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>» Multiple Choice Questions (MCQs) \\; DIRECTIONS : This section contains multiple choice questions. Each question has four choices (a), (b), (c) and (d) out of which only one is correct. 1. The electric potential inside a conducting sphere (a) increases from centre to surface (b) decreases from centre to surface (c) remains constant from centre to surface (d) is zero at every point inside In a region of constant potential (a) the electric field is uniform (b) the electric field is zero (c) the electric field shall necessarily change if a charge is placed outside the region (d) None of these It becomes possible to define potential at a point in an electric field because electric field (a) 1s aconservative field (b) is a non-conservative field (c) isa vector field (d) obeys principle of superposition Which of the following about potential at a point due toa given point charge is true ? The potential at a point P due to a given point charge (a) isa function of distance from the point charge. (b) varies inversely as the square of distance from the point charge. (c) is a vector quantity (d) is directly proportional to the square of distance from the point charge. A cube of a metal is given a positive charge Q. For this system, which of the following statements is true? (a) Electric potential at the surface of the cube is zero (b) Electric potential within the cube is zero (c) Electric field is normal to the surface of the cube (d) Electric field varies within the cube >»>>> 6. 10. 11. 12. 13. Electrostatic Potential and Capacitance There are two metallic spheres of same radii but one is solid and the other is hollow, then (a) solid sphere can be given more charge (b) hollow sphere can be given more charge (c) they can be charged equally (maximum) (d) None of the above The electric potential due to the pair of charges (+ 10pc and + 20 pic the middle of the line joing them is [if sepration is 2 cm] (a) 27MV_ (b) 35MV_ (c) 37MV_ (d) 40MV Potential due to electric dipole along equatorial line is. (a) maximum (b) increasing (c) zero (d) None of these Figure below shows a hollow conducting body placed in an electric field. Which of the quantities are zero inside the body? , ES Zs __ (b) Electric field and charge density Py — (c) Electric potential and charge density. (a) Electric field and potential (d) Electric field, potential and charge density. The positive terminal of 12 V battery is connected to the ground. Then the negative terminal will be at (a) -6V (b) +12V_ (c) zero (d) -12V Let V be the electric potential at a given point. Then the electric field E, along x-direction at that point is given by o dV , _ dV _ eat? @) J, Vax) —- © - @ -VE The electric field is along the direction in which the potential (a) increases at max™ rate (b) decreases at max™ rate (c) increases at min™ rate (d) None of these Potential at any point inside a charged hollow sphere (a) increases with distance (b) is a constant (c) decreases with distance from centre (d) is zero 14. 15. 16. 17. 18. 19. 20. 21. A solid sphere of radius R has uniform volume charge density. The electric potential at a points (r (c) same at all the three points A, B and C (d) maximumatA Identify the false statement. (a) Inside a charged or neutral conductor, electrostatic field is zero (b) The electrostatic field at the surface of the charged conductor must be tangential to the surface at any point (c) There is no net charge at any point inside the conductor (d) Electrostatic potential is constant throughout the volume of the conductor Three charges 2 q,— q and—q are located at the vertices of an equilateral triangle. At the centre of the triangle (a) the field is zero bul potential is non-zero (b) the field is non-zero, but potential is zero (c) both field and potential are zero (d) both field and potential are non-zero The electrostatic potential energy of a system of two charges is negative when (a) both the charges are positive (b) both the charges are negative (c) one charge is positive and other is negative (d) both the charges are separated by infinite distance Two conducting spheres of radii RK, and R, having charges Q, and Q, respectively are connected to each other. There is (a) no change in the energy of the system (b) an increase in the energy of the system (c) always a decrease in the energy of the system (d) a decrease in the energy of the system unless OR, = OR, A ball of mass | g carrying a charge 10~* C moves from a point A at potential 600 V to a point B at zero potential. The change in its K.E. is (a) —6x10-% erg (b) —6x 10-6 J (c) 6x10°J (d) 610° erg On moving a charge of 20 coulomb by 2 cm, 2 J of work is done, then the potential difference between the points is (a) O1V (b) 8V (c) 2V (d) OSV. 22. 