ELECTROSTATICS 1 & 2

Subject: PHYSICS (042) Max. Marks: 70

Time: 3 hours
General Instructions:
• There are 33 questions in all. All questions are compulsory.
• This question paper has five sections: Section A, Section B, Section C,
Section D and Section E. All sections are compulsory.
• Section A has sixteen questions, twelve MCQ and four assertion reasoning
questions of 1 mark each.
• Section B has five questions of 2 marks each.
• Section C has seven questions of 3 marks each.
• Section D has two case study-based questions of 4 marks each.
• Section E has three long answer questions of 5 marks each.
• There is no overall choice. However internal choice is provided in sections
B, C, D and E. You have to attempt only one of the choices in such
questions.
• Use of calculators is not allowed.

SECTION A

1. An electric dipole having dipole moment 𝑝⃑ = 𝑝0 𝑖̂ − 𝑝0 𝑗̂ is placed in an electric field 1

𝐸⃑⃑ = 𝐸1 𝑖̂ + 𝐸2 𝑗̂, where 𝑝0 , 𝐸1 and 𝐸2 are constants. The torque acting on the dipole
is
(a) 𝑝0 (𝐸2 − 𝐸1 )𝑘̂ (b) 𝑝0 (𝐸2 + 𝐸1 )𝑘̂ (c) −𝑝0 (𝐸2 + 𝐸1 )𝑘̂ (d) 𝑝0 (𝐸1 − 𝐸2 )𝑘̂

2. When a negative charge (-Q) is brought near one face of a metal cube, the 1
(a) cube becomes positively charged
(b) cube becomes negatively charged
(c) face near the charge becomes positively charged and the opposite face
becomes negatively charged
(d) face near the charge becoes negatively charged and the opposite face
becomes positively charged.

3. A point charge q is kept at a distance r from an infinitely long straight wire with 1
charge density λ. The magnitude of the electrostatic force experienced by charge q
is:
𝑞𝜆 𝑞𝜆 𝑞𝜆
(a) zero (b) 2𝜋𝜀 (c) 4𝜋𝜀 (d) 𝜀
0𝑟 0𝑟 0𝑟

4. Two charges 𝑞1 and 𝑞2 are placed at the centres of two spherical conducting shells 1
of radius 𝑟1 and 𝑟2 respectively. The shells are arranged such that their centres are
d [ > (𝑟1 + 𝑟2 )] distance apart. The force on 𝑞2 due to 𝑞1 is :
1 𝑞 𝑞 1 𝑞1 𝑞2 1 𝑞 𝑞2
(a) 4𝜋𝜀 𝑑1 22 (b) 4𝜋𝜀 (𝑑−𝑟 (c) zero (d) 4𝜋𝜀 [𝑑−(𝑟1 +𝑟
0 0 1)2 0 1 ]2
2
5. An electron experiences a force (1.6 x 10-16 N ) 𝑖̂ in an electric field 𝐸⃑⃑ . The electric 1
field 𝐸⃑⃑ is :
(a) (1.0 x 103 N/C) 𝑖̂ (b) - (1.0 x 103 N/C) 𝑖̂
(c) (1.0 x 10-3 N/C) 𝑖̂ (d) - (1.0 x 10-3 N/C) 𝑖̂

6. An electric dipole of dipole moment 2 x 10 -8 Cm in a uniform electric field 1

experiences a maximum torque of 6 x 10-4 Nm. The magnitude of electric field is :
(a) 2.2 x 103 V/m (b) 1.2 x 104 V/m (c) 3 x 104 V/m (d) 4.2 x 103 V/m

7. A point charge 𝑞0 is moving along a circular path of radius a, with a point charge - 1
Q at the centre of the circle. The kinetic energy of 𝑞0 is:
𝑞 𝑄 𝑞 𝑄 𝑞 𝑄 𝑞 𝑄
(a) 4𝜋𝜀0 𝑎 (b) 8𝜋𝜀0 𝑎 (c) 4𝜋𝜀0 𝑎2 (d) 8𝜋𝜀0 𝑎2
0 0 0 0

