire as shown in Fig, The total electric ux passing through the eylindrieal surface is im [Boem 2 1009 Or a @ 22 (a We Te Rey ‘Acylinder of radius rand length 1 is placed in an uniform electric field in such a way that the axis of the eylinder is parallel to the field. The flux of the field through the cylindrical surface is w at % &% o = © 200. A charge q is enclosed by an imaginary Gaussian surface, Gaussian surece itera tte, en (1) flux linked with surface is increasing ata rate ae oak (2) fiux linked with surface is decreasing at arate ay, a G) flux linked wit cays aK surface is decreasing ata rate (4) flux linked with surface is % 146. 447. 148, 149, 150, 151. CD , ed QD & GD (1) 10! Nemtic 2) 10! Nemec @) 10° Nemtic (4) 8.8610 Nem?/C ‘The inward and outward electric flux fora closed surface in units of N-m"/C are respectively 8 x 10° and 4 x 10°. ‘Then the total charge inside the surface is [where & = permittivity constant] () 4x 10°C (@) 4x10°C @ SMe 4x10'gc If the electric flux entering and leaving an enclosed surface respectively is ¢, and g the electric charge inside the surface will be OO + Oe 2 Ge @) 1+ 6 OG le ‘An electric dipole is put in north-south direction in a sphere filled with water. Which statement is correct (1) Electric flux is coming towards sphere (2) Electric flux is coming out of sphere ) Electric flux entefing into sphere and leaving the sphere are same (4) Water does not permitelectri flux to enter into sphere A cube of side / is placed in a uniform field E, where = Ei. The net electric flux through the cube is (1) Zero @ PE (3) 4PE (4) PE A square surface of side L meterg isin the plane of the paper. A uniform electric field (in Vim), also in the plane of the paper, is limited only to the lower half of the square surface, as shown in figure. The electric flux in ST units associated with the surface is given as : (1) zer0 @ EP ne, @ EP () EL'2F122 Fiyice 152. A charge q is placed at the centre of a cube, Then the passing through one face of cube will be 4 ‘ OF @ 4 OF aan oZ ot 154. A charge g is placed at the centre of the open end of cylindrical vessel. The flux of the electric field through the surface of the vessel is a) (@ Zer0 az 4 24 @ 7 @) % 185. It is not convenient to use a spherical Gaussian surface to find the electric field due to an electric dipole using Gauss's theorem because (1) Gauss's law fails in this case (2) This problem does not have spherical symmetry 3) Coulomb's law is more fundamental than Gauss's law (4) Spherical Gaussian surface will alter the dipole ‘moment 156, In Figure (a) given, in a cubical surface of side 1/2, a uniformly charged rod of length L moves towards left at a constant speed v. At 1 = 0, the left end of the rod Jjust touches the centre of the face of the cube as shown, ‘Which ofthe graphs shown in the figure (b) represents the electric flux through the cube as the rod passes through it: 4) ly y Wu z 1 v7 ' @ (b) at Qu @m @v 157. Electric feld intensity at a point in between tw: at a point in ro parallel re with like charges of same surface charge densities OF ae ©) Zex0 @ % % 158. 160. 161. 162. 163. . lectrie feld at a point v Q 30 © Treg © Fregk 30 49 © Fregr™ © reg —| “Asphere of radius R has a uniform distribution of electric iarge in its volume. Ata distance x from its centre, fog <2, the electric field is direetly proportional to os @t QB) * ae as? for (1) An electri dipole @) Apoint charge @) A plane infinite sheet of charge (4) A line charge of iafinite length ‘A solid metallic sphere has a charge +30. Concentric with this sphere is a conducting spherical shel having charge -Q. The radius of the sphere is a and that of he spherical shell is (6 > a). What is the electric field ata distance R(a < R-<6) from the centre ‘Apoint charge q is placed at a distance a2 directly above the centre of a square of side a. The electric flux through the square is 4 nae Ot Cr nm A. Og OB ‘Three infinitely long charge sheets are placed as shown in figure. The electric field at point P is 6 te ‘Two infinitely long parallel conducting plates having surface charge densities +0 and -c respectively, a7 separated by a small distance. The medium between the plates is vacuum. If ¢, is the dielectric permittivity of vacuum, then the electric field in the region between the plates is164. () ovoltsimeter @) voter (3) Zvolisimeter (4) 72 volismoter ‘Ata point 20 em from the centre of a uniformly charged dielectric sphere of radius 10 em, the elecirie field is 100 Vim. The electri field at 3 em from the centre of the sphere will be () 150 Vim (2) 125 Vim (3) 120 Vim (a) Zero ctl Charges and Fields XC 23 SG Ina region of space the electric field isin the x-direction Proportional to x, ic, E= Eyal. Consider an imaginary cubical volume of edge a with its edges Parallel to the axes of coordinates. The charge inside this volume will be (1) 2070 2) Eye ot % 1 4) Le Ba? (4) 5| 6) ) 4 8. | 6) | |) 1G) 3 @ |. 5 84 @ | .[ @ | 90.) ay 34. Fe) | | a) [98] 2) | 99.| @) | 100.) (4) ron. ca) | 102] (1) | 103.) 3) [404] "(y | 108. | (4) [t06.| () | 107. | @) | 108. 2) | 109.[ @ | at0.| ay m.| @) [112.[ @) [a13. ra) @ | n6.[@ fr. [@ [8.) @ [ 9. a) [120.2 wai. @) |122,] @ |123. @) | 126. [" ay [127.| ay [428.[ @) [129.[ @ [130.1 @ 3. | @) /132.| @) [133, @ [136 a) [37.| @ [138,[ @) [139. [ @) [140.1 G) aat.| (4) | 142. [ay | 143. @) | 146. @ 147. | (4) [148. | @ [149.[ @) [150.| Cy 151.| (1) | 152.| (4) | 153.] (4) | 154. 188.| (2) | 156.| (4) | 157.| @) [158.| (3) | 159.[ @) | 160.| @) 61.| (4) |162.[ @) [163.] @) [64 168. @)