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PHYSICS FIRST PART QUESTIONS

Class 12 - Physics
Time Allowed: 6 weeks, 2 days and 22 hours Maximum Marks: 183

Section A

1. If 109 electrons move out of a body to another body every second, how much time is required to get a total [2]

charge of 1 C on the other body?

2. How can you charge a metal sphere positively without touching it? [3]
3. How much positive and negative charge is there in a cup of water? [2]
4. Coulomb’s law for the electrostatic force between two point charges and Newton’s law for gravitational force [5]
between two stationary point masses, both have inverse-square dependence on the distance between the charges
and masses respectively.
a. Compare the strength of these forces by determining the ratio of their magnitudes
i. for an electron and a proton and
ii. for two protons.
b. Estimate the accelerations of electron and proton due to the electrical force of their mutual attraction when
o
they are 1A (= 10-10 m) apart? (mp = 1.67 × 10-27 kg, me = 9.11 × 10-31 kg).

5. An early model for an atom considered it to have a positively charged point nucleus of charge Ze, surrounded by [5]
a uniform density of negative charge up to a radius R. The atom as a whole is neutral. For this model, what is the
electric field at a distance r from the nucleus?

6. An electric field is a uniform, and in the positive x-direction for positive x, and uniform with the same [5]
magnitude but in the negative x-direction for negative x. It is given that E = 200
⃗ ^
i N/C for x > 0 and E = –200
⃗ ^
i

N/C for x < 0. A right circular cylinder of length 20 cm and radius 5 cm has its centre at the origin and its axis
along the x-axis so that one face is at x = +10 cm and the other is at x = -10 cm (Fig).

a. What is the net outward flux through each flat face?

b. What is the flux through the side of the cylinder?
c. What is the net outward flux through the cylinder?

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 d. What is the net charge inside the cylinder?

7. The electric field components in fig. are Ex = αx1/2, Ey = Ez = 0, in which α = 800 N/C m1/2. Calculate [3]

a. the flux through the cube, and

b. the charge within the cube. Assume that a = 0.1 m.
8. Two charges ± 10 μ C are placed 5.0 mm apart. Determine the electric field at [2]
a. a point on the axis of the dipole 15 cm away from its centre O on the side of the positive charge, as shown in
figure.

b. a point Q, 15 cm away from O on a line passing through O and normal to the axis of the dipolem, as shown
in figure.

9. Two-point charges q1 and q2, of magnitude +10-8 C and -10-8 C, respectively, are placed 0.1 m apart. Calculate [3]

the electric fields at points A, B, and C shown in fig.

10. An electron falls through a distance of 1.5 cm in a uniform electric field of magnitude 2.0 × 104 N C-1 [Fig (a)]. [2]
The direction of the field is reversed keeping its magnitude unchanged and a proton falls through the same
distance [Fig (b)]. Compute the time of fall in each case. Contrast the situation with that of free fall under

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 gravity.

11. Consider the charges q, q, and –q placed at the vertices of an equilateral triangle, as shown in fig. What is the [3]
force on each charge?

12. Consider three charges q1, q2, q3 each equal to q at the vertices of an equilateral triangle of side l. What is the [3]

force on a charge Q (with the same sign as q) placed at the centroid of the triangle, as shown in a fig?

13. A charged metallic sphere A is suspended by a nylon thread. Another charged metallic sphere B held by an [3]
insulating handle is brought close to A such that the distance between their centres is 10 cm, as shown in Fig (a).
The resulting repulsion of A is noted (for example, by shining a beam of light and measuring the deflection of its
shadow on a screen). Spheres A and B are touched by uncharged spheres C and D respectively, as shown in Fig
(b). C and D are then removed and B is brought closer to A distance of 5.0 cm between their centres, as shown
in Fig (c). What is the expected repulsion of A on the basis of Coulomb’s law? Spheres A and C and spheres B
and D have identical sizes. Ignore the sizes of A and B in comparison to the separation between their centres.

