Coulomb’s Law Problems

This section provides 100 problems to test your understanding of Coulomb’s law, including electric forces, vector analysis, superposition principle, equilibrium positions, and electric fields. Inspired by JEE Main, JEE Advanced, and NEET exam patterns, these problems are tailored for exam preparation, offering a mix of numerical, conceptual, and derivation-based challenges. NEET-style problems (66–100) are formatted as multiple-choice questions (MCQs) to match the exam’s objective format. Problems are organized by type to support progressive learning and build confidence in mastering electrostatics, a key topic for JEE/NEET success.

Numerical Problems

  1. Two charges $q_1 = +3 , \mu\text{C}$ and $q_2 = -6 , \mu\text{C}$ are separated by $r = 0.2 , \text{m}$ in vacuum. Calculate the force magnitude ($k = 9 \times 10^9 , \text{N·m}^2/\text{C}^2$).

    • (a) $4.03 , \text{N}$
    • (b) $4.04 , \text{N}$
    • (c) $4.05 , \text{N}$
    • (d) $4.06 , \text{N}$

  2. Two charges $q_1 = +4 , \text{nC}$ and $q_2 = +4 , \text{nC}$ are separated by $r = 0.1 , \text{m}$ in vacuum. Calculate the force magnitude.

    • (a) $1.43 \times 10^{-5} , \text{N}$
    • (b) $1.44 \times 10^{-5} , \text{N}$
    • (c) $1.45 \times 10^{-5} , \text{N}$
    • (d) $1.46 \times 10^{-5} , \text{N}$

  3. Two charges $q_1 = +2 , \mu\text{C}$ and $q_2 = -5 , \mu\text{C}$ are separated by $r = 0.5 , \text{m}$ in water ($\epsilon_r = 80$). Calculate the force magnitude.

    • (a) $0.0289 , \text{N}$
    • (b) $0.0290 , \text{N}$
    • (c) $0.0291 , \text{N}$
    • (d) $0.0292 , \text{N}$

  4. A charge of $+10 , \mu\text{C}$ is created by removing electrons. How many electrons were removed? ($e = 1.6 \times 10^{-19} , \text{C}$)

    • (a) $6.24 \times 10^{13}$
    • (b) $6.25 \times 10^{13}$
    • (c) $6.26 \times 10^{13}$
    • (d) $6.27 \times 10^{13}$

  5. Charges $q_1 = +2 , \mu\text{C}$ at $(0, 0)$ and $q_2 = -3 , \mu\text{C}$ at $(0.4, 0)$. Calculate the force on $q_1$ (vector form).

    • (a) $-0.843 \hat{i} , \text{N}$
    • (b) $-0.844 \hat{i} , \text{N}$
    • (c) $-0.845 \hat{i} , \text{N}$
    • (d) $-0.846 \hat{i} , \text{N}$

  6. Charges $q_1 = +5 , \mu\text{C}$ at $(0, 0)$ and $q_2 = +5 , \mu\text{C}$ at $(0, 0.3)$. Calculate the force vector on $q_1$.

    • (a) $0.499 \hat{j} , \text{N}$
    • (b) $0.500 \hat{j} , \text{N}$
    • (c) $0.501 \hat{j} , \text{N}$
    • (d) $0.502 \hat{j} , \text{N}$

  7. Charges $q_1 = +3 , \mu\text{C}$ at $(0, 0)$, $q_2 = -2 , \mu\text{C}$ at $(0.2, 0)$, $q_3 = +4 , \mu\text{C}$ at $(0, 0.2)$. Calculate the net force on $q_1$ (magnitude).

    • (a) $2.19 , \text{N}$
    • (b) $2.20 , \text{N}$
    • (c) $2.21 , \text{N}$
    • (d) $2.22 , \text{N}$

  8. Charges $q_1 = +q$ at $(0, 0)$, $q_2 = +q$ at $(a, 0)$. Where should $q_3 = -q$ be placed on the x-axis for zero net force?