23. 24, 25. 26. Zi. 28. 29. 30. 31. Two points P and Q are maintained at the potentials of 10 V and —4 V, respectively. The work done in moving 100 electrons from P to Gis: (a) 9.601017) (b) -2.24x 10°!) (c) 2.24 10°'6J (d) -9.60x 10°'7J A and B are two points in an electric field. If the work done in carrying 4.0C of electric charge from A to Bis 16.0 J, the potential difference between A and B is (a) zero (b) 20V (c) 40V (d) 160V A system of three positive charges placed at the vertices ofan equilateral triangle. To decrease the potential energy of the system, (a) a positive charge should be placed at centroid (b) anegative charge should be placed at centroid. (c) distance between the charges should be decreased. (d) it should be rotated by an angle of 5 radian. The work done in carrying a charge g once around a circle of radius r with a charge Q placed at the centre will be (a) Og(4negr*) (b) Oq/(4negr) (c) zero (d) Og? (Anegr) On decreasing the distance between the plates ofa parallel plate capacitor, its capacitance (a) remains unaffected (b) decreases (c) first increases then decreases. (d) increases A sheet of aluminium foil of negligible thickness is introduced between the plates of a capacitor. The capacitance of the capacitor (a) decreases (b) (c) becomes infinite (d) increases The potential gradient at which the dielectric of a condenser just gets punctured is called (a) dielectric constant (b) dielectric strength (c) dielectric resistance (d) dielectric number When air in a capacitor is replaced by a medium of dielectric constant A, the capacity (a) decreases K times (b) increases K times (c) increases K* times (d) remains constant Capacitors are used in electrical circuits where appliances need more (a) voltage (b) current (c) resistance (d) power A parallel plate capacitor is charged by connecting it toa battery. Now the distance between the plates of the capacitor is increased. Which of the following remains constant ? (a) Capacitance (b) Charge on each plate of the capacitor. (c) Potential difference between the plates of capacitor (d) Energy stored in the capacitor. remains unchanged 47. 48. 49, 50. a2. 53. Figure shows two hollow charged =, conductors A and B having same positive surface charge densities. B is placed inside A and does not touches it. On connecting them with a conductor (a) charge will flow from Ato B (b) charge will flow from BtoA (c) charge oscillates between A and B (d) nocharge will flow. Two equally charged spheres of radii a and b are connected together. What will be the ratio of electric field intensity on their surfaces? a a? b b @ > (b) ye (Cc) F (d) a2 Four points a, b, c and d are set at equal distance from the centre of a dipole as shown in figure. The electrostatic potential V., V,, V,, and V,, would satisfy the following 4 2 relation: al (a) V,>V,>V.FVq eal (b) V,>Vi=Vy>V. d +——+ b (c) Vi>V.=V,=Vq ~ qt (d) Vi=Vy>V,>V. C The electric potential at a point (x, y) in the x — y plane is given by V =—kxy. The field intensity at a distance r from the origin varies as (a) 2 1 ] (b) (c) — (J) = 2 r r In a hollow spherical shell, potential (V) changes with respect to distance (s) from centre as (a) T (b) f “~——s — = <———_S—ar (c) Ff (d) 7 Vv aN ¥ zx —— 5 ——-»1 k—— S — A charge q is projected into a uniform electric field E, work done when it moves a distance y is, (a) qEy (b) qywE (©) qE/y (d) yqE Consider the following statements and select the true/ false statements lL In an external electric field, the positive and negative charges of a non-polar molecule are displaced in opposite directions. I. — n non —polar molecules displacement stops when he external force on the constituent charges of the molecule is balanced by the restoring force. Ill. The non-polar molecule develops an induced dipole moment. (a) T,T,F (b) ET,T (ce) T, ET ma (4) TTT 54. 56. D7 58. 59. 