8. An isolated point charge particle produces an electric field 𝐸⃑⃑ at a point 3m away 1
𝐸⃑⃑
from it. The distance of the point at which the field is 4 will be
(a) 2 m (b) 3 m (c) 4 m (d) 6 m

9. The magnitude of the electric field due to a point charge object at a distance of 4.0 1
m is 9 N/C. From the same charged object the electric field of magnitude, 16 N/C
will be at a distance of
(a) 1 m (b) 2 m (c) 3 m (d) 6 m

10. A point P lies at a distance x from the mid point of an electric dipole on its axis. The 1
electric potential at point P is proportional to
1 1 1 1
(a) 𝑥2 (b) 𝑥3 (c) 𝑥4 (d) 𝑥1/2

11. A point charge situated at a distnace r from a short electric dipole on its axis 1
experiences a force 𝐹⃑ . If the distance of the charge is 2r, the force ion the charge will
be :
𝐹⃑ 𝐹⃑ 𝐹⃑ 𝐹⃑
(a) 16
(b) 8 (c) 4 (d) 2

12. A metal sphere A of radius 𝑟1 charged to a potential 𝜑1 is enveloped by a thin 1

walled conducting spherical shell B of radius 𝑟2 . Then potential 𝜑2 of the sphere A
after it is connected to the shell B by a thin conducting wire will be

𝑟 𝑟 𝑟2 𝑟 𝑟
𝜑1 𝑟1 (b) 𝜑1 𝑟2 (c) 𝜑1 (1 − ) (d) 𝜑1 (𝑟 1+𝑟2 )
2 1 𝑟1 1 2

For question numbers 13, 14, 15 and 16, two statements are given, one labelled
Assertion (A) and the other labelled Reason (R). Select the correct answer to these
questions from the codes (a), (b), (c) and (d) as given below.
(A) Both A and R are true and R is the correct explanation of A
 (B) Both A and R are true and R is NOT the correct explanation of A
(C) A is true but R is false
(D)Both A and R are false

13. Assertion (A): A parallel plate capacitor is connected across a battery through a 1
key. A dielectric slab of dielectric constant K is introduced between the plates. The
energy, which is stored, becomes K times.
Reason (R): The surface charge density of charge on the plate remains
unchanged.

14. Assertion (A) The equipotential surfaces corresponding to a constant electric field 1
along X direction are equidistant planes parallel to YZ plane
Reason (R): Electric field is normal to every point on an equipotential surface.

15. Assertion (A): Work done in moving a charge around a closed path, in an electric 1
field is always zero.
Reason (R): Electrostatic force is a conservative force.

16. Assertion (A): When the electric flux through a closed surface is zero, then electric 1
field at every point of the gaussian surface must be zero.
Reason (R): When the net charge inside a closed surface is zero then electric field
at every point of the gaussian surface must be zero.

SECTION B

𝑁
17. A uniform electric field is represented as 𝐸⃑⃑ = (3 × 103 𝐶 )𝑖̂ . Find the electric flux 2
of this field through a square of side 10 cm when the :
(a) plane of the square is parallel to y-z plane, and
(b) the normal to the plane of the square makes an angle of 600 with the X axis.

18. Obtain an expression for electrostatic potential energy of a system of three charges 2
q, 2q and -3q placed at the vertices of an equilateral triangle of side a.

OR

Two small conducting balls A and B of radius 𝑟1 and 𝑟2 have charges 𝑞1 and 𝑞2
respectively. They are connected by a wire. Obtain the expression for charges on A
and B in equilibrium.

19. A uniform electric field E of 500 N/C is directed along +X axis. O, B and A are three 2
points in the field having x and y coordinates (in cm) (0, 0), (4, 0) and (0, 3)
respectively. Calculate the potential difference between the points (i) O and A and
(ii) O and B.

