# PHYSICS. Electrostatics

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1 Electrostatics

2 Coulomb s Law: SYNOPSIS

3 SI unit of electric intensity is NC -1 Dimensions

4 The electric intensity due to isolated point charge, Electric dipole moment, P = q (2a), SI unit is C m

5 Torque on a dipole, If θ = 0 or 180 then Electric potential, V =. Its SI unit is volt and dimensions

6 Electric potential due to isolated point charge, V = Work done to move a charge q from one point to another, W = Pot. diff x q

7 Electric flux, ø= Ʃ E Cos θ ds, Electric flux is scalar quantity. Capacitance of conductor, Its SI unit is farad. Capacitance of spherical conductor, Energy stored in a capacitor,

8 Relation between electric intensity and potential, Gauss theorem

9 Capacitance of parallel plate capacitor, C= Capacitance of spherical capacitor, Capacitance of cylindrical capacitor,

10 Series combination of capacitors, For n identical capacitors,

11 Parallel combination of capacitors, Cp = C1 + C2 + C3 For n identical capacitors, Cp=n C For two capacitors in parallel, the common potential, V = If n small drops each having a charge q, capacity C and potential V combine to form a big drop, then

12 1. The charge on big drop, Q = n q 2. The surface density of charge of big drop, 3. Capacitance of big drop, =

13 1)Two charges 4q and q are placed a distance r apart. A charge Q is placed exactly mid-way between them. What will be the value of Q so that charge 4q experiences no net force? q/4 -q/4 4q -4q

14 F 1 4q F 2 Q -q r/2 r/2

15 Two charges 4q and q are placed a distance r apart. A charge Q is placed exactly mid-way between them. What will be the value of Q so that charge 4q experiences no net force? q/4 -q/4 4q -4q

16 2)Two point charges of +4µC and +2µc repel each other with a force of 8N. If a charge of 4µ C is added to each of these charges, the force would be Zero 8N 4N 12N

17

18 Two point charges of +4 µc and +2µc repel each other with a force of 8N. If a charge of 4 µc is added to each of these charges, the force would be Zero 8N 4N 12N

19 3)Force between two charges separated by a certain distance in air is F. If each charge were doubled and distance between them also doubled, Force would be 2F F 4F F/4

20

21 Force between two charges separated by a certain distance in air is F. If each charge were doubled and distance between them also doubled, Force would be 2F F 4F 14F

22 4)Two point charges certain distance apart in air repel each other with a force F. A glass plate is introduced between the charges. The force becomes F 1 where 1) F 1 < F 2) F 1 =F 3) F 1 > F 4)Data is insufficient.

23

24 Two point charges certain distance a port in air repel each other with a force F. A glass plate is introduced between the charges. The force becomes F 1 where 1) F 1 < F 2) F 1 =F 3) F 1 > F 4)Data is insufficient.

25 5)Two equally charged identical metal spheres A and B repel each other with a force 3X10-5 N. Another identical uncharged sphere c is touched with A and then placed at the mid point between A and B. Net force on c is 1) 1x10-5 N 2) 2x10-5 N 3) 1.5x10-5 N 4) 3x10-5 N

26 q/2 q A r q/2 q B q A C B

27 Two equally charged identical metal spheres A and B repel each other with a force 3X10-5 N. Another identical uncharged sphere c is touched with A and then placed at the mid point between A and B. Net force on c is 1) 1x10-5 N 2) 2x10-5 N 3) 1.5x10-5 N 4) 3x10-5 N

28 6) If charge q is placed at the centre of the line joining two equal charges Q. The system of three charges will be in equilibrium if q is -Q/2 -Q/4-4Q +Q/2

29 Q q Q x x

30 If charge q is placed at the centre of the line joining two equal charges Q. The system of three charges will be in equilibrium if q is -Q/2 -Q/4-4Q +Q/2

31 7) In one gram of a solid, there are 5x10 21 atoms. If one electron is removed from every one of 0.01% of the solid, the charge gained by the solid is +0.08c +0.8c -0.08c -0.8c

