KENDRIYA VIDYALAYA NO1, GAYA

SUMMER VACATION HOME WORK

Instructions :
1. Holiday Home Work should be neat and clean and to be done in Separate Copy.
2. Use pencil for figures and diagram.
3. 1-15 Questions --- First Week of Vacation
16-30 Questions--- Second Week of Vacation
30-45 Questions – Third Weak of Vacation
46-60 Questions – Fourth Weak of Vacation
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1. Which orientation of an electric dipole in a uniform electric field would correspond to stable
equilibrium?
2. If the radius of the Gaussian surface enclosing a charge is halved, how does the electric flux
through the Gaussian surface change ?
3. Define the term electric dipole moment of a dipole. State its S.I. unit
4. Figure shows three point charges, +2q, -q and + 3q. Two charges +2q and -q are enclosed within a
surface ‘S’. What is the electric flux due to this configuration through the surface ‘S’ (Delhi 2010)

5. Why should electrostatic field be zero inside a conductor? (Delhi 2012)

6. A charge ‘q’ is placed at the centre of a cube of side l. What is the electric flux passing through
each face of the cube? (All India 2012)
7. Two charges of magnitudes -3Q and + 2Q are located at points (a, 0) and (4a, 0) respectively.
What is the electric flux due to these charges through a sphere of radius ‘5a’ with its centre at the
origin?
8. Draw a plot showing variation of electric field with distance from the centre of a solid conducting
sphere of radius R, having a charge of +Q on its surface.
9. Derive an expression for the torque experienced by an electric dipole kept in a uniform electric
field. (Delhi 2017)
10. Show that the electric field at the surface of a charged conductor is given by E→=(σ/ε0 ) n^,
where σ is the surface charge density and h is a unit vector normal to the surface in the outward
direction. (All India 2010)
11. A thin straight infinitely long conducting wire having charge density X is enclosed by a
cylindrical surface of radius r and length l, its axis coinciding with the length of the wire. Find the
expression for the electric flux through the surface of the cylinder. (All India 2011)
12. Plot a graph showing the variation of coulomb force (F) versus (1/R2), where r is the distance
between the two charges of each pair of charges : (1µC, 2µC) and (2µC, – 3µC). Interpret the
graphs obtained. (All India 2010)
13. A hollow cylindrical box of length 1m and area of cross-section 25 cm2 is placed in a three
dimensional coordinate system as shown in the figure. The electric field in the region is given
by E→=50xi^ where E is in NC-1 and x is in metres. Find
A.Net flux through the cylinder.
B.Charge enclosed by the cylinder. (Delhi 2013)

DR. P K Sinha, PGT (Physics). PM SHRI K V NO.1 GAYA 1

 14. Two charged spherical conductors of radii R1 and R2 when connected by a conducting wire
acquire charges q1 and q2 respectively. Find the ratio of their surface charge densities in terms of
their radii. (Delhi 2014)
15. A charge is distributed uniformly over a ring of radius ‘a’. Obtain an expression for the electric
intensity E at a point on the axis of the ring. Hence show that for points at large distances from
the ring, it behaves like a point charge. (Delhi 2016)
16. Draw the pattern of electric field lines, when a point charge –Q is kept near an uncharged
conducting plate. (CBSE Delhi 2019)
17. In the figure given below, at which point electric field is maximum?

18. What will be the total flux through the faces of the cube (figure) with the side of length ‘a’ if a
charge q is placed at
(a) A: a corner of the cube. (b) B: mid-point of an edge of the cube.
(c) C: center of the face of the cube.(d) D: mid-point of B and C. {NCERT Exemplar)

