1. The SI unit of electric charge is:
Correct Answer: B (Coulomb)
The SI unit of electric charge is the coulomb (C). One coulomb is defined as the charge transported by a constant current of one ampere in one second.
2. Which of the following is conserved when two identical metal spheres are charged by contact and then separated?
Correct Answer: A (Charge only)
When two identical metal spheres are charged by contact and separated, the total charge is conserved. However, energy is not conserved because some energy is lost as heat during the charge transfer process.
3. The force between two point charges is F. If the distance between them is doubled, the new force will be:
Correct Answer: B (F/4)
According to Coulomb's Law: \( F = k\frac{q_1 q_2}{r^2} \)
If distance is doubled (r → 2r), the new force becomes:
\( F' = k\frac{q_1 q_2}{(2r)^2} = k\frac{q_1 q_2}{4r^2} = \frac{F}{4} \)
If distance is doubled (r → 2r), the new force becomes:
\( F' = k\frac{q_1 q_2}{(2r)^2} = k\frac{q_1 q_2}{4r^2} = \frac{F}{4} \)
4. Which of the following materials is the best conductor of electricity?
Correct Answer: C (Silver)
Silver is the best conductor of electricity among the given options due to its high number of free electrons. It has the highest electrical conductivity of all metals.
5. The quantization of electric charge implies that:
Correct Answer: C (Charge exists in discrete packets)
Quantization of charge means that charge exists as integer multiples of the elementary charge (e = 1.6 × 10⁻¹⁹ C). Any charge Q can be expressed as Q = ne, where n is an integer.
6. Two charges +Q and -Q are placed at a distance d apart. The force between them is:
Correct Answer: A (Attractive and proportional to Q²/d²)
According to Coulomb's Law: \( F = k\frac{q_1 q_2}{r^2} \)
For charges +Q and -Q: \( F = k\frac{(Q)(-Q)}{d^2} = -k\frac{Q^2}{d^2} \)
The negative sign indicates attractive force, and the magnitude is proportional to Q²/d².
For charges +Q and -Q: \( F = k\frac{(Q)(-Q)}{d^2} = -k\frac{Q^2}{d^2} \)
The negative sign indicates attractive force, and the magnitude is proportional to Q²/d².
7. When a glass rod is rubbed with silk, the rod becomes positively charged because:
Correct Answer: C (Electrons are transferred from rod to silk)
When glass is rubbed with silk, electrons are transferred from the glass rod to the silk cloth. This leaves the glass rod with a deficiency of electrons, making it positively charged.
8. The electric field inside a charged spherical conductor is:
Correct Answer: D (Zero)
Inside a charged spherical conductor, the electric field is zero. This is a fundamental property of conductors in electrostatic equilibrium - the charges redistribute themselves to cancel any internal electric field.
9. If the charge on an electron is 1.6 × 10⁻¹⁹ C, how many electrons constitute 1 coulomb of charge?
Correct Answer: A (6.25 × 10¹⁸)
Number of electrons = Total charge / Charge on one electron
\( n = \frac{1 \text{ C}}{1.6 \times 10^{-19} \text{ C/electron}} = 6.25 \times 10^{18} \) electrons
\( n = \frac{1 \text{ C}}{1.6 \times 10^{-19} \text{ C/electron}} = 6.25 \times 10^{18} \) electrons
10. Two point charges +4μC and -2μC are placed 3m apart in air. The force between them is:
Correct Answer: A (8 × 10⁻³ N, attractive)
Using Coulomb's Law: \( F = k\frac{q_1 q_2}{r^2} \)
\( F = (9 \times 10^9) \frac{(4 \times 10^{-6})(-2 \times 10^{-6})}{3^2} \)
\( F = (9 \times 10^9) \frac{-8 \times 10^{-12}}{9} = -8 \times 10^{-3} \) N
The negative sign indicates attractive force.
\( F = (9 \times 10^9) \frac{(4 \times 10^{-6})(-2 \times 10^{-6})}{3^2} \)
\( F = (9 \times 10^9) \frac{-8 \times 10^{-12}}{9} = -8 \times 10^{-3} \) N
The negative sign indicates attractive force.