OR

Three point charges 1µC, -1µC and 2µC are kept at the vertices A, B and C
respectively of an equilateral triangle of side 1m. A1, B1 and C1 are the midpoints of
 the sides AB, BC and CA respectively. Calculate the net amount of work done in
displacing the charge from A to A1, from B to B1 and from C to C1.

20. The inward and the outward electric flux through a Gaussian surface are 2φ and φ 2
respectively.
(a) What is the net charge enclosed by the surface?
(b) If the net outward flux through the surface were zero, can it be concluded
that there were no charges inside the surface? Justify your answer.

21. Two identical dipoles are arranged in XY plane as shown in the figure. Find the 2
magnitude and the direction of net electric field at the origin O.

SECTION C

22. Two charged conducting spheres of radii a and b are connected to each other by a
wire. Find the ratio of the electric fields at their surfaces.
3
23. A parallel plate capacitor (A) of capacitance C is charged by a battery to voltage V. 3
The battery is disconnected and an uncharged capacitor (B) of capacitance 2C is
connected across A. Find the ratio of
(i) final charges on a and B.
(ii) total electrostatic energy stored in A and B finally and that stored in A
initially.

24. Three point charges Q1 (-15 µC), Q2 (10 µC) and Q3 (16 µC) are located at (0 cm, 0 3
cm), (0 cm, 3 cm) and (4 cm, 3 cm) respectively. Calculate the electroststic potential
energy of this system of charges.

25. A 100 µF capacitor is charged by a 12 V battery. 3

(a) How much electrostatic energy is stored by the capacitor?
(b) The capacitor is disconnected from the battery and connected in parallel to
another uncharged 100 µF capacitor. What is the electrostatic energy stored
by the system?
26. (i) Twelve negative charges of same magnitude are equally spaced and fixed on 3
the circumference of a circle of radius R as shown in figure (i). Relative to
potential being zero at infinity, find the electric potential and electric field at the
centre C of the circle.

(ii) If the charges are unequally spaced and fixed on an arc of 1200 of radius R as
shown in figure (ii), find electric potential at the centre C.

27. Two metal spheres A and B of radius r and 2r whose centres are separated by a 3
distance of 6r are given charge Q, are at potential V1 and V2. Find the ratio of V 1/V2.
These spheres are connected to each other with the help of a connecting wire
keeping the separation unchanged, what is the amount of charge that will flow
through the wire?

28. Two charges each of magnitude -q are 2r distance apart. A positive charge q is 3
lying at the middle of them. The potential energy of the system is U 1. If the two
nearest charges are mutually exchanged, the potential energy becomes U 2, then
𝑈
what is the ratio 𝑈1?
2
SECTION D

29.

A parallel plate capacitor is an arrangement of two identical metal plates kept

parallel, a small distance apart. The capacitance of a capacitor depends on the size
and separation of the two plates and also on the dielectric constant of the medium
between the plates. Like resistors, capacitors can also be arranged in series or
 parallel or a combination of both. By virtue of electric field between the plates,
charged capacitors store energy.
(a) The capacitance of a parallel plate capacitor increases from 10 µF to 80 µF on
introducing a dielectric medium between the plates. Find the dielectric
constant of the medium.
(b) n capacitors, each of capacitance C are connected in series. Find the 4
equivalent capacitance of the combination.
(c) A capacitor is charged to a potential V by connecting it to a battery. After
sometime, the battery is disconnected and a dielectric is introduced between
the plates. How will the potential difference between the plates and the
energy stored in it be affected? Justify your answer.
OR
(c) Find the equivalent capacitance between points A and B, if capacitance of
each capacitor is C.

