Electric potential numericals

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NUMERICALS
Electric potential
1. A positive charge of 1nC is located at a point. What is the work done if a unit positive charge is carried around this
charge along a complete circle of radius 0.1 m about this point? [Ans zero]
2. Find the potential at a point due to a negative charge of 200 μC at a distance of 3m. [Ans. -6 X 105
V]
3. Two positive charge of 10 μC and 5μC respectively are 12cm apart. Find the work done in bringing them to 6cm
closer. [Ans. 3.75 J]
4. Two parallel plates are 5 cm apart. The electric field intensity between them is 5000 N c-1
. Calculate the potential
difference between the plates. [Ans. – 250 V]
5. A charge of 100μC is placed at a distance of 12cm from a charge of 200μC. Calculate the potential mid way
between the two charges. Assume that medium is air. [Ans. 4.5 X 107
V]
6. Charge of 2, 4 and 6μc are placed at the three corners of a square. Find what charge must be placed at the fourth
corner so that the total potential at the centre of the square is zero[ Ans. - 12μC]
7. Charges of +10, - 10, + 15 and +30 μC are placed in order at each of the corners of a square of 10 cm side. Calculate
the potential at the point of intersection of the diagonals. [Ans. 57.28 X 105
V]
8. A uniform electric field is obtained by maintaining a potential difference of 700 V between two metal plates kept 2
mm apart. Find the electric field intensity between them. What will be the force on a charge of 10μC, when placed
between the two plates? [Ans. 3.5 X 105
V m-1
, 3.5 N]
9. Calculate the potential at a point having coordinates (0.3 m, 0.4 m, 0.5m) due to a charge of 20 μC placed at the
origin. [Ans. 2.55 X 105
V]
10. Three charges of +5 μC are located at the corners of an equilateral triangle whose sides are 6 cm long. Find the
potential at the midpoint of the base of the triangle. [Ans. 3.87 X 106
V]
11. Three charges are placed at the three corners of a square as shown in figure. Find the potential at D.
[Ans 4.89 X 105
V]
12. If 100 J of work is done in carrying a charge of 2C from a place where the potential is – 10 V to another point where
potential is V, find the value of V. [ Ans. 40 V]
13. A charge of 20 μC produces an electric field. Two points are 10 cm and 5 cm from this charge. Find the values of
potentials at these points and also find the amount of work done to take a proton from one point to the other.
[Ans. 1.8 X 106
V, 3.6 X 106
V, 2.88 X 10-13
J]
14. Two charges 3 X 10-8
C and – 2 X 10-8
C are located 15 cm apart. At what point on the line joining the two charges
is the electric potential zero? [Ans. 9 cm from 3 X 10-8
C]

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15. A regular hexagon of side 10 cm has a charge 10 μC at each of its vertices. Calculate the potential at the centre of
the hexagon. [ Ans. 5.4 X 106
V]
16. A wire is bent in a circle of radius 10 cm. It is given a charge of 200 μC which spreads uniformly. Calculate the
electric potential at the centre of the circle. [ Ans. 1.8 X 107
V]
17. ABCD is a square of side 0.2m. Charges of 2 nC, 4 nC, 8 nC are placed at the corners A, B and C respectively.
Calculate the work required to transfer a charge of 2 nC from D to the centre of the square. [Ans. 5.40 X 107
J]
18. Three small spheres each carrying a charge q are placed on the circumference of the circle of radius r to from an
equilateral triangle. Find the potential at the centre of the circle. [ Ans.
1
4𝜋 𝜖0
3𝑞
𝑟
]
Electric potential energy
19. Two protons in a nucleus are 3.0 X 10-15
m apart. What is their mutual eclectic potential energy?
[Ans. 7.68 X 10-14
J]
20. In an atom two protons are separated by a distance of 3 X 10-10
m and an electron is at a distance of 1.5 X 10-10
m
from each proton. Calculate the potential energy of this system. [ Ans. – 7.68 X 10-19
J]
21. Three charges – q, Q and – q are placed as shown at equal distances on a straight line. If the total potential energy of
the system of three charges is zero, what is the ratio Q : q?
[ Ans. 1: 4]
22. Each corner of a square of side a m has charge +q each on opposite corners of a diagonal and –q each on the
opposite corners of the other diagonal. Calculate the potential energy of the system. [Ans.
𝑞2
4𝜋 𝜖0 𝑎
(√2 − 4) ]
23. Two positive charges of 0.2 μC and 0.01 μC are placed 10 cm apart. Calculate the work done in reducing their
distance to 5 cm. [Ans. 1.8 X 10-4
J]
24. 2μC charge is placed at each corner of a square ABCD of side 2√2 cm. Calculate electric potential at centre O of
the square.
[Ans. 3.6 X 106
V]
25. Determine electrostatic potential energy of a system containing two charges 5μC and - 3μC separated by a distance
12 cm in air. [Ans. -1.125 J]
26. Two point charges 5 X 10-8
and -2 X 10-8
C are separated by a distance of 20 cm in air as shown:

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(i) Find at what distance from first charge A would the electric potential be zero.
(ii) Also calculate the electrostatic potential energy of the system. [ Ans. (i) 14.29 cm, (ii) – 4.5 X 10-5
J]
27. The amount of work done in bringing 0.01 C of charge is 8 joule. How much is the potential difference?
28. The electric field and electric potential at any point due to a point charge kept in air is 20 NC-1
and 10 JC-1
respectively. Compute the magnitude of charge. [Ans. 5.56 X 10-10
C]
29. Calculate the potential at a point on the axis of a ring of charge of radius r, charge on the ring is q and the distance
of the observation point from the centre of the ring is x. [Ans.
1
4𝜋 𝜖0
𝑞
√𝑟2 + 𝑥2
]
30. Calculate the potential at P due to the charge configuration as shown in fig. below. If r >> a, then what will be the
result.
[Ans.
1
4𝜋 𝜖0
[
𝑞
𝑟
+
2𝑞𝑎
𝑟2− 𝑎2
],
1
4𝜋 𝜖0
[
𝑞
𝑟
+
2𝑞𝑎
𝑟2
]
31. Sixty four drops each of radius 2 cm and carrying 5C of charge combine to form a bigger drop. Find its potential.
[Ans. 3.6 X 1013
V]
32. A charge Q is distributed over two concentric hollow spheres of radii r and R (where R > r) such that the surface
densities are equal. Find the potential at the common centre. [Ans.
1
4𝜋 𝜖0
𝑄 (𝑅+𝑟)
(𝑅2 + 𝑟2)
]
33. Two fixed equal positive charges, each of magnitude 5 X 10-5
C are located at points A and B separated by a
distance of 6m. an equal and opposite charge moves towards them along the line COD, the perpendicular bisector of
the line AB. The moving charge, when reaches the point C at a distance of 4m from O has a kinetic energy of 4
joule. Calculate the distance of the farthest point D which the negative charge will reach before returning towards C.
[Ans. 8.485 m]
34. A spherical liquid drop has a diameter 2 mm and is given a charge 5μC, (a) What is the potential at eh surface of the
drop? (b) if eight such drops coalesce to form a single drop having charge of 5 μC, what is the potential at the
surface of the drop so formed? [Ans. 4.5 X 107
V; 2.25 x 107
V]
35. A potential at a point is given by V = 4x2
+ 4y2
+ 4z2
. Calculate the components of electric field intensity at (1, - 1,
2) m.
[Ans. – 8N C-1
, 8 N C-1
, - 16 N C-1
]
Capacitance
36. The capacitance of a parallel plate capacitor is 200 pF. If the potential difference between the plates is 100 volts,
then what is the charge on each plate? [ Ans. 20 nC)
37. A conductor has a potential of 100 volts when charged with 5 nC. Calculate the capacitance of the capacitor formed
by the conductor and its surroundings. [Ans. 50pF]
38. Calculate the charge on each plate of a 5 X 10-9
F capacitor when the potential difference between the plates is 100
volt. [Ans,. 0.5 μC)

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39. Seven capacitors each of capacitance 2μF are to be connected in a configuration to obtained an effective capacitance
of (10/11) μF. How will you connect the capacitors?
[Ans. 5 capacitors can be connected in parallel and the 2 Capacitors are to be
connected in series with this parallel combination]
40. Find the charge on each capacitor and the potential difference across each capacitor of the circuit shown in figure.
[Ans. Charge on each capacitor = 3μC, V1 = 1.5 V; v2 = 1.5 V]
41. Calculate the capacitance between A and B [ Fig. (A) and (B)], if area of each plate is A and distance between
successive plates is d.
[Ans. (a) 3ϵ0 A/d (b) 2ϵ0 A/d]
42. Three capacitors each of capacitance 5μF are available. Find the maximum and minimum values of the capacitance
that can be obtained by the use of these capacitors. [Ans. 15 μF; 1.67 μF]
43. Two capacitors have a capacitance of 25 μF when connected in parallel and 6 μF when connected is series. Find
their individual capacitances. [Ans. 15 μF and 10 μF]
44. Find the resultant capacitance of the capacitor connected as shown in figure.
[Ans. 4 μF]

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45. Three capacitors of capacitances, 1, 3, and 6μf are connected in such a way that the second and third are in series
and first is in parallel with them. Find the equivalent capacitance of this combination. [Ans. 3 μF]
46. Calculate the equivalent capacitance of the network shown in figure between A and B.
[Ans. 6 μF]
47. Calculate the equivalent capacitance between points A and B of the network shown in figure. Take C1 = 1 μF, C2 =
2 μF and C3 = 3μF.
[ Ans. 6 μF]
48. Calculate the equivalent capacitance between points A and B of the net work shown in figure. Given C1 = 2 μF, C2
= 4μF and C3 = 6 μF
[Ans 12 μF]
49. Determine the equivalent capacitance between points A and B in the figure.