32

33 In one gram of a solid, there are 5x10 21 atoms.if one electron is removed from every one of 0.01% of the solid, the charge gained by the solid is +0.08c +0.8c -0.08c -0.8c

34 8) When air is replaced by dielectric medium of constant k the maximum force of attraction between two charges separated by a distance Increases k -1 times Increases k times Remains unchanged decreases k times

35

36 When air is replaced by dielectric medium of constant k the maximum force of attraction between two charges separated by a distance Increases k -1 times Increases k times Remains unchanged decreases k times

37 9) In paper and cotton industries, the atmosphere is kept moist. This is to Remove dust and dirt Conduct the charges produced due to friction as material is dried Reduce the temperature of surrounding Prolong process of drying

38 Due to action of points, sparking occurs. Hence conduct the charges

39 In paper and cotton industries, the atmosphere is kept moist. This to Remove dust and dirt Conduct the charges produced due to friction as material is dried Reduce the temperature of surrounding Prolong process of drying

40 10) The statement which is incorrect is Gravitational force may be attractive while electrostatic force may be attractive or repulsive Both gravitational and electrostatic forces very inversely as the square of the distance Gravitational force is a short range force while electrostatic force is a long range force Gravitational force is very weak compared to electrostatic force

41 Gravitational force and electrostatic force are long range forces

42 The statement which is incorrect is Gravitational force may be attractive while electrostatic force may be attractive or repulsive Both gravitational and electrostatic forces very inversely as the square of the distance Gravitational force is a short range force while electrostatic force is a long range force Gravitational force is very weak compared to electrostatic force

43 11) There is an electric field E in X-direction. If work done in moving a charge 0.2C through a distance of 2m along a line making an angle of 60 0 with X-axis is 4J, what is the value of E?

44

45 There is an electric field E in X-direction. If work done in moving a charge 0.2c through a distance of 2m along a line making are angle of 60 0 with X-axis is 4J, what is the value of E?

46 12) Shown below is a distribution of charges. The flux of electric field due to these charges through the surface is +q. -q.. +q

47 Charges present outside the surface make no contribution to electric flux

48 Shown below is a distribution of charges. The flux of electric field due to these charges through the surface is 4) zero

49 13) If the electric flux entering and leaving an enclosed surface respectively is ø1 and ø2 the electric charge inside the surface will be

50

51 If the electric entering and leaving an enclosed surface respectively is ø1 and ø2 the electric charge inside the surface will be

52 14) Two metal pieces having a potential difference of 800V are 0.02m apart horizontally. A particle of mass 1.96x10-15 Kg is suspended in equilibrium between the plates. If e is the elementary charge, then charge on particle is 8e 6e 3e e

53

54 Two metal pieces having a potential difference of 800v are 0.02m apart horizontally. A particle of mass 1.96x10-15 Kg is suspended in equilibrium between the plates. If e is the elementary charge, then charge on particle is 8e 6e 3e e

55 15) An electron is projected into a region of uniform electric field with a velocity v such that it moves in the direction of the field. As the electron moves, its velocity Remains the same Increases Decreases Continuously charges in direction

56 Since electron is negatively charged, it experiences a force opposite to the direction of the field E. This means the electron moves against the force acting on it. Hence its velocity decreases.

57 An electron is projected into a region of uniform electric field with a velocity v such that it moves in the direction of the field. As the electron moves, its velocity Remains the same Increases Decreases Continuously charges in direction

58 16) If a particle of mass m and charge +q moves from rest in an electric field from a point at a higher potential to a point at a lower potential and V be the potential difference between the two points, then the velocity acquired by the particle is

59

60 If a particle of mass m and charge +q moves from rest in an electric field from a point at a higher potential to a point at a lower potential and V 1 be the potential difference between the two points, then the velocity acquired by the particle is

61 17) A point charge of +1nc is at centre of circle of radius 5cm as shown in the diagram. A, B, C and D are points on the circumference of the circle. The amount of work done in taking +1c of charge is Greatest for the path AD Greatest for the path AB Same for the paths AC & BD Zero for all the paths B C A Q=+1nc D

62 A, B, C and D are points on an equi potential line. Therefore work done is zero for all paths

63 A point charge of +1nc is at centre of circle of radius 5c.m. as shown in the diagram. A, B, C and D are points on the circumference of the circle. The amount of work done in taking +1c of charge is Greatest for the path AD Greatest for the path AB Same for the paths AC & BD Zero for all the paths

64 18) A particle of mass 6mg carrying a charge of - 1µc is projected with a velocity v towards a charge of -10µc from a point A as shown in the diagram. It comes to rest at a point B distant 1m from O and then turns back. Then v is nearly 1)100ms -1 2) 173ms -1 3) 500ms -1 4) 325ms -1 B O -10 c A

65

66 A particle of mass 6mg carrying a charge of -1µc is projected with a velocity v towards a charge of - 10µc from a point A as shown in the diagram. It comes to rest at a point B distant 1m from O and then turns back. Then v is nearly 100ms ms ms ms -1

67 19) The number of electrons to be removed from a neutral copper sphere of radius 1m in order that there exists an electric intensity of 9vm -1 on the surface of the sphere is 1) 625x10 7 2) 6.25x10 7 3) 625x10 8 4) 6.25x10 8

68

69 The number of electron to be removed from a neutral copper sphere of radius 1m in order that there exists an electric intensity of 9vm -1 on the surface of the sphere is 625x x x x10 8

70 20) Can a sphere of radius 1m hold a charge of 1c? Yes No Depends upon the metal of the sphere Depends upon whether the charge is +ve or-ve

71

72 Can a sphere of radius 1m hold a charge of 1c? Yes No Depends upon the metal of the sphere Depends upon whether the charge is +ve or-ve

73 21) The energy stored in a capacitor is actually stored Between the plates On the positive plate On the negative plate On the outer surface of the plates

74 We know that the energy stored in a capacitor is in the form of electrostatic energy. It is actually stored in the electric field between the plates of the capacitor

75 The energy stored in a capacitor is actually stored Between the plates On the positive plate On the negative plate On the outer surface of the plates

76 22) If an uncharged capacitor is charged by connecting it to a battery, then the amount of energy lost as heat is

77

78 If an uncharged capacitor is charged by connecting it to a battery, then the amount of energy lost as heat is

79 23) A variable capacitor is permanently connected to a 100volt battery. If the capacity is changed from 2µF to 10µF, then the change in energy is equal to 2x10-1 J 2.2x10-2 J 3.5x10-2 J 4x10-2 J

80

81 A variable capacitor is permanently connected to a 100volt battery. If the capacity is changed from 2µF to 10µF, then the change in energy is equal to 2x10-1 J 2.2x10-2 J 3.5x10-2 J 4x10-2 J

82 24) The capacity of a parallel plate capacitor depends on The type of metal used The thickness of plates The potential applied across the plates The separation between the plates

83

84 The capacity of a parallel plate capacitor depends on The type of metal used The thickness of plates The potential applied across the plates The separation between the plates

85 25) A capacitor of capacitance 6µF was originally charged to 10volt. Now the potential difference is made 20volt. What is the increase in its potential energy? 3x10-4 J 6x10-4 J 9x10-4 J 12x10-4 J

86

87 A capacitor of capacitance 6µF was originally charged to 10volt. Now the potential difference is made 20volt. What is the increase in its potential energy? 3x10-4 J 6x10-4 J 9x10-4 J 12x10-4 J

88 26) Two copper spheres of same radius, one hollow and the other solid are charged to the same potential, then The hollow sphere will hold more charge The solid sphere will hold more charge Both of them will hold same charge Hollow sphere cannot hold any charge

89 Charge resides only on the outer surface of the conductor

90 Two copper spheres of same radius, one hollow and the other solid are charged to the same potential, then The hollow sphere will hold more charge The solid sphere will hold more charge Both of them will hold same charge Hollow sphere cannot hold any charge

91 27) The capacitance of a capacitor does not depend upon Distance between the plates Area of the plates Curvature of the plates Material of the plates

92

93 The capacitance of a capacitor does not depend upon Distance between the plates Area of the plates Curvature of the plates Material of the plates

94 28) Two capacitors with capacitances c 1 and c 2 are charged to potentials v 1 and v 2 respectively. When they are connected in parallel, the ratio of their respective charges is

95 c 1 v 1 c 2 v 2 In parallel combination they attain common p.d. Q 1 =c 1 v Q 2 =c 2 v

96 Two capacitors with capacitances c 1 and c 2 are charged to potentials v 1 and v 2 respectively. When they are connected in parallel, the ratio of their respective charges is

97 29) Three capacitors each of capacity 4µF are to be connected in such a way that the effective capacitance is 6µF, this can be done by Connecting all of them in series Connecting all of them in parallel Connecting two in series and one in parallel Connecting two in parallel and one in series

98

99 Three capacitors each of capacity 4µF are to be connected in such a way that the effective capacitance is 6µF, this can be done by Connecting all of them in series Connecting all of them in parallel Connecting two in series and one in parallel Connecting two in parallel and one in series

100 30) Three capacitors of capacity C each are joined first in series and then in parallel. The capacity becomes n times, where n is

101

102 Three capacitors of capacity C each are joined first in series and then in parallel. The capacity becomes n times, where n is

103 31) The effective capacitance between A and B is A B

104 5 A 10 B

105 The effective capacitance between A and B is A B

106 32) In a parallel plate capacitor of capacitance c, a sheet of copper is inserted between the plates, parallel to them. The thickness of the sheet is half the separation between the plates. The capacitance now becomes 2c c/2 4c c/4

107

108 In a parallel plate capacitor of capacitance c, a sheet of copper is inserted between the plates, parallel to them. The thickness of the sheet is half the separation between the plates. The capacitance now becomes 2c 4c c/4 c/2

109 33) Two conducting spheres of radii R 1 and R 2 are given the same charge. The ratio of their potentials will be

110

111 Two conducting spheres of radii R 1 and R 2 are given the same charge. The ratio of their potentials will be

112 34) Two conducting spheres of radii r 1 and r 2 are charged such that they have the same electric field on their surfaces. The ratio of the charge on them is

113

114 Two conducting spheres of radii r 1 and r 2 are charged such that they have the same electric field on their surfaces. The ratio of the charge on them is

115 35) A parallel plate capacitor is charged and is disconnected from the battery. If the plates of the capacitor are moved apart by means of insulating handles, The charge on the capacitor becomes zero The capacitance becomes infinity The charge on capacitor increases Voltage across the plates increases

116 If the plates of capacitor are moved apart its capacitance c decreases. But charge Q remains the same. Since Q=cv, voltage across the plates increases

117 A parallel plate capacitor is charged and is disconnected from the battery. If the plates of the capacitor are moved apart by means of insulating handles The charge on the capacitor becomes zero The capacitance becomes infinity The charge on capacitor increases Voltage across the plates increases

118 36) A parallel plate capacitor with oil between the plates (dielectric constant of oil K=5) has capacitance c. If the oil is removed, then capacitance of the capacitor becomes

119

120 A parallel plate capacitor with oil between the plates (dielectric constant of oil K=5) has capacitance c. If the oil is removed, then capacitance of the capacitor becomes

121 37) A parallel plate air capacitor has a capacitance of 1µF. The space between its plates is then filled with two slabs of dielectric constants K 1 =2 and K 2 =4 as shown. The new capacitance is A/2 A/2 K 1 K 2

122

123 A parallel plate air capacitor has a capacitance of 1µF. The space between its plates is then filled with two slabs of dielectric constants K 1 =2 and K 2 =4 as shown. The new capacitance is A/2 A/2 K 1 K 2

124 38) A particle of mass m and charge q is placed at rest in a uniform electric field E and then released. The kinetic energy attained by the particle after moving a distance y is qey 2 qe 2 y qey q 2 Ey

125 K.E. acquired=work done =force x distance =qe x y =qey

126 A particle of mass m and charge q is placed at rest in a uniform electric field E and then released. The kinetic energy attained by the particle after moving a distance y is qey 2 qe 2 y qey q 2 Ey

127 39) An alpha particle is accelerated through a potential difference of 10 6 volt. Its kinetic energy will be 1Mev 2Mev 4Mev 8Mev

128 Charge on alpha particle =q=2e K.E.=work done =q x v =2e x 10 6 =2Mev

129 An alpha particle is accelerated through a potential difference of 10 6 volt. Its kinetic energy will be 1Mev 2Mev 4Mev 8Mev

130 40) In bringing an electron towards another electron, the electrostatic potential energy of the system remains same becomes zero increases decreases

131

132 In bringing an electron towards another electron, the electrostatic potential energy of the system remains same becomes zero increases decreases

133 41) Two spheres of radii R 1 and R 2 respectively are charged and joined by a wire. The ratio of electric field of sphere is

134

135 Two spheres of radii R 1 and R 2 respectively are charged and joined by a wire. The ratio of electric field of sphere is

136 42) The electric potential v is given as a function of distance x (metre) by v=5x 2 +10x-4. Value of electric field at x=1metre is -23v/m 11v/m 6v/m -20v/m

137

138 The electric potential v is given as a function of distance x (metre) by v=5x 2 +10x-4. Value of electric field at x=1metre is -23v/m 11v/m 6v/m -20v/m

139 43) An alpha particle and a proton are accelerated through same potential difference from rest. Find the ratio of their final velocity.

140

141 An alpha particle and a proton are accelerated through same potential difference from rest. Find the ratio of their final velocity.

142 44) The potential difference applied to a x-ray tube is 5kv and current through it is 3.2mA. Then the number of electrons striking the target per second is 2x x10 6 1x10 7 4x10 15

143

144 The potential difference applied to a x-ray tube is 5kv and current through it is 3.2mA. Then the number of electrons striking the target per second is 2x x10 6 1x10 7 4x10 15

145 45) Equal charges q each are placed at the vertices A and B of an equilateral triangle of side a. the magnitude of electric intensity at the point c is

146

147 Equal charges q each are placed at the vertices A and B of an equilateral triangle of side a. the magnitude of electric intensity at the point c is

148 46) 27 identical drops of mercury are charged simultaneously to the same potential of 10volt each. Assuming drops to be spherical, if all the charged drops, are combined to form a single large drop, then potential, of larger drop would be 45v 135v 270v 90v

149

150 27 identical drops of mercury are charged simultaneously to the same potential of 10volt each. Assuming drops to be spherical, if all the charged drops, are combined to form a single large drop, then potential, of larger drop would be 45v 135v 270v 90v

151 47) The capacitance of arrangement of 4 plates of area A at a distance d as shown in figure is A d B

152

153 The capacitance of arrangement of 4 plates of area A at a distance d as shown in figure is A d B

154 48) A parallel plate capacitor is first charged and then a dielectric slab is introduced between the plates. The quantity that remains unchanged is Charge Potential Capacity energy

155 Once charged battery is disconnected. On introducing the slab charge remains unchanged

156 A parallel plate capacitor is first charged and then a dielectric slab is introduced between the plates. The quantity that remains unchanged is Charge Potential Capacity energy

157 49) Two capacitors of capacitances c 1 and c 2 are connected in parallel across a battery. If Q 1 and Q 2 respectively be the charges on the capacitors, then Q 1 /Q 2 will be equal to

158

159 Two capacitors of capacitances c 1 and c 2 are connected in parallel across a battery. If Q 1 and Q 2 respectively be the charges on the capacitors, then Q 1 /Q 2 will be equal to

160 50) The surface encloses an electric dipole. The electric flux through the surface is Zero Positive Negative infinity

161

162 The surface encloses an electric dipole. The electric flux through the surface is Zero Positive Negative infinity

163 Thank you Wish you all the best

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