30. Electrostatics deals with the study of forces, fields and potentials arising from static
charges. Force and electric field, due to a point charge is basically determined by
Coulomb’s law. For symmetric charge configurations, Gauss’ law, which is also
based on Coulomb’s law, helps us to find the electric field. A charge/a system of
charges like a dipole experience a force/torque in an electric field. Work is required
to be done to \provide a specific orientation to a dipole with respect to an electric
field.
Answer the following questions based on the above :
(a) Consider a uniformly charged thin conducting shell of radius R. Plot a graph
showing the variation of |𝐸⃑⃑| with distance r from the centre, for points 0 ≤
𝑟 ≤ 3𝑅. 4
(b) The figure shows the variation of potential V with 1/r for two point charges
Q1 and Q2, where V is the potential at a distance r due to a point charge. Find
Q1/Q2.

(c) An electric dipole of dipole moment of 6 x 10-7 Cm is kept in a uniform

electric field of 104 N/C such that the dipole moment and the electric field
are parallel. Calculate the potential energy of the dipole.
 OR
(d) An electric dipole of dipole moment 𝑝⃑ is initially kept in a uniform electric
field 𝐸⃑⃑ such that 𝑝⃑ is perpendicular to 𝐸⃑⃑ . Find the amount of work done in
rotating the dipole to a position at which 𝑝⃑ becomes antiparallel to 𝐸⃑⃑ .

SECTION E

31(a) (i) Define electric flux and write its SI unit.

(ii) Use Gauss’ law to obtain the expression for the electric field due to a
uniformly charged infinite plane sheet.
(iii) A cube of side L is kept in space, as shown in the figure. An electric
𝑁
field 𝐸⃑⃑ = (𝐴𝑥 + 𝐵)𝑖̂ 𝐶 exists in the region. Find the net charge enclosed
by the cube.

OR 5

(b) (i) Define electric potential at a point and write its SI unit.
(ii) Two capacitors are connected in series. Derive an expression of the
equivalent capacitance of the combination.
(iii) Two point charges +q and -q are located at points (3a, 0) and (0, 4a)
respectively in XY plane. A third charge Q is kept at the origin. Find the
value of Q, in terms of q and a, so that the electrostatic potential energy
of the system is zero.

32(a) (i) Use Gauss’ law to obtain an expression for the electric field due to an
infinitely long thin straight wire with uniform linear charge density λ.
(ii) An infinitely long positively charged straight wire has a linear charge
density λ. An electron is revolving in a circle with a constant speed v
such that the wire passes through the centre, and is perpendicular to the
plane of the circle. Find the kinetic energy of the electron in terms of
magnitudes of its charge and linear charge density λ on the wire.
(iii) Draw a graph of kinetic energy as a function of linear charge density λ.

OR 5

(b) (i) Consider two identical point charges located at points (0,0) and (a,0).
(1) Is there a point on the line joining them at which the electric field is
zero?
(2) Is there a point on the line joining them at which the electric
potential is zero?
 Justify your answers for each case.
(ii) State the significance of negative value of electrostatic potential energy
of a system of charges.
(iii) Three charges are placed at the corners of an equilateral triangle ABC of
side 2.0 m as shown in figure. Calculate the electric potential energy of
the system of three charges.

33(a) (i) State Coulomb’s law in electrostatics and write it in vector form for two
charges.
(ii) Gauss’ law is based on the inverse square dependence on distance
contained in the Coulomb’s law. Explain.
(iii) Two charges A (charge q) and B (charge 2q) are located at points (0, 0)
and (a, a) respectively. Let 𝑖̂ and 𝑗̂ be the unit vectors along X axis and Y
axis respectively. Find the force exerted by A on B, in terms of 𝑖̂ and 𝑗̂.

(b) OR 5

(i) Derive an expression for the electric field at a point on the equatorial
plane of an electric dipole consisting of charges q and -q separated by a
distance 2a.
(ii) The distance of a far off point on the equatorial plane of an electric
dipole is halved. How will the electric field be affected for the dipole?
(iii) Two identical electric dipoles are placed along the diagonals of a square
ABCD of side √2 m as shown in the figure. Obtain the magnitude and
direction of the net electric field at the centre (O) of the square.

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