19. State Gauss’s law in electrostatics. Derive an expression for the electric field due to an infinitely
long straight uniformly charged wire
20. (a) Define electric flux. Write its S.I. units.
(b) Using Gauss’s law, prove that the electric field at a point due to a uniformly charged infinite
plane sheet is independent of the distance from it.
(c) How is the field directed if
(i) the sheet is positively charged,
(ii) negatively charged? (Delhi 2012)
21. Draw the equipotential surfaces due to an isolated point charge. (CBSE Delhi 2019)‘For any
charge configuration, equipotential surface through a point is normal to the electric field’. Justify.
(CBSE Delhi 2014)
22. Why is the electrostatic potential inside a charged conducting shell constant throughout the
volume of the conductor? (CBSE AI 2019)
23. Does the charge given to a metallic sphere depend on whether it is hollow or solid? (CBSE Delhi
2017)
24. Draw a plot showing the variation of (i) electric field (E) and (ii) electric potential (V) with
distance r due to a point charge Q. (CBSE Delhi 2012)
25. Two identical capacitors of 10 pF each are connected in turn (i) in series and (ii) in parallel across
a 20 V battery. Calculate the potential difference across each capacitor in the first case and the
charge acquired by each capacitor in the second case. (CBSE AI 2019)
26. A test charge ‘q’ is moved without acceleration from A to C along the path from A to B and then
from B to C in electric field E as shown in the figure, (i) Calculate the potential difference

DR. P K Sinha, PGT (Physics). PM SHRI K V NO.1 GAYA 2

 between A and C, (ii) At which point (of the two) is the electric potential more and why? (CBSE

AI 2012)
27. Four-point charges Q, q, Q., and q are placed at the corners of a square of side ‘a’ as shown in the
figure. Find the potential energy of this system. (CBSEAI, Delhi 2018)

28. (a) Obtain the expressions for the resultant capacitance when the three capacitors C1, C2, and
C3 are connected (i) in parallel and then (ii) in series (b) Draw the equipotential surfaces
corresponding to a uniform electric field in the z-direction. (ii) Derive an expression for the
electric potential at any point along the axial line of an electric dipole. (CBSE Delhi 2019)
29. A charge Q is distributed over the surfaces of two concentric hollow spheres of radii r and R (R
>> r), such that their surface charge densities are equal. Derive the expression for the potential at
the common center.
30. Three concentric metallic shells A, B, and C of radii a, b, and c (a <b < C) have surface charge
densities +a, -a, and + o respectively as shown. Obtain the expressions for the potential of three
shells A, B, and C. If shells A and C are at the same potential, obtain the relation between a, b
and c. (CBSE Al 2019)

31. Electric field intensity at point B due to a point charge Q kept at point A is 24 N C -1 and the
electric potential at point B due – to the same charge is 12 J C-1. Calculate the distance AB and
also the magnitude of the charge Q
32. Two identical capacitors of 12 pF each are connected in series across a 50 V battery. Calculate the
electrostatic energy stored in the combination. If these were connected in parallel across the same
battery, find out the value of the energy stored in this combination. (CBSE Al 2019)

DR. P K Sinha, PGT (Physics). PM SHRI K V NO.1 GAYA 3

 33. (a) Find equivalent capacitance between A and B in the combination given below.Each capacitor

is of 2 μF capacitance.
(b) If a DC source of 7 V is connected across AB, how much charge is drawn from the source and
what is the energy stored in the network? (CBSE Delhi 2017)
34. Derive an expression for the potential energy of an electric dipole of dipole movement p⃗ in the
electric field E(Delhi 2008)
35. Estimate the total number of electrons present in 100g of water. How much is the total negative
charge carried by these electrons? Avogadro’s number = 6.023×10 23 and molecular mass of water
= 18u.
(Ans = 5.35×106 C)
36. It is now believe that protons and neutrons are themselves built out of more elementary units
called quarks. A proton and neutrons consists of three quarks each. Two types of quarks, the so
called up quarks (u) of charge (+2/3) e and down quarks (d) of charge (-1/3) e, together with
electrons build up ordinary matter. Suggest a possible quark composition of a proton and
neutron.
(Ans= uud, udd)
37. A free pith ball A of 8g carries a positive charge of 5×10-8C. What must be the nature and
magnitude of charge that should be given to a second pith ball B fixed 5cm below the former ball
so that the upper ball is stationary. (Ans= 4.36×10-7, repulsive)

