STD: XII PSBB SR. SEC. SCHOOL K.K.

NAGAR, CH-78 (2025 – 2026)

PHYSICS HOLIDAY HOMEWORK

2526XIIWS1.1 (ELECTRIC CHARGES AND FIELDS)
MCQs
1. A wire bent into a ring of radius R is given a charge q. The magnitude of the electrical field at the
centre of the ring is:
a) 1/2 b) zero c) 2 d) ∞
2. Consider a uniform electric field 𝐸⃗ = 3 × 10 𝑖̂ N/C. What is the flux of this field through a square of
3

10 cm on a side whose plane is parallel to the y-z plane?

a) 30 Nm2/C b) 20 Nm2/C c) 40 Nm 2/C d) 25 Nm2/C
3. Two charges A = - 25 μC and B = 36 μC are at a distance of 1 m from each other. Distance from A
on the line joining the two chargers where the electric field is zero is
a) 5 m away from B b) 5 / 11 m away from B c) 5 m towards B. d) 5 / 11 m towards B
4. A charge Q is placed at the mouth of a conical flask. The flux of the electric field through the flask is
a) Q / 𝜺o b) zero c) Q / 2𝜺o d) Q2/ 2𝜺o
5. A charged oil drop is suspended in uniform field of 3 ×104 N/C so that it neither falls nor rises. The
charge on the drop will be: (take the mass of the charge 9.9 × 10-15 kg and g =10 ms-2)
a) 3.3 × 10−18 C b) 4.8 × 10−18 C c) 1.6 × 10−18 C d) 4.3 × 10−18 C
6. A metallic solid sphere is placed in a uniform electric field. In the
figure, which path will the field lines follow?

a) 2 b) 1 c) 3 d) 4
7. Hollow spherical conductor with a charge of 500 C is acted upon by a force 562.5 N. What is E
at its surface?
a) zero b) 4.5 × 10−4 N/C c) 1.125 N/ C d) 2.25 × 10−6 N/C
8. A force of repulsion between two-point charges is F when these are at a distance 0.1 m apart. Now
the point charges are replaced by conducting spheres of radii 5 cm each having the same charge as
that of the respective point charges. The distance between their centres is again kept 0.1 m, then the
force of repulsion will:
a) remain F b) decrease c) increase d) become 10 F / 9
9. If electric field in a region is radially outward with magnitude E = Ar, the charge contained in a
sphere of radius r centred at the origin is:
a) 4πε0Ar3 b) 4πε0A / r3 c) A / 4πε0r3 d) Ar3 / 4πε0
10. The electric flux emerging out from 1 C charge is
a) 4π / ε0 b) 4π c) 1 / ε0 d) ε0
11. A conducting sphere of radius 10 cm is charged with 10 μC. Another uncharged sphere of radius
10 cm is allowed to touch it for some time. After that if the spheres are separated, then ratio of surface
density of charges on the sphere A before and after contact with B will be
a) 1 : 1 b) 2 : 1 c) 1 : 3 d) 1 : 2
12. Five charges, each equal to +q, are placed at the corners of a regular hexagon of side a. The electric
field at the point of intersection of diagonals is
a) √3q / 4πε0A 2a2 b) zero c) 6q / 4πε0a2 d) q / 4πε0a2
13. The unit of permittivity of free space (∈0) is
a) C N-1 m-1 b) N m2 C-2 c) C2 N-2 m-2 d) C2 N-1 m-2
14. A pendulum bob of mass m carrying a charge q is at rest with its string making an angle with the
vertical in a uniform horizontal electric field E. The tension in the string is
a) qE / cos𝜃 b) mg c) qE / sin𝜃 d) mg / sin𝜃
15. A particle of mass m and charge q is released from rest in a uniform electric field E. The kinetic
energy attained by the particle after moving a distance x is
a) q2Ex b) qEx2 c) qEx d) qE2xv
16. The electric flux through the surface
a) In fig(iv) is the largest
b) In fig (iii) us the least
c) In fig (ii) us same as fig(iii)
but is smaller than fig (iv)
d) Is the same for all the figures

