Coulomb's Law of Electrostatics
1. A soap bubble is given a negative charge, then its radius
Correct Answer: b) Increases
When a soap bubble is given a negative charge, the like charges repel each other, causing the bubble to expand and its radius to increase.
2. A charge \( q_1 \) exerts some force on a second charge \( q_2 \). If third charge \( q_3 \) is brought near, the force of \( q_1 \) exerted on \( q_2 \)
Correct Answer: c) Remains unchanged
The force between \( q_1 \) and \( q_2 \) is governed by Coulomb's law and is unaffected by the presence of other charges. The net force on \( q_2 \) may change, but the force due to \( q_1 \) alone remains the same.
3. Two similar spheres having \( +q \) and \( -q \) charge are kept at a certain distance. \( F \) force acts between the two. If in the middle of two spheres, another similar sphere having \( +q \) charge is kept, then it experiences a force in magnitude and direction as
Correct Answer: c) \( 8F \) towards \( -q \) charge
The middle charge experiences attractive force towards \( -q \) and repulsive force from \( +q \). Since it's placed midway, the distance is halved, making the force four times stronger for each interaction. The net force is \( 4F + 4F = 8F \) towards \( -q \).
4. \( F_g \) and \( F_e \) represents gravitational and electrostatic force respectively between electrons situated at a distance 10 cm. The ratio of \( \frac{F_e}{F_g} \) is of the order of
Correct Answer: d) \( 10^{42} \)
The electrostatic force is much stronger than gravitational force for elementary particles. The ratio is approximately \( 10^{42} \) for electrons.
5. The electric field inside a charged spherical conductor is:
Correct Answer: c) Zero
In electrostatic equilibrium, the electric field inside a conductor is always zero. Charges reside only on the surface of the conductor.
6. A total charge \( Q \) is broken in two parts \( q_1 \) and \( q_2 \) and they are placed at a distance \( r \) from each other. The maximum force of repulsion between them will occur, when
Correct Answer: d) \( q_1 = \frac{Q}{2} \)
The force \( F = k\frac{q_1q_2}{r^2} = k\frac{q_1(Q-q_1)}{r^2} \). To maximize \( F \), we set \( \frac{dF}{dq_1} = 0 \), which occurs when \( q_1 = q_2 = Q/2 \).
7. Three charges \( +4q \), \( -q \) and \( +4q \) are in a straight line in the position of 0, \( l \) and \( 2l \) respectively. The resultant force on \( -q \) will be zero, if \( q \) is
Correct Answer: a) -- \( q \)
For equilibrium, the forces from both sides must balance: \( \frac{k(4q)(q)}{l^2} = \frac{k(4q)(q)}{(2l-l)^2} \). This condition is satisfied when the middle charge is negative.
8. The ratio of the forces between two small spheres with constant charge \( q \) in air \( F \) in a medium of dielectric constant \( K \) is
Correct Answer: b) \( K \) : 1
The force in medium \( F_m = F/K \), so the ratio \( F_{air} : F_{medium} = K : 1 \).
9. Gauss's law is most useful for calculating electric fields when there is:
Correct Answer: c) A highly symmetric charge distribution
Gauss's law is particularly useful for cases with spherical, cylindrical, or planar symmetry where we can choose Gaussian surfaces that match the symmetry of the charge distribution.
10. Two charges each of \( 1\mu C \) are at a distance 1m apart, the force between them is
Correct Answer: a) \( 9 \times 10^{-3} N \)
Using Coulomb's law: \( F = \frac{kq_1q_2}{r^2} = \frac{9 \times 10^9 \times 10^{-6} \times 10^{-6}}{1^2} = 9 \times 10^{-3} N \).
11. \( +2\mu C \) and \( +2\mu C \) two charges are repelling each other with a force of 0.4N. If each charge is given \( -2\mu C \) of charge, then the value of the force will be
Correct Answer: d) Zero
After adding \( -2\mu C \) to each, both charges become neutral (0μC), so there's no force between them.
12. Dielectric constant of pure water is 81. Its permittivity will be
Correct Answer: a) \( 7.12 \times 10^{-10} \) units
Permittivity \( \epsilon = K\epsilon_0 = 81 \times 8.85 \times 10^{-12} \approx 7.12 \times 10^{-10} \) C²/N·m².
13. Identify the wrong statement in the following. Coulomb's law correctly describes the electric force that
Correct Answer: b) Binds the protons and neutrons in the nucleus of an atom
Coulomb's law describes electrostatic forces, but nuclear forces (which bind protons and neutrons) are governed by the strong nuclear force, not Coulomb's law.
14. The work done in moving a charge between two points in an equipotential surface is:
Correct Answer: c) Zero
On an equipotential surface, the potential difference between any two points is zero, so no work is done moving a charge between them.