38. A particle of mass m and carrying charge –q1 is moving around a charge +q2 along a circular
path of radius r. Prove that the period of revolution of the charge –q1 about +q2 is given by

T= √(16r3 ε0mπ3 )
q1 q2
39. Two identical charges, Q each are kept at a distance r from each other. A third charge q is placed
on the line joining above two charges such that all the three charges are in equilibrium. What is
the magnitude, sign and position of the charge q?
( Ans : Q=q4, opposite, x=r/2 )
40. Define the term electric dipole moment.
41. Sketch the electric field lines due to two equal positive charges placed near each other.
42. Give the units of i) line integral of electric field and ii) surface integral of electric field.
43. What would be the work done if a point charge +q, is taken from a point A to B on the
circumference of a circle drawn with another point charge +q at the centre.
44. An uncharged insulated conductor A is brought near a charged insulated conductor B. What
happens to charge and potential of B?
45. Why does the electric field inside a dielectric decrease when it is placed in an external field?
46. In a parallel plate capacitor, the capacitance increases from 4µf to 80µf, on introducing a
dielectric medium between the plates. What is the dielectric constant of the medium?
47. Derive an expression for the electric field intensity at any point along the axial line of an electric
dipole.
48. Two point electric charges of unknown magnitude and sign are placed a distance ‘d’ apart. The
electric field intensity is zero at a point, not between the charges but on the line joining them.
Write two essential conditions for this to happen.
49. Derive an expression for the energy stored in a parallel plate capacitor with air as the medium
between its plates.
50. Find the ratio of linear momenta acquired by a α-particle and a proton accelerated through the
same potential.

DR. P K Sinha, PGT (Physics). PM SHRI K V NO.1 GAYA 4

 51. Using Gauss’s law, show that no electric field intensity exists inside a hollow charged conductor.
52. An electric dipole is free to move in a uniform electric field. Explain its motion when it is placed i)
parallel to the field and ii) perpendicular to the field.
53. Calculate the distance between two protons such that the electrostatics repulsive force between
them is equal to the weight of either.
54. Two point charges q and 2q are kept at a distance d apart from each other in air. A third charge
Q is to be kept along the same line in such a way that the net force on q and 2q is zero. Calculate
the position of Q in terms of q and d.
55. An electric flux of -6 x 10³ NM²/C passes normally through a spherical Gaussian surface radius
10cm, due to point charge placed at the centre. What is the charge enclosed by the Gaussian
surface? If the radius of Gaussian surface is doubled, how much flux would pass through the
surface?
56. Is electric flux a scalar or vector quantity? Give its SI units.
57. (i) A charge of 2micro coulomb is placed at the center of a sphere of radius 1m. What is the
electric flux passing through sphere if another charge of -2microcoulomb is placed at a distance
of (a) 0.5m (b) 1.5m from its center.
58. Two equal charges each of -√2µC are placed 2m apart and a third charge 2√2µC is placed at
mid point of line joining them. Calculate total electric field intensity at a distance of 1m from
third charge on perpendicular bisector of the line joining the charges.
59. An electric dipole is held in a uniform electric field.
(a) Show that no translatory force acts on it.
(b) Derive an expression for the torque acting on it.
60. (i) Consider three metal spherical shells A, B and C, each of radius R. Each shell is having a
concentric metal ball of radius R/10. The spherical shells A, B and C are given charges +6q, -4q,
and 14q respectively. Their inner metal balls are also given charges -2q, +8q and-10q respectively.
Compare the magnitude of the electric fields due to shells A, B and C at a distance 3R from their
centres.
(ii) A charge -6 μC is placed at the centre B of a semicircle of radius 5 cm, as shown in
the figure. An equal and opposite charge is placed at point D at a distance of 10 cm from
B. A charge +5 µC is moved from point C to point 'A' along the circumference. Calculate
the work done on the charge.

Date of Submission –21/07/2025

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DR. P K Sinha, PGT (Physics). PM SHRI K V NO.1 GAYA 5