14. What is the force between two small charged spheres having charges of 2 × 10-7C and 3 × 10-7C placed 30 cm [1]

apart in air?

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15. The electrostatic force on a small sphere of charge 0.4 μ C due to another small sphere of charge -0.8 μ C in air is [2]
0.2 N.
a. What is the distance between the two spheres?
b. What is the force on the second sphere due to the first?
2

16. Check that the ratio ke

Gme mp
is dimensionless. Look up a table of physical constants and determine the value of [3]
this ratio. What does this ratio signify?
17. a. Explain the meaning of the statement, electric charge of a body is quantized. [2]
b. Why can one ignore quantization of electric charge when dealing with macroscopic i.e. large scale charges?
18. When a glass rod is rubbed with a silk cloth, charges appear on both. A similar phenomenon is observed with [3]
many other pairs of bodies. Explain how this observation is consistent with the law of conservation of charge.
19. Four point charges qA = 2μ C, qB = -5μ C, qC = 2μ C and qD = -5μ C are located at the corners of a square ABCD [2]

of side 10 cm. What is the force on a charge of 1μ C placed at the centre of the square?
20. Two-point charges qA = +3μ C and qB = -3μ C are located 20 cm apart in vacuum, [3]

a. What is the electric field at the midpoint O of the line AB joining the two charges?
b. If a negative test charge of magnitude 1⋅ 5× 10-9 C is placed at this point, what is the force experienced by
the test charge?

21. A system has two charges qA = 2.5 × 10-7C and qB = -2.5 × 10-7C located at points A: (0, 0, -15 cm) and B : [2]

(0, 0, +15 cm), respectively. What is the total charge and electric dipole moment of the system?
22. a. An electrostatic field line is a continuous curve. That is, a field cannot have sudden breaks. Why not? [2]
b. Explain why two field lines never cross each other at any point?

23. A polythene piece rubbed with wool is found to have a negative charge of 3 × 10-7C. [3]

a. Estimate the number of electrons transferred (from which to which)?

b. Is there a transfer of mass from wool to polythene?

24. An electric dipole with dipole moment 4 × 10-9 Cm is aligned at 30o with the direction of a uniform electric [1]

field of magnitude 5 × 104 NC-1. Calculate the magnitude of the torque acting on the dipole.
25. a. Two insulated charged copper spheres A and B have their centres separated by a distance of 50 cm. What is [3]
the mutual force of electrostatic repulsion if the charge on each is 6.5 × 10 −7
C ? The radii of A and B are
negligible compared to the distance of separation.
b. What is the force of repulsion if each sphere is charged double the above amount, and the distance between
them is halved?
26. Figure shows tracks of three charged particles in a uniform electrostatic field. Give the signs of the three [2]
charges. Which particle has the highest charge to mass ratio?

27. Consider a uniform electric field E = 3 × 10

3^
i N /C . [3]
a. What is the flux of this field through a square of 10 cm on a side whose plane is parallel to the yz plane?
b. What is the flux through the same square if the normal to its plane makes a 60° angle with the x-axis?

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28. What is the net flux of the uniform electric field of E⃗ = 3 × 103 ^i N/C through a cube of side 20 cm oriented so [2]

that its faces are parallel to the co-ordinate planes?

29. Careful measurement of the electric field at the surface of a black box indicates that the net outward flux through [2]

the surface of the box is 8.0 × 103 N m2 C-1.

i. What is the net charge inside the box?
ii. If the net outward flux through the surface of the box were zero, could you conclude that there were no
charges inside the box? Why or why not?
30. A point charge +10μC is a distance 5 cm directly above the center of a square of side 10 cm, as shown in [3]
figure. What is the magnitude of the electric flux through the square? (Hint: Think of the square as one face of a
cube with edge 10 cm)