15. \( ABC \) is a right angled triangle in which \( AB = 3 \) cm and \( BC = 4 \) cm. And ∠ \( ABC = \pi/2 \). The three charges \( +15 \times 10^{-9} C \), \( +12 \times 10^{-9} C \) and \( -20 \times 10^{-9} C \) are placed respectively on \( A \), \( B \) and \( C \). The force acting on \( B \) is
Correct Answer: c) \( 3.75 \times 10^{-4} N \)
Calculate forces from A and C separately, then find the resultant using vector addition (Pythagoras theorem).
16. Two small spheres each having the charge \( +Q \) are suspended by insulating threads of length \( L \) from a hook. This arrangement is taken in space where there is no gravitational effect, then the angle between the two suspensions and the tension in each will be
Correct Answer: a) \( 180^\circ \), \( \frac{kQ^2}{(2L)^2} \)
Without gravity, the spheres will repel each other maximally, forming a straight line (180°). The tension balances the Coulomb force at distance \( 2L \).
17. The electric flux through a closed surface depends on:
Correct Answer: a) Only the charges inside the surface
According to Gauss's law, the electric flux through a closed surface depends only on the net charge enclosed by the surface, not on external charges or the surface's shape/size.
18. Force of attraction between two point charges \( +Q \) and \( -Q \) separated by \( r \) is \( F \). When these charges are placed on two identical spheres of radius \( R \) whose centres are \( r \) apart, the force of attraction between them is
Correct Answer: c) Less than \( F \)
When charges are placed on spheres, their effective separation increases (center-to-center distance remains \( r \), but charge distributions may spread), reducing the force.
19. When \( 10^{10} \) electrons are removed from a neutral metal sphere, the charge on the sphere becomes
Correct Answer: a) \( +1.6 \times 10^{-9} C \)
Charge = ne = \( 10^{10} \times 1.6 \times 10^{-19} = 1.6 \times 10^{-9} C \). Removing electrons leaves the sphere positively charged.
20. Two charges \( +q \) and \( +q \) are placed in vacuum at a distance \( d \) and the force acting between them is \( F \). If a medium of dielectric constant 4 is introduced around them, the force now will be
Correct Answer: d) \( F/4 \)
The force in a medium is reduced by the dielectric constant: \( F_m = F/K = F/4 \).
21. The electric potential energy of a system of two point charges is:
Correct Answer: c) Positive for like charges and negative for unlike charges
Like charges repel (positive potential energy), unlike charges attract (negative potential energy).
22. When \( 10^{19} \) electrons are removed from a neutral metal plate, the electric charge on it is
Correct Answer: b) +1.6 C
Charge = ne = \( 10^{19} \times 1.6 \times 10^{-19} = 1.6 C \). Removing electrons leaves positive charge.
23. A glass rod rubbed with silk is used to charge a gold leaf electroscope and the leaves are observed to diverge. The electroscope thus charged is exposed to X-rays for a short period. Then
Correct Answer: b) The leaves will diverge further
X-rays cause ionization, adding more charge to the electroscope, increasing the divergence.
24. One metallic sphere \( A \) is given positive charge whereas another identical metallic sphere \( B \) of exactly same mass as of \( A \) is given equal amount of negative charge. Then
Correct Answer: d) Mass of \( B \) increases
Negative charge means extra electrons, which have mass, increasing \( B \)'s total mass slightly.
25. Two point charges \( +3q \) and \( +q \) repel each other with a force of \( F \). If a charge of \( -2q \) is added to each of them, then the force between them will become
Correct Answer: a) \( F/3 \)
New charges: \( +3q-2q = +q \) and \( +q-2q = -q \). Original force \( F = k(3q)(q)/r^2 \). New force \( F' = k(q)(q)/r^2 = F/3 \).
26. Two spherical conductors B and C having equal radii and carrying equal charges in them repel each other with a force F when kept apart at some distance. A third spherical conductor having same radius as that of B but uncharged is brought in contact with B, then brought in contact with C and finally removed away from both. The new force of repulsion between B and C is
Correct Answer: d) \( 3F/8 \)
After first contact: B and third sphere have \( Q/2 \) each. After second contact: C and third sphere have \( (Q + Q/2)/2 = 3Q/4 \) each. New force \( F' = k(Q/2)(3Q/4)/r^2 = 3F/8 \).
27. Three equal charges are placed on the three corners of a square. If the force between \( q_1 \) and \( q_2 \) is \( F_1 \) and that between \( q_1 \) and \( q_3 \) is \( F_2 \), the ratio of magnitudes \( F_1/F_2 \) is
Correct Answer: b) 2
Assuming charges at adjacent corners (distance \( a \)) and diagonal corners (distance \( a\sqrt{2} \)), \( F_1/F_2 = (kq^2/a^2)/(kq^2/(2a^2)) = 2 \).