17. Figure shows electric field lines in

which an electric dipole P is
placed as shown. Which of the following statements is correct?
a) The dipole will not experience any force
b) The dipole will experience a force towards right
c) The dipole will experience a force towards left
d) The dipole will experience a force upwards
18. Dielectric constant of a metal is
a) 1 b) 0 c) −1 d) ∞
19. An electric dipole is placed in a uniform electric field. The net electric force on the dipole
a) Can never be zero
b) Is always zero
c) Depends on the orientation of the dipole
d) Depends on the strength of the dipole
20. Two point charges Q and − 2Q are placed some distance apart. If the electric field at the location
of Q is E, then the electric field at the location of − 2Q will be
a) E/2 b) − 3E/2 c) − E d) − 2E
21. If Ea be the electric field at an axial point of a dipole and E e be the electric field at an equatorial
point of the same dipole, the relation between Ea and Ee is
a) Ea = Ee b) Ea = −2Ee c) Ea = −Ee /2 d) Ea = 2Ee
22. A charged ball B hangs from a silk thread S, which makes an angle  with
a large charged conducting sheet P, as shown in the figure. The surface
charge density  of the sheet is proportional to
a) tan
b) sin
c) cot
d) cos
23. Two identical metal balls with charges +2Q and -Q are separated by some distance, and exert a
force F on each other. They are joined by a conducting wire, which is then removed. The force
between them will now be
a) F b) F/2 c) F/4 d) F/8
24. Dimensional formula of permittivity of vacuum is
a) [M-1 L -3 T2 A] b) [M-1 L -3 T4A2] c) [M-1 L 3 T-1 A-2] d) [M-1 L 3 T-1 A]
25. The inward and outward electric flux from a closed surface are respectively 8  103 and 4  103
S.I. units. Then the net charge inside the closed surface is
a) − 4  103 C b) 4  103 C c) − 4/0  103 C d) − 40  103 C
26. Two charged particles P and Q, having the same charge but different masses mP and mQ, start from
rest and travel equal distances in a uniform electric field 𝐸⃗ in time tP and tQ respectively. Neglecting
the effect of gravity, the ratio tP / tQ is:
a) mP / mQ b) mQ / mP c) (mP / mQ)1/2 d) (mQ / mP)1/2
27. Two charges 2 C and 6 C are separated by a finite distance. If a charge of − 4 C is added to each of
them, the initial force of 12 ×103 N will change to
a) 4 × 103 N repulsion b) 4 ×102 N repulsion c) 6 × 103 N attraction d) 4 ×103 N attraction
28. Three identical charges of magnitude 2 μ C are placed at the corners of a right-angled triangle ABC
whose base BC and height BA are respectively 4 cm and 3 cm. Forces on the charge at the right-
angled corner B due to the charges at A and C are respectively F1 and F2. The angle between their
resultant force and F2 is
a) tan-1 (9 / 16) b) tan-1 (16 / 9) c) sin-1 (16 / 9) d) cos-1 (16 / 9)

Answer the following questions:

29. Two-point charges having equal magnitudes separated by 1m distance experience a force of 8N.
What will be the force experienced by them, if they are held in water, at the same distance?
(Given: r of water = 80)
30. Find the ratio of the electric and gravitational forces between two protons separated by the same
distance in air.
31. Two charges q and 4q are placed a distance r apart. A third charge qo is placed at a point between
them on the line joining them so that the three charges are in equilibrium. What should be (a)
position (b) magnitude and (c) the sign of the charge q 0.
32. Four particles, each having a charge q are placed on the vertices of a regular pentagon. The
distance of each corner from the centre is ‘a’. Determine the electric field at the centre of the
pentagon.
33. Four equal point charges 16 𝜇𝐶 are placed on the four corners of a square of each side 0.2 m.
Calculate the force on any one of the charges.
34. A proton and an alpha particle enter into a region of uniform electric field. What is the ratio of the
force on the proton to that on the alpha particle?
35. A free proton and a free electron are placed in a uniform electric field. Who will experience a
greater acceleration? Why?
36. Two charges of magnitudes − 2Q and +Q are located at points (a, 0) and (4a, 0) respectively. What
is the electric flux due to these charges through a sphere of radius 3a with its centre at the origin?
37. Consider two hollow concentric spheres, S1 and S2, enclosing charges
2Q and 4Q respectively as shown.
(i) Find out the ratio of the electric flux through them.
(ii) How will the electric flux through the sphere S1 change, if a
medium of dielectric constant r is introduced in the space
inside S1 in place of air?
38. Two small conducting spheres of equal radii have charges 10 C and – 20 C respectively and
placed at a distance R from each other experience force F 1. If they are brought in contact and
separated to the same distance, they experience force F2. Find the ratio of F1 and F2.
39. Two long straight parallel wires carry charges 𝜆1 and 𝜆2 per unit length. The separation between
their axes is d. Find the magnitude of the force exerted on unit length of one due to the charge on
the other.
40. An electric dipole consists of charges ± 2 × 10-8 C, separated by a distance of 2 mm. It is placed
near a long line charge of density 4 × 10-4 Cm-1, its axis perpendicular to the line charge, such that
the negative charge is at a distance of 2 cm from the line charge and positive charge further away
from the wire. Calculate the force acting on the dipole.
41. An electron is revolving around a long line charge having charge density 2 × 10-8 Cm-1. Find the
kinetic energy of the electron, assuming that it is independent of the radius of the electron’s orbit.
42. 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.
43. Two identical electric dipoles are placed along the diagonals of a square
ABCD of side √2 m as shown in the adjacent figure. Obtain the
magnitude and direction of the net electric field at the centre (O) of the
square.
44. In Bohr-Rutherford model, the hydrogen atom consists of a proton
around which an electron is revolving. If the radius of the atom is 5.3 ×
10-11 m, calculate the centripetal force and orbital speed of the
electron.
45. Two infinitely long straight wires 1 and 2 having linear charge densities 𝜆1 = 10 𝜇𝐶/𝑚 and 𝜆2 =
−20 𝜇𝐶/𝑚 respectively are kept parallel along x-axis separated by 30 cm. Find the net force
experienced by an electron held at a point P which is 10 cm below wire 1 and 20 cm above wire
2.
46. Draw graphs for the following cases:
a) Field due to an infinitely long uniformly charged wire v/s distance
b) Field due to an infinite uniformly charged plane v/s distance
c) Field due to a uniformly charged shell v/s distance
47. Draw graphs for the following cases:
a) Coulomb force(F) between two charges and distance of separation (r)
b) Coulomb force(F) between two charges and inverse of distance of separation (1/r)
c) Electric field due to a point charge and distance
d) Dipole field and distance (both axial and equatorial)
e) Torque on a dipole (𝜏) and angle of its orientation in a uniform electric field (𝜃)