60. Which of the following about potential difference between any two points, are true/false. L It depends only on the initial and final position. fl. Itis the work done per unit positive charge in moving from one point to other. Ul. It is more for a positive charge of two units as compared to a positive charge of one unit. (@) T.EKF () ETF © LLF @ LTT On decreasing the distance between the plates ofa parallel plate capacitor, its capacitance (a) remains unaffected (b) decreases (c) first increases then decreases. (d) increases The potential energy of a charged parallel plate capacitor is Up. Ifaslab of dielectric constant k is inserted between the plates, then the new potential energy will be (a) Usk ©) UK © UK @W@ UZ A capacitor is charged by using a battery which is then disconnected. A dielectric slab of dielectric k is then inserted between the plates, which results in (a) Reduction of charge on the plates and increase of potential difference across the plates. (b) Increase in the potential difference across the plate, reduction in stored energy, but no change in the charge on the plates. (c) Decrease in the potential difference across the plates, reduction in the stored energy, but no change in the charge on the plates. (d) None of these Find the capacitance between P and Q (Fig). Each Capacitor has capacitance C. P @ 2c [ty (b) 3C (c) 8c in = a . A i} += 1} C (d) 6C ID 1F~ An electric dipole consisting of charges +g and —qg separated by a distance ZL is in stable equilibrium in a uniform electric field & . The electrostatic potential energy of the dipole is [CBSE 2020] (a) qgLlE (b) zero (c) -ghLE (d) —2qEL A capacitor of 4 uF is connected as shown in the circuit. The internal resistance of the battery is 0.502. The amount of charge on the capacitor plates will be 4 uF r 109 | WV i | LT 2.5V VV 20, (a) OnC (b) 4uC (c) 16pC (d) 8pC 61. 62. 63. 64. A positively charged particle is released from rest in an uniform electric field. The electric potential energy of the charge (a) remains a constant because the electric field is uniform (b) increases because the charge moves along the electric field (c) decreases because the charge moves along the electric field (d) decreases because the charge moves opposite to the electric field Figure shows some equipotential lines distributed in space. A charged object is moved from point A to point B. (a) The work done in Fig. (1) is the greatest (b) The work done in Fig. (ii) is least (c) The work done is the same in Fig. (i), Fig.(ii) and Fig. (iti) (d) The work done in Fig. (iii) is greater than Fig. (ii) but equal to that in ' 1 t ' ' _20V | 40 1 H i oF &F Pr ori ot of H H a Pie oF f of ] I I | I El i] I | pA ¢ FB Y Aif f 74] H H H H H Prog or of 10V 20V 30V 40V 50V 10V 30V 30V Fig. (i) Fig. (ii) . 30V | it | iho | H if i i Poo gt od E , ear 7 | 1 1 1 i ' a8 1! . r aon ' rE r a8 ! E ' aon ‘ ‘ i a8 ' : . . 10V 20V 40V. 50V Fig. (iii) The electrostatic potential on the surface of a charged conducting sphere is 100V. Two statements are made in this regard S, at any point inside the sphere, electric intensity is zero. S, at any point inside the sphere, the electrostatic potential is 100V. Which of the following isa correct statement? (a) S, is true but S, is false (b) Both S, and S, are false (c) S, is true, S, is also true and S, is the cause of S, (d) S, is true, S, is also true but the statements are independant A parallel plate capacitor is made of two dielectric blocks in series. One of the blocks has thickness d, and dielectric constant K, and the other has thickness d, and dielectric constant K.,, as shown in figure. This arrangement can be thought as a dielectric slab of thickness d (=d, + d,) and effective dielectric constant K. The K is (a) Kd, +K,d, (b) Kd, +K,d, d, +d, K,+K, (c) KK, (d, +d,) (d) 2K\K, (Kd, +K,d,) K, +Ky 65. Charges are placed on the vertices of a square as shown. Let E bethe electric field and V the potential at the centre. Ifthe charges on A and B are interchanged with those on D and C respectively, then q q A B D C q —q (a) £ changes, V remains unchanged (b) £ remains unchanged, V changes (c) both £ and V change (d) £ and V remain unchanged 66. Two conducting spheres of radii R, and &, having charges Q, and Q, respectively are connected to each other. There is (a) no change in the energy of the system (b) an increase in the energy of the system (c) always a decrease in the energy of the system (d) a decrease in the energy of the system unless Q,R, = OR, >> Case/Passage Based Questions \\\\ ——— DIRECTIONS : Study the given Case/Passage and answer the »>>> following questions. Case/Passage-l Electrostatic potential energy of a system of point charges is the total amount of work done in bringing various charges to their respective positions from infinitely large mutual separations. If two charges having charge q, and q, are placed at a distance r from each other, then the potential energy of the system is given by y= 4192 4néy 1 80. 