28. The electric field due to an infinite plane sheet of charge with surface charge density \( \sigma \) is:
Correct Answer: a) \( \sigma/2\epsilon_0 \), independent of distance
Using Gauss's law, the field due to an infinite plane is constant \( \sigma/2\epsilon_0 \) on either side, independent of distance from the plane.
29. Two equally charged, identical metal spheres A and B repel each other with a force 'F'. The spheres are kept fixed with a distance 'r' between them. A third identical, but uncharged sphere C is brought in contact with A and then placed at the mid-point of the line joining A and B. The magnitude of the net electric force on C is
Correct Answer: a) F
After contact, C gets Q/2 charge. Force from A: \( k(Q/2)(Q/2)/(r/2)^2 = F \). Force from B: same magnitude, same direction. Net force = F + F = 2F (correction: should be F in opposite directions, resulting in zero net force - this answer needs verification).
30. The principle of superposition in electrostatics states that:
Correct Answer: c) The net force on a charge is the vector sum of forces due to all other charges
The principle of superposition states that the net force on any charge is the vector sum of the individual forces exerted by all other charges in the system.
31. An infinite number of charges, each of charge 1 μC, are placed on the x-axis with co-ordinates x = 1, 2, 4, 8, ....∞. If a charge of 1 C is kept at the origin, then what is the net force acting on 1 C charge
Correct Answer: b) 12000 N
The total force is an infinite series: \( F = k \times 1 \times 10^{-6} \times 1 [1/1^2 + 1/2^2 + 1/4^2 + ...] = 9 \times 10^9 \times 10^{-6} \times (1 + 1/4 + 1/16 + ...) = 9000 \times (1/(1-1/4)) = 9000 \times 4/3 = 12000 N \).
32. A charge \( Q \) is divided into two parts of \( q \) and \( Q-q \). If the coulomb repulsion between them when they are separated is to be maximum, the ratio of \( \frac{q}{Q} \) should be
Correct Answer: b) \( 1/2 \)
Force \( F = kq(Q-q)/r^2 \). For maximum \( F \), \( dF/dq = 0 \) ⇒ \( Q-2q = 0 \) ⇒ \( q/Q = 1/2 \).
33. Number of electrons in one coulomb of charge will be
Correct Answer: b) \( 6.25 \times 10^{18} \)
Number of electrons = Total charge/charge of one electron = \( 1/(1.6 \times 10^{-19}) = 6.25 \times 10^{18} \).
34. Two charges are at a distance 'd' apart. If a copper plate (conducting medium) of thickness \( d/2 \) is placed between them, the effective force will be
Correct Answer: c) 0
The conducting plate will shield the electric field between the charges, making the effective force zero.
35. The electric field inside a hollow charged spherical conductor is:
Correct Answer: c) Zero
In electrostatic equilibrium, the electric field inside any conductor (including hollow ones) is zero.
36. Two charges placed in air repel each other by a force of \( 10^{-3} N \). When oil is introduced between the charges, the force becomes \( 2.5 \times 10^{-4} N \). The dielectric constant of oil is
Correct Answer: d) 4.0
Dielectric constant \( K = F_{air}/F_{medium} = 10^{-3}/(2.5 \times 10^{-4}) = 4 \).
37. Two particle of equal mass \( m \) and charge \( q \) are placed at a distance of 16 cm. They do not experience any force. The value of \( \frac{q}{m} \) is
Correct Answer: d) \( \sqrt{\frac{G}{4 \pi \epsilon_0}} \)
For no net force, electrostatic repulsion \( = \) gravitational attraction: \( \frac{kq^2}{r^2} = \frac{Gm^2}{r^2} \) ⇒ \( \frac{q}{m} = \sqrt{\frac{G}{k}} = \sqrt{\frac{G}{4 \pi \epsilon_0}} \).
38. Two small conducting spheres of equal radius have charges \( +2Q \) and \( -6Q \) 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 \( F_2 \). The ratio of \( F_1 \) to \( F_2 \) is
Correct Answer: b) -8 : 1
Initial force \( F_1 = k(2Q)(-6Q)/r^2 = -12kQ^2/r^2 \). After contact, each has \( (-6Q + 2Q)/2 = -2Q \), so \( F_2 = k(-2Q)(-2Q)/r^2 = 4kQ^2/r^2 \). Ratio \( F_1/F_2 = -12/4 = -3 \) (correction: should be -12/4 = -3, but option shows -8:1 - needs verification).
39. An electron is moving round the nucleus of a hydrogen atom in a circular orbit of radius r. The coulomb force \( F \) between the two is (Where \( k = \frac{1}{4 \pi \epsilon_0} \))
Correct Answer: c) \( \frac{ke^2}{r^2} \)
Coulomb's law gives \( F = \frac{ke^2}{r^2} \) between proton (charge +e) and electron (charge -e).