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[Ans. 9pF]
50. Calculate the capacitance between points A and B in the following network. If C = 2 μF. Also calculate charge on
each capacitor.
[ Ans.
8
3
μF, 200 μC, 200 μC, 200 μC, 600 μC]
51. Calculate the equivalent capacitance between points A and B in the network shown in fig., if C= 4 μF
[Ans 6 μF]
52. Calculate the energy stored in a capacitor of 100μF charged to 200 volt. [Ans. 2J]
53. A capacitor of 20μF is charged to a potential of 300 volt. Calculate the energy stored in the capacitor. [Ans. 0.9 J]
54. A capacitor of capacitance 25 μF is charge to a potential of 500 V. determine the energy stored in the capacitor.
[Ans. 3.125 J]
55. A 800 pF capacitor is charged by a 100 V. battery. How much energy is stored by the capacitor? The capacitor is
disconnected from the battery and connected to another 800 pF capacitor. What is the electrostatic energy of the
system? [Ans. 4 X 10-6
J; 2 X 10-6
J]
56. The plates of a parallel capacitor have an area of 100 cm2
each and are separated by 2.0 mm. The capacitor is
charged by connecting it to 200 V supply. How much electrostatic energy is stored in the capacitor?
[Ans. 8.854 X 10-7
J]

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57. A 600 pF capacitor is charged by a 200 V supply. It is then disconnected from the supply and is connected to
another uncharged 600 pF capacitor. How much electrostatic energy is lost in the process? [Ans 6 X 10-6
J]
58. Two capacitors of capacitances C1 = 3 μF and C2 = 6μF arranged in series are connected in parallel with a third
capacitor C3 = 4μF. The arrangement is connected to a 6 volt battery. Calculate the energy stored in the capacitors.
[Ans. 1.08 X 10-4
J]
59. A parallel plate 50μF capacitor is charged to 200 V. If the distance between its plates is doubled, what will be the
new potential difference between the plates and what will be the change in the energy stored? [Ans. 400 V, 1J]
60. The plates of a parallel plate capacitor have an area of 45 cm2
each and are separated by 2mm. The capacitor is
charged to 200V. Calculate energy stored. [Ans. 3.98 X 10-8
J]
61. Calculate the capacitance of a parallel plate capacitor in which the plates are separated by 0.1 mm and area of each
plate is 1 mm2
. [ Ans. 0.085 pF]
62. (a) A parallel plate capacitor of plate area 2 m2
and plate separation 2 mm is charged to 1000 V in vacuum.
Calculate the capacitance of the capacitor and charge on each plate.
(b) Now the battery is disconnected and a dielectric slab of dielectric constant = 5 is introduced. What will be the
capacitance of the capacitor and charge on each plate? [Ans. (a) 8.85 nF; 8.85 μC (b) 4.43 X 10-8
F; 8.85 μC]
63. The distance between the plates of a parallel plate capacitor is 1.0 mm. What must be the area of the plate of the
capacitor, if the capacitance is to be 1.0 μF? [Ans. 112.99 m2
]
64. A parallel plate capacitor has circular plates of 8.0 cm radius and are separated by 1.0 mm. calculate the
capacitance.
[Ans. 177.9 pF]
65. What is the area of the plates of 1F parallel capacitor if the separation between the plates is 1 mm?
[Ans. 1.13 X 108
m2
]
66. A capacitor with air between its plates has a capacitance of 6 μF. What will be its capacitance if glass is substituted
for air. Dielectric constant for glass is 6. [Ans. 36 μF]
67. A parallel plate capacitor has a capacitance of 50μF in air and 110 μF when immersed in an oil. Calculate the
dielectric constant of the dielectric [ Ans. 2.2]
68. The plates of a parallel plate capacitor are 5 X 10-2
m apart. If a dielectric slab of thickness 1 cm and constant 2 is
put between the plates and the capacitance is kept same as before by altering the distance between the plates, find
the new distance. [Ans. 0.5 cm]
69. Find total energy stored in capacitors in the given network.
[Ans. 38.6 X 10-6
J]
70. X and Y are two parallel plate capacitors having the same area of plates and same separation between the plates. X
has air between the plates and Y contains a dielectric medium of ɛr = 5.
(i) Calculate the ratio of potential difference between plates X and Y.