81. >> Assertion & Reason \\\\ —— A combination of parallel plate capacitors is maintained at a certain potential difference. | Foon-wall | 1+ When a 3 mm thick slab is introduced between all the plates, in order to maintain the same potential difference, the distance between the plates is increased by 2.4 mm. Find the dielectric constant of the slab. (a) 3 (b) 4 (c) 5 (d) 6 Two capacitors of capacitances 3uF and 6uF are charged to a potential of 12V each. They are now connected to each other, with the positive plate of each joined to the negative plate of the other. The potential difference across each will be (a) zero (b) 4V (c) 6Y = (d):12V DIRECTIONS : Each of these questions contains an assertion followed by reason. Read them carefully and answer the question on the basis of following options. You have to select the one that best describes the two statements. (a) (b) (c) (d) 82. 83. 84. 85. 86. Ifboth Assertion and Reason are correct and the Reason is the correct explanation of the Assertion. If both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion. Ifthe Assertion is correct but Reason is incorrect. Ifthe Assertion is incorrect but the Reason is correct. Assertion: The potential difference between any two points in an electric field depends only on initial and final position. Reason: Electric field is a conservative field so the work done per unit positive charge does not depend on path followed. Assertion : Polar molecules have permanent dipole moment. Reason : In polar molecules, the centres of positive and negative charges coincide even when there is no external field. Assertion : Dielectric polarisation means formation of positive and negative charges inside the dielectric. Reason: Free electrons are formed in this process. Assertion : In the absence of an external electric field, the dipole moment per unit volume ofa polar dielectric is zero. Reason : The dipoles of a polar dielectric are randomly oriented. Assertion : A parallel plate capacitor is connected across battery through a key. A dielectric slab of dielectric constant k is introduced between the plates. The energy stored becomes k times. Reason : The surface density of charge on the plate remains constant. >>>? 87. Assertion : Iftwo metal plates having charges QO, —Q face each other at some separation are dipped into an oil tank, then electric field between the plates decreases. E, alr Reason : Electric field between the plates, E44 = due to polarization of dielectrical materials. Assertion : A dielectric is inserted between the plates of a battery connected capacitor. The potential difference between the plates remains constant. Reason : As the battery remains connected maintaining the same potential difference. Assertion : Charges are given to plates of two plane parallel plate capacitors C, and C, (such that C, = 2C, ) as shown in figure. Then the key K is pressed to complete the circuit. Finally the net charge on upper plate and net charge on lower plate of capacitor C, is negative. K ms & 2 ene C, C, —————) ————— ee 88. 89. Reason : In a parallel plate capacitor both plates always carry equal and positive charge. 90. Assertion : Rate of change of potential is maximum at right angles to an equipotential surface. Reason : There is no net force is acting on the dipole ina uniform electric field. 91. Assertion: A dielectric is inserted between the plates of a battery connected capacitor. The potential difference between the plates remains constant. Reason : As the battery remains connected maintaining the same potential ditference. >> Match the Following »>» DIRECTIONS : Each question contains statements given in two columns which have to be matched. Statements (A, B, C, D) in column-I have to be matched with statements (1, 2, 3, 4) in column-ll. 92. Match the entries of Column I and Column I] Column I Column II (A) Inside a conductor (1) Potential energy = 0 placed in an external electric field. (B) At the centre ofa dipole (2) Electric field =0 (C) Dipole in stable (3) Electric potential = 0 equilibrium (D) Electric dipole perpendicular to uniform electric field. (4) Torque=0 >> Fill in the Blanks \ (a) (A) > (2); (B) >): (©) > (3); (D) > (1) (b) (A) (2); (B) > (3); (C) > (4); (D) > (1) (c) (A) > (2); (B) > (3); (©) >); (D) > A) (d) (A) (1); (B) > (3); (C) >); (D) > (2) In the given circuit diagram, both capacitors are initially uncharged. The capacitance C, = 2F and C, = 4F emf of battery A and B are2V and4V respectively. = l [os 1 | | wy > A . 