11. The principle of superposition for electric charges states that:
Correct Answer: C (The net force on a charge is the vector sum of forces due to other charges)
The principle of superposition states that the net force on any charge is the vector sum of the forces exerted on it by all other charges in the system, with each individual force calculated independently.
12. A charge q is placed at the center of a cube. The electric flux through any one face of the cube is:
Correct Answer: B (q/6ε₀)
According to Gauss's Law, total flux through the cube is \( \phi_{total} = \frac{q}{\epsilon_0} \).
Since the cube has 6 identical faces and the charge is symmetrically placed, flux through one face is:
\( \phi_{face} = \frac{\phi_{total}}{6} = \frac{q}{6\epsilon_0} \)
Since the cube has 6 identical faces and the charge is symmetrically placed, flux through one face is:
\( \phi_{face} = \frac{\phi_{total}}{6} = \frac{q}{6\epsilon_0} \)
13. Which of the following is NOT a property of electric field lines?
Correct Answer: C (They are closed loops)
Electric field lines are not closed loops (except in the case of changing magnetic fields, which is not considered in electrostatics). They begin on positive charges and terminate on negative charges.
14. The dielectric constant K of a medium is defined as:
Correct Answer: D (Both B and C)
Dielectric constant \( K = \frac{\epsilon}{\epsilon_0} \) (ratio of permittivities)
Also, since \( F_{medium} = \frac{F_{vacuum}}{K} \), we can write \( K = \frac{F_{vacuum}}{F_{medium}} \)
Also, since \( F_{medium} = \frac{F_{vacuum}}{K} \), we can write \( K = \frac{F_{vacuum}}{F_{medium}} \)
15. Three charges q, q, and -q are placed at the corners of an equilateral triangle. The net force on any charge is directed:
Correct Answer: B (Away from the center of the triangle)
For the two positive charges, the net force is repulsive from the other positive charge and attractive toward the negative charge. The resultant force on each positive charge is directed away from the triangle's center.
16. The work done in moving a charge between two points in an electric field depends on:
Correct Answer: D (Only the end points and the charge)
The electric field is conservative, so work done depends only on the initial and final positions (potential difference) and the charge, not on the path taken.
17. A charge Q is divided into two parts q and (Q-q). The maximum Coulombic repulsion between them occurs when:
Correct Answer: B (q = Q/2)
Force \( F = k\frac{q(Q-q)}{r^2} \)
For maximum F, differentiate with respect to q and set to zero:
\( \frac{dF}{dq} = k\frac{(1)(Q-q) + q(-1)}{r^2} = 0 \)
\( Q - q - q = 0 \) ⇒ \( Q = 2q \) ⇒ \( q = Q/2 \)
For maximum F, differentiate with respect to q and set to zero:
\( \frac{dF}{dq} = k\frac{(1)(Q-q) + q(-1)}{r^2} = 0 \)
\( Q - q - q = 0 \) ⇒ \( Q = 2q \) ⇒ \( q = Q/2 \)
18. The electric field due to an infinite plane sheet of charge with surface charge density σ is:
Correct Answer: B (σ/2ε₀, independent of distance)
Using Gauss's Law for an infinite plane sheet:
\( E \times 2A = \frac{\sigma A}{\epsilon_0} \)
\( E = \frac{\sigma}{2\epsilon_0} \)
The field is uniform and independent of distance from the sheet.
\( E \times 2A = \frac{\sigma A}{\epsilon_0} \)
\( E = \frac{\sigma}{2\epsilon_0} \)
The field is uniform and independent of distance from the sheet.
19. Two identical charges are placed at a distance r apart. If one charge is doubled and distance is halved, the force becomes:
Correct Answer: C (8 times)
Original force: \( F = k\frac{q \times q}{r^2} \)
New situation: \( F' = k\frac{(2q) \times q}{(r/2)^2} = k\frac{2q^2}{r^2/4} = 8k\frac{q^2}{r^2} = 8F \)
New situation: \( F' = k\frac{(2q) \times q}{(r/2)^2} = k\frac{2q^2}{r^2/4} = 8k\frac{q^2}{r^2} = 8F \)
20. A conductor with a positive charge:
Correct Answer: B (Has deficiency of electrons)
A positively charged conductor has a deficiency of electrons. The number of protons in the nuclei remains unchanged - it's the mobile electrons that are transferred when charging occurs.