31. A point charge of 2.0 μ C is at the centre of a cubic Gaussian surface 9.0 cm on edge. What is the net electric [1]
flux through the surface?
32. A point charge causes an electric flux of −1.0 × 10 3 2
N m /C to pass through a spherical Gaussian surface of [2]
10.0 cm radius centered on the charge.
a. If the radius of the Gaussian surface were doubled, how much flux would pass through the surface?
b. What is the value of the point charge?
33. A conducting sphere of radius 10 cm has an unknown charge. If the electric field, 20 cm from the centre of the [2]
sphere is 1.5 × 10 3
N /C and points radially inward, what is the net charge on the sphere?
34. It is now believed that protons and neutrons (which constitute nuclei of ordinary matter) are themselves built out [3]
of more elementary units called quarks. A proton and a neutron consists of three quarks each. Two types of
quarks, the so called 'up' quark (denoted by u) of charge + (2/3) e, and the 'down' quark (denoted by d) of charge
, together with electrons build up ordinary matter. (Quarks of other types have also been found which give rise to
different unusual varieties of matter). Suggest a possible quark composition of a proton and a neutron.
35. Two large, thin metal plates are parallel and close to each other. On their inner faces, the plates have surface [3]
charge densities of opposite signs and of magnitude 17.0 × 10-22 C/m2. What is E:
a. in the outer region of the first plate,
b. in the outer region of the second plate, and
c. between the plates?

36. An infinite line charge produces a field of 9 × 104 NC-1 at distance of 2 cm. Calculate the linear charge density. [1]

37. A uniformly charged conducting sphere of 2.4 m diameter has a surface charge density of 80.0 μ Cm-2. [2]

a. Find the charge on the sphere.

b. What is the total electric flux leaving the surface of the sphere?
Section B
[2]
38. a. Calculate the potential at a point P due to a charge of 4 × 10-7 C located 9 cm away.

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 b. Hence, obtain the work done in bringing a charge of 2 × 10-9 C from infinity to the point P. Does the answer
depend on the path along which the charge is brought?

39. Two charges 3 × 10-8 C and -2 × 10-8 C are located 15 cm apart. At what point on the line joining the two [2]

charges is the electrical potential zero? Take the potential at infinity to be zero.
40. Figure (a) and (b) shows the field lines of a single positive and negative charge respectively: [5]

(a) (b)

a. Give the sign of the potential difference VP - VQ and VB - VA.

b. Give the sign of the potential energy difference of a small negative charge between the points Q and P; A and
B.
c. Give the sign of the work done by the field in moving a small positive charge from point Q to P.
d. Give the sign of the work done by an external agency in moving a small negative charge from point B to A.
e. Does the kinetic energy of a small negative charge increase or decrease in going from point B to A?
41. Four charges are arranged at the corners of a square ABCD of side d, as shown in fig. [5]

a. Find the work required to put together this arrangement.

b. A charge q0 is brought to the center E of the square, the four charges being held fixed at its corners. How
much extra work is needed to do this?

42. a. Determine the electrostatic potential energy of a system consisting of two charges 7 μ C and -2 μ C (and with [3]
no external field) placed at (-9 cm, 0, 0) and (9 cm, 0, 0) respectively.
b. How much work is required to separate the two charges infinitely away from each other?
c. Suppose that the same system of charges is now placed in an external electric field E = A ( ); A = 9 × 105
1

2
r

NC-1 m2. What would the electrostatic energy of the configuration be?

43. A molecule of a substance has permanent electric dipole moment equal to 10-29 Cm. A mole of this substance is [2]

polarized (at low temperature) by applying a strong electrostatic field of magnitude 106 Vm-1. The direction of
the field is suddenly changed by an angle of 60o. Estimate the heat released by the substance in aligning its
dipoles along the new direction of the field. For simplicity, assume 100% polarization of the sample.
44. a. A comb runs through one’s dry hair attracts small bits of paper. Why? What happens if the hair is wet or if it [2]
is a rainy day? (Remember, a paper does not conduct electricity.)
b. Ordinary rubber is an insulator. But special rubber tyres of aircraft are made slightly conducting. Why is this
necessary?