21 SS / Column | Column II 64 (A) On closing switch S, (1) 7 with S, open work done by battery A is (B) Switch S, is open and (2) 4 S, is closed, work done by battery B is (C) Charge on capacitor GB) 8 C, is (after S, open and 5, closed) 16 (D) Charge on C, when (4) 3 both are closed (a) (A) (1); (B) > (2): (C) > (2); (D) > (4) (b) (A) >): (B) (3): (CE) > (3); (D) > 1) ° (A) > (2); (B) (3); (C) > (2); (D) > (1) ) (A) (3): (B) (1); (C) > (4); (D) > (2) >»>>»> DIRECTIONS : Complete the following statements with an 94. 95, appropriate word / term to be filled in the blank space(s). The electric potential inside a conducting sphere. An electric dipole of moment 7 is placed normal to the lines of force of electric intensity E , then the work done in deflecting it through an angle of 180° is 96. 97. 98. 89. 100. a \—$§ DIRECTIONS : Read the following statements and write your Three capacitors each of capacitance C and break down voltage V are joined in series. The capacitance of the combination will be and break down voltage of the combination will be _ , C Three capacitors are connected in the arms ofa triangle ABC as shown in figure 5 Vis 2,5 /\, 3yF applied between A and B. The voltage i : A B between B and C is 5 2uF The electric potential V is given as a function of distance x (metre) by V=(5x*+10x-4) volt. Value of electric field at x = 1 mis A dielectric of dielectric constant k is inserted in a capacitor after it is disconnected from the battery. As a result, the potential energy A parallel plate capacitor is made by stacking equally spaced plates connected alternatively. If the capacitance between any two adjacent plates is ‘C’ then the resultant capacitance is »>>> answer as true or false. 101. 102. 103. 104. 105. 106. 107. 108. Electric potential and electric potential energy are different quantities. For a system of positive test charge and point charge electric potential energy = electric potential. When a dielectric slab is pulled out slowly from an isolated charged parallel plate capacitor, its energy increases. Work done by external force is negative. Electric potential due to dipole x es ; ; 1 Electric potential due toa point charge « E . For a non-uniformly charged thin circular ring with net charge is zero, the electric field at any point on axis of the ring is Zero. For a non-uniformly charged thin circular ring with net charge zero, the electric potential at each point on axis of the ring is maximum. 35. 36. 38. 39. 40. 41. 42. 43. 44, 45. (a) Due to insertion of a dielectric slab capacitance increase by K times. The potential difference, the electric | field and the stored energy decreases by ma times. (a) In parallel grouping of capacitors Cog = PCs recs C (b) Energy will be lost during transfer of charge (heating effect). (c) 2x2 ce) C= +2=3 uF (c) 55 Ht (b) In series combination of capacitors Veg = VtV+V=3V ! 1 1 : Cc = + + = Cop = = Cw CCC 3 Thus, the capacitance and breakdown voltage of the combination will be 5 and 3V. l (c) Energy of given to conductor, U= Zz Cy l or U=>x5x10" x (800)” = 1.6 joule (a) C= equivalent capacitance 1 1 1 1 —S—t-4+-5 %. C= 1pF Cc 2 3 © Charge in series circuit will be same. ~ q=CV=(1x10-°) x10 =10nC Charge across *3uF’ capacitor will be 10uC. (b) Potential at any point inside the sphere = potential at the surface of the sphere = LOV. (a) Let the side length of square be 'a' then potential at centre Ois ~OK, rs “4 20 Vy = k(-Q) _ keg) , kK) _£Q) =() (Given) a =—Q-q+2q+20=0=0+q=0>0=-q (c) The potential at P due to whole disc is V= © | JR? +p | 2€ I 29 Now potential due to quarter disc, V= Fo | dptag | a 4 8e 46. 47. 48. 49. 50. 51. 52. 