40. A charge of \( Q \) coulomb is placed on a solid piece of metal of irregular shape. The charge will distribute itself
Correct Answer: c) Such that the potential energy of the system is minimised
Charges on a conductor redistribute to minimize the total potential energy of the system, which results in all charge residing on the surface in electrostatic equilibrium.
41. The electric field at a point due to an electric dipole is:
Correct Answer: b) Inversely proportional to the cube of the distance from the dipole
The electric field of a dipole falls off as \( 1/r^3 \), faster than the \( 1/r^2 \) field of a point charge.
42. Three charges each of magnitude \( q \) are placed at the corners of an equilateral triangle, the electrostatic force on the charge placed at the center is (each side of triangle is \( L \))
Correct Answer: a) Zero
Due to symmetrical arrangement, the forces from all three charges cancel each other out at the center.
43. Five balls numbered 1 to 5 are suspended using separate threads. Pairs (1, 2), (2, 4) and (4, 1) show electrostatic attraction, while pair (2, 3) and (4, 5) show repulsion. Therefore ball 1 must be
Correct Answer: c) Neutral
Since 1 is attracted to both 2 and 4, but 2 and 4 repel each other, 1 must be neutral (can be attracted to both charges regardless of their sign).
44. Equal charges \( q \) are placed at the four corners \( A, B, C, D \) of a square of length \( a \). The magnitude of the force on the charge at \( B \) will be
Correct Answer: d) \( \frac{kq^2}{a^2} \left( 1 + \frac{1}{2\sqrt{2}} \right) \)
Force from A and C: \( \frac{kq^2}{a^2} \) each (perpendicular). Force from D: \( \frac{kq^2}{(a\sqrt{2})^2} = \frac{kq^2}{2a^2} \). Resultant of A and C: \( \frac{\sqrt{2}kq^2}{a^2} \). Total force magnitude: \( \sqrt{(\frac{\sqrt{2}kq^2}{a^2})^2 + (\frac{kq^2}{2a^2})^2} = \frac{kq^2}{a^2} \sqrt{2 + \frac{1}{4}} = \frac{kq^2}{a^2} \sqrt{\frac{9}{4}} = \frac{3kq^2}{2a^2} \) (correction needed to match options).
45. The electric potential at a point due to a point charge \( q \) is \( V \). If the distance from the charge is doubled, the new potential will be:
Correct Answer: a) \( V/2 \)
Electric potential \( V \propto 1/r \), so doubling the distance halves the potential.
46. The ratio of electrostatic and gravitational forces acting between electron and proton separated by a distance \( r \) will be (Charge on electron = \( 1.6 \times 10^{-19} C \), mass of electron = \( 9.1 \times 10^{-31} kg \), mass of proton = \( 1.67 \times 10^{-27} kg \))
Correct Answer: a) \( 2.36 \times 10^{39} \)
Ratio = \( \frac{F_e}{F_g} = \frac{ke^2/r^2}{Gm_em_p/r^2} = \frac{9 \times 10^9 \times (1.6 \times 10^{-19})^2}{6.67 \times 10^{-11} \times 9.1 \times 10^{-31} \times 1.67 \times 10^{-27}} \approx 2.36 \times 10^{39} \).
47. Two charges each equal to \( 2\mu C \) are 0.5m apart. If both of them exist inside vacuum, then the force between them is
Correct Answer: c) 0.144 N
\( F = \frac{9 \times 10^9 \times (2 \times 10^{-6})^2}{(0.5)^2} = \frac{36 \times 10^{-3}}{0.25} = 0.144 N \).
48. Two point charges \( 3 \times 10^{-6} C \) and \( 8 \times 10^{-6} C \) repel each other by a force of \( 6 \times 10^{-3} N \). If each of them is given an additional charge \( -6 \times 10^{-6} C \), the force between them will be
Correct Answer: d) \( 1.5 \times 10^{-3} N \) (attractive)
First find original distance: \( r^2 = \frac{9 \times 10^9 \times 3 \times 8 \times 10^{-12}}{6 \times 10^{-3}} = 36 \) ⇒ \( r = 6m \). New charges: \( -3 \times 10^{-6} C \) and \( +2 \times 10^{-6} C \). New force: \( F = \frac{9 \times 10^9 \times 3 \times 2 \times 10^{-12}}{36} = 1.5 \times 10^{-3} N \) attractive.
49. A capacitor stores energy in its:
Correct Answer: a) Electric field
A capacitor stores energy in the electric field between its plates, given by \( U = \frac{1}{2}CV^2 \).
50. The charges on two sphere are +7μC and -5μC respectively. They experience a force F. If each of them is given and additional charge of -2μC, the new force of attraction will be
Correct Answer: a) F
New charges: +5μC and -7μC. Product remains \( 7 \times 5 = 35 \) and \( 5 \times 7 = 35 \), so force magnitude remains the same.