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 c. Vehicles carrying inflammable materials usually have metallic ropes touching the ground during motion.
Why?
d. A bird perches on a bare high power line, and nothing happens to the bird. A man standing on the ground
touches the same line and gets a fatal shock. Why?
45. A slab of material of dielectric constant K has the same area as the plates of a parallel-plate capacitor but has a [2]
thickness ( )d, where d is the separation of the plates. How is the capacitance changed when the slab is inserted
3

between the plates?

46. A network of four 10 μ F capacitors is connected to a 500 V supply, as shown in fig. Determine [3]

a. the equivalent capacitance of the network and

b. the charge on each capacitor.
(Note, the charge on a capacitor is the charge on the plate with higher potential, equal and opposite to the
charge on the plate with lower potential.)

47. a. A 900 pF capacitor is charged by 100 V battery [in a fig]. How much electrostatic energy is stored by the [3]
capacitor?

b. The capacitor is disconnected from the battery and connected to another 900 pF capacitor [in a fig]. What is
the electrostatic energy stored by the system?

48. Two charges 5 × 10-8 C and -3 × 10-8 C are located 16 cm apart. At what point (s) on the line joining the two [2]

charges is the electrical potential zero? Take the potential at infinity to be zero.
49. Two charges 2μC and −2μC are placed at points A and B, 6 cm apart. [2]
a. Identify an equipotential surface of the system.
b. What is the direction of electric field at every point on this surface?
50. A regular hexagon of side 10 cm has a charge 5μC at each of its vertices. Calculate the potential at the centre of [2]
the hexagon.
51. A spherical conductor of radius 12 cm has a charge of 1.6 × 10 −7
C distributed uniformly on its surface. [3]

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 What is the electric field
a. inside the sphere?
b. just outside the sphere?
c. at a point 18 cm from the centre of the sphere?

52. A parallel plate capacitor with air between the plates has a capacitance of 8pF (1pF = 10-12F). What will be the [1]

capacitance if the distance between the plates is reduced by half, and the space between them is filled with a
substance of dielectric constant 6?
53. Three capacitors of capacitances 2 pF, 3 pF and 4 pF are connected in parallel. [2]
a. What is the total capacitance of the combination?
b. Determine the charge on each capacitor if the combination is connected to a 100 V supply.
54. Three capacitors each of capacitance 9 pF are connected in series. [3]
a. What is the total capacitance of the combination?
b. What is the potential difference across each capacitor if the combination is connected to a 120 V supply?
55. In a parallel plate capacitor with air between the plates, each plate has an area of 6 × 10 −3 2
m and the distance [1]
between the plates is 3 mm. Calculate the capacitance of the capacitor. If this capacitor is connected to a 100 V
supply, what is the charge on each plate of the capacitor?
56. Explain what would happen if in the capacitor of 17.7 pF, a 3 mm thick mica sheet of electric constant = 6 were [2]
inserted between the plates
a. while the voltage supply remained connected.
b. after the supply was disconnected.
57. A 12 pF capacitor is connected to a 50 V battery. How much electrostatic energy is stored in the capacitor? [1]
58. A 600 pF capacitor is charged by a 200 V supply. It is then disconnected from the supply and is connected to [3]
another uncharged 600 pF capacitor. How much electrostatic energy is lost in the process?
Section C
[5]
59. a. Estimate the average drift speed of conduction electrons in a copper wire of cross-sectional area 1.0 × 10–7
m2 carrying a current of 1.5 A. Assume that each copper atom contributes roughly one conduction electron.