53. (c) Electric field lines are always perpendicular to equipotential surface so, they cannot be in a direction of tangent to an equipotential surface. (b) Irrespective of the charges on the inner and outer conductors, the inner conductor is always at a higher potential as long as the charge on inner conductor is not zero. Therefore charge flows from B to A. When the whole charge of B flows to A and charge on B becomes zero then A and B are at same potential. Let charge on each sphere =q when they are connected together their potential will be equal. Now let charge on a= q, and onb=2q-q, i [ 2q- =>V, =V, or all A 4ne, a 4ne, b = dW 4 2q-q, b Loa E, 4m&, a? ( qi b?2 E, 1 2 | 2q-q, Ja? Ane, b- _ab* _b " =e b ae a (b) ph - Dad b) © A! aa" LEE Kx +9) =k Given v =—kvy Eor . E=hithj (b) In shell, q charge is uniformly distributed over its surface, it behaves as a conductor. + V= potential at surface = 4 4megR i + and inside V = 2 + ° 4megR + Because of this it behaves as an equipotential surface. (a) Force on acharge g in a uniform electric field E is, F =q E, work done = force * distance = qEy. (d) In an external electric field, the positive and negative charges of a non-polar molecule are displaced in opposite directions. The displacement stops when the external force on the constituent charges of the molecule is balanced by the restoring force (due to internal fields in the molecule). The non-polar molecule thus develops an induced dipole moment. The dielectric is said to be polarised by the external field. 54. 56. a7. 58. 59. 60. 61. ; W i (c) Since V =—, more work will be done for a positive charge of two units as compared to positive charge of one W unit, but the ratio 0 is same. Therefore potential difference is same. . ; «Bight (d) Since capacitance C= , as d decreases d capacitance increases. (a) PE,U)=Q?/2C When a slab of dielectric constant k is inserted, then C’= Ck U'- Q*_ Q VU 2C' 2Ck k (c) Battery is disconnected so Q will be constant as C 64. The positively charged particle experiences the electrostatic force in the direction of electric field i.e., from high electrostatic potential to low electrostatic potential. Thus, the work done by the electric field on the positive charge, so electrostatic potential energy of the positive charge decreases because speed of charged particle moves in the direction of field due to force gE. (c) The work done (in displacing a charge particle) by a electric force is given by W,, =q(V.,-—V,). Here initial and final potentials are same in all three cases are equal (20V) and same charge is moving from A to B, so work done is (AVq) same in all three cases. (c) As we know that the relation between electric field intensity E and electric potential V is p--2% dr ' dV Electric field intensity E=0 then ae =0 This imply that V = constant Thus, E =0 inside the charged conducting sphere then the constant electrostatic potential 100V at every where inside the sphere and it verifies the shielding effect also. (c) The capacitance of parallel plate capacitor filled with dielectric of thickness d, and dielectric constant K, is _Ke,A ] d, Similarly, capacitance of parallel plate capacitor filled with dielectric of thickness d, and dielectric constant K, is _ K,s,A C= i Since both capacitors are in series combination, then the equivalent capacitance is ] l l =—+ Cc Gg & C- CCp dy oO Chl KyeoA , KoeoA dy dy K,K2e9A C= K,d5 +K5d, AD So multiply the numerator and denominator of equation (1) with (d, + dy) Kd) +Kyd,) (d; +d>) ( _ K,K>, (d, +d,) % Eg A (Kid, +K>d)) (d, + d>) ...(ii) So, the equivalent capacitances is =e .. (1 (d; + d5) (a) Inthe batteryconnected capacitor V remains constant The equivalent capacitance between A and B is while C increases with the introduction of dielectric C= 2H F x 3pF + 2uF = 16 uF (b) A>(2);B>(3);C>4); D> (1) “4 2uF +3yF 5 di 8a & _ ; Total charge of the given circuit is Electrice field is zero inside a conductor placed in an c e external field. Q= "Cur xSV = 16 nC Electrice potential is zero at the centre of a dipole. Torque is zero when a dipole in stable equilibrium. QO) = (2HF) xSV =10nC Potential energy is zero ifa electric dipole perpendicular to “ Q)=Q—Q, = 16 pC— 10 uC = 6 pC uniform electice field. .. Voltage between B and C is @ A)>B):B)>():©) 24); (D)>@) Vac = 22 = HE ay | 3uF 3yF W.d. by battery A, — 2 Sew? | aid 36 2° = $8] 98. (-20 Vin) V=5 x? +10x-—4 : p=—* 10x +10), W.d. by battery B, = a > cr} | . Atx= 1m,E=—20 V/m. { de® oc) 64 99. (decreases) ~ ce 442 xa) = re 100. (14-1) C Asn plates are joined, it means (n — 1) - combination joined in parallel. 1, 