    • (a) $x = 0.49a$
    • (b) $x = 0.50a$
    • (c) $x = 0.51a$
    • (d) $x = 0.52a$

  9. Calculate the electric field at $(0, 0.4)$ due to $q = +6 , \mu\text{C}$ at $(0, 0)$.

    • (a) $3.37 \times 10^5 \hat{j} , \text{N/C}$
    • (b) $3.38 \times 10^5 \hat{j} , \text{N/C}$
    • (c) $3.39 \times 10^5 \hat{j} , \text{N/C}$
    • (d) $3.40 \times 10^5 \hat{j} , \text{N/C}$

  10. Charges $q_1 = +2 , \mu\text{C}$ at $(0.2, 0)$, $q_2 = -2 , \mu\text{C}$ at $(-0.2, 0)$. Calculate the electric field at $(0, 0.3)$ (magnitude).

    • (a) $0 , \text{N/C}$
    • (b) $1 \times 10^5 , \text{N/C}$
    • (c) $2 \times 10^5 , \text{N/C}$
    • (d) $3 \times 10^5 , \text{N/C}$

  11. A ring of charge (radius $R = 0.1 , \text{m}$, total charge $Q = 5 , \mu\text{C}$) lies in the xy-plane. Calculate the electric field on the axis at $z = 0.1 , \text{m}$.

    • (a) $1.59 \times 10^6 , \text{N/C}$
    • (b) $1.60 \times 10^6 , \text{N/C}$
    • (c) $1.61 \times 10^6 , \text{N/C}$
    • (d) $1.62 \times 10^6 , \text{N/C}$

  12. Two charges $q_1 = +8 , \mu\text{C}$ and $q_2 = -4 , \mu\text{C}$ are separated by $r = 0.3 , \text{m}$ in vacuum. Calculate the force magnitude.

    • (a) $3.19 , \text{N}$
    • (b) $3.20 , \text{N}$
    • (c) $3.21 , \text{N}$
    • (d) $3.22 , \text{N}$

  13. Charges $q_1 = +3 , \mu\text{C}$ at $(0.1, 0.1)$ and $q_2 = -3 , \mu\text{C}$ at $(0, 0)$. Calculate the force on $q_1$ (magnitude).

    • (a) $0.955 , \text{N}$
    • (b) $0.956 , \text{N}$
    • (c) $0.957 , \text{N}$
    • (d) $0.958 , \text{N}$

  14. Charges $q_1 = +q$, $q_2 = +4q$ at $x = 0$ and $x = a$. Where should $q_3 = -q$ be placed for equilibrium?

    • (a) $x = 0.32a$
    • (b) $x = 0.33a$
    • (c) $x = 0.34a$
    • (d) $x = 0.35a$

  15. Calculate the electric field at $(0.2, 0)$ due to $q = -4 , \mu\text{C}$ at $(0, 0)$.

    • (a) $-8.99 \times 10^5 \hat{i} , \text{N/C}$
    • (b) $-9.00 \times 10^5 \hat{i} , \text{N/C}$
    • (c) $-9.01 \times 10^5 \hat{i} , \text{N/C}$
    • (d) $-9.02 \times 10^5 \hat{i} , \text{N/C}$

  16. Two charges $q_1 = +5 , \mu\text{C}$ and $q_2 = -5 , \mu\text{C}$ are separated by $r = 0.4 , \text{m}$ in air ($\epsilon_r = 1$). Calculate the force magnitude.

    • (a) $1.40 , \text{N}$
    • (b) $1.41 , \text{N}$
    • (c) $1.42 , \text{N}$
    • (d) $1.43 , \text{N}$

  17. Charges $q_1 = +2 , \mu\text{C}$ at $(0, 0)$, $q_2 = -3 , \mu\text{C}$ at $(0.5, 0)$, $q_3 = +1 , \mu\text{C}$ at $(0, 0.5)$. Calculate the net force on $q_1$ (magnitude).

    • (a) $0.509 , \text{N}$
    • (b) $0.510 , \text{N}$
    • (c) $0.511 , \text{N}$
    • (d) $0.512 , \text{N}$

  18. Calculate the electric field at $(0, 0.5)$ due to $q = +8 , \mu\text{C}$ at $(0, 0)$.

    • (a) $2.87 \times 10^5 \hat{j} , \text{N/C}$
    • (b) $2.88 \times 10^5 \hat{j} , \text{N/C}$
    • (c) $2.89 \times 10^5 \hat{j} , \text{N/C}$
    • (d) $2.90 \times 10^5 \hat{j} , \text{N/C}$

  19. A line charge with $\lambda = 2 \