The density of copper is 9.0 × 103 kg/m3, and its atomic mass is 63.5 u.
b. Compare the drift speed obtained above with,
i. thermal speeds of copper atoms at ordinary temperatures,
ii. speed of propagation of electric field along the conductor which causes the drift motion.
[5]
60. a. In Example 3.1, the electron drift speed is estimated to be only a few mm s–1 for currents in the range of a
few amperes? How then is current established almost instant a circuit is closed?
b. The electron drift arises due to the force experienced by electrons in the electric field inside the conductor.
But force should cause acceleration. Why then do the electrons acquire a steady average drift speed?
c. If the electron drift speed is so small, and the electron’s charge is small, how can we still obtain large
amounts of current in a conductor?
d. When electrons drift in metal from lower to higher potential, does it mean that all the free electrons of the
metal are moving in the same direction?
e. Are the paths of electrons straight lines between successive collisions (with the positive ions of the metal) in
the

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 i. absence of electric field,
ii. presence of electric field?
61. An electric toaster uses nichrome for its heating element. When a negligibly small current passes through it, its [2]
resistance at room temperature (27.0 °C) is found to be 75.3 Ω . When the toaster is connected to a 230 V supply,
the current settles, after a few seconds, to a steady value of 2.68 A. What is the steady temperature of the
nichrome element? The temperature coefficient of resistance of nichrome averaged over the temperature range

involved, is 1.70 × 10–4 °C–1.

62. The resistance of the platinum wire of a platinum resistance thermometer at the ice point is 5 Ω and at the steam [2]
point is 5.23 Ω . When the thermometer is inserted in a hot bath, the resistance of the platinum wire is 5.795 Ω .
Calculate the temperature of the bath.
63. A battery of 10 V and negligible internal resistance is connected across the diagonally opposite corners of a [3]
cubical network consisting of 12 resistors each of resistance 1 Ω (Fig.). Determine the equivalent resistance of
the network and the current along each edge of the cube.

64. Determine the current in each branch of the network shown in Fig. [3]

65. The four arms of a Wheatstone bridge (Fig.) have the following resistances: [3]
AB = 100Ω , BC = 10Ω , CD = 5Ω , and DA = 60Ω .

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 A galvanometer of 15Ω resistance is connected across BD. Calculate the current through the galvanometer when
a potential difference of 10 V is maintained across AC.
66. The storage battery of a car has an emf of 12 V. If the internal resistance of the battery is 0.4Ω , what is the [1]
maximum current that can be drawn from the battery?
67. A battery of emf 10 V and internal resistance 3Ω is connected to a resistor. If the current in the circuit is 0.5 A, [1]
what is the resistance of the resistor? What is the terminal voltage of the battery when the circuit is closed?
68. At room temperature (27.0°C) the resistance of a heating element is 100Ω. What is the temperature of the [1]
element if the resistance is found to be 117Ω. Given that the temperature co-efficient of the material of the
resistor is 1.70 × 10 −4 ∘
C
−1
.
69. A silver wire has a resistance of 2.1Ω at 27.5°C and a resistance of 2.7Ω at 100°C. Determine the temperature [1]
co-efficient of resistivity of silver.
70. A heating element using nichrome connected to a 230 V supply draws an initial current of 3.2 A which settles [1]
after a few seconds to a steady value of 2.8 A. What is the steady temperature of the heating element if the room
temperature is 27.0°C? Temperature co-efficient of resistance of nichrome averaged over the temperature range
involved is 1.70 × 10 −4 ∘
C
−1
.
71. A negligibly small current is passed through a wire of length 15 m and uniform cross section 6.0 × 10 −7
m
2
, [1]
and its resistance is measured to be 5.0Ω . What is the resistivity of the material at the temperature of the
experiment?
72. Determine the current in each branch of the network shown in figure. [5]

73. A storage battery of emf 8.0 V and internal resistance 0.5 Ω is being charged by a 120 V dc supply using a series [3]
resistor of 15.5 Ω . What is the terminal voltage of the battery during charging? What is the purpose of having a
series resistor in the charging circuit?
74. The number density of free electrons in a copper conductor is 8.5 × 1028 m-3 . How long does an electron take [1]

to drift from one end of a wire 3.0 m long to its other end? The area of cross section of the wire is 2.0 × 10-6 m2
and it is carrying a current of 3.0 A.

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