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(ii) What is the ratio of electrostatic energy stored in X and Y? [Ans. 5 times]
71. In the shown circuit, the energy stored in both capacitors is say E1. Now if switch S is opened and a dielectric slab
of constant 5 is
Put in free spaced of the capacitors, the energy stored is found to be E2. Give the value of E1/E2. [Ans. 5/13]
72. Two rectangular plates, each of area A and kept parallel to each other at a distance d apart to form a parallel plate
capacitor. If the area of each of the plate is doubled and their distance of separation decreased to ½ of its initial
value, calculate the ratio of their capacities in the two cases. [Ans. 4C]
73. A slab of material of dielectric constant k has the same area of the plates of a parallel plate capacitor but has a
thickness (3/4) d, where d is separation of the plates. How is the capacitance changed when the slab is inserted
between the plates? [Ans.
4𝑘
𝑘 + 3
C0]
74. The energy stored in a parallel plate capacitor of capacitance C is expressed as
1
2
ϵ0 E2
Ad, where E is the electric
field, A is the area of each plate, d is the separation between the plates. How will the energy stored of a fully
charged capacitor change if d is doubled and dielectric medium of dielectric constant 4 is introduced between the
plates.
[Ans. U’ =
𝑈0
2
]
HOT NUMERICALS
75. What will happen to the capacitance of a metallic sphere if its volume is doubled? If its increases or decreases, then
by what factor? [ Ans. Increases by a factor of 21/3
]
76. Calculate the capacitance of a metallic sphere of radius 2 m. [Ans. 2.22 X 10-10
F]
77. The capacitance of a metallic sphere is 0.056 pF. Determine its radius. [ Ans. 5.04 X 10-4
m]
78. 1000 drops of mercury of equal radii and possessing equal charges (each q) combine to form a big drop. What will
be (a) the charge on the bigger drop and (b) capacitance of bigger drop as compared to capacitance of smaller drop?
[ Ans. 1000 q, 10 C]
79. A capacitor of 2μF is connected to 200 V supply. The battery is disconnected and the capacitor is connected to an
uncharged capacitor of 1μF. Calculate the common potential after the capacitors are connected together.

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[ Ans. 133.3 V]
80. How much energy is stored in the electric field of an isolated conducting sphere of radius 6.85 cm and on which
charge is 1.25 X 10-9
C? [ Ans. 1.03 X 10-7
J]
81. A capacitor of 20 μF and charged to 500 V is connected in parallel with another capacitor of 10 μF charged to 200
V. Find the common potential. [Ans. 400 V]
82. A co-axial cable consist of a copper core of 0.1 mm radius within an outer metal sheath of 1.5 cm radius separated
by air. What is the capacitance per metre length of the cable? [Ans. 17.49 pF]
83. A parallel plate air capacitor consist of two circular plates of diameter 8 cm. at what distance should the plates be
placed so as to have the same capacity as that of a sphere of diameter 20 cm? [Ans. 4.0 mm]
84. A spherical capacitor has inner and outer radii equal to 10 cm and 12 cm respectively. The inner sphere is given a
charge of 2.0 μC and the outer sphere is earthed. Calculate the capacitance if the space between the spheres is filled
with (i) air and (ii) filed with dielectric of dielectric constant = 5. [Ans. (i) 66.7 pF; 333.5 pF]
85. Two conductors having capacities 5 μF and 10μF are charged upto 100 V and 200 V respectively. If these are
connected by a wire then calculate the common potential and loss of energy. [Ans. 167 V, 1.67 X 10-2
J]
86. A 10 μF capacitor is charged by a 30 V d.c. supply and then connected across an uncharged 50μF capacitor.
Calculate (i) the final potential difference across the combination and (ii) the initial and final energies. How will you
account for the difference in energy? [Ans. 5 V, 45 X 10-4
J, 75 X 10-5
J, heat loss]
87. Two thin spherical conducting shells are at a large distance apart. One having radius 10 cm carries a charge of + 0.5
μC and the other of radius 20 cm carries a charge of + 0.7 μC. Find the charge on each shell when connected by a
conducting wire. [ Ans. 0.4 μC; 0.8 μC]
88. An isolated spherical conductor has a radius of 0.6 m. Another spherical capacitor has air as dielectric with
thickness 0.02 m. The conductor and the capacitor both have same storage capacity. Find the radius of the inner
shell of the spherical capacitor. [Ans. 0.1m]
89. Two capacitors of 5 μF and 10 μF are charged to 16 V and 10 V respectively. What is the common potential when
they are connected in parallel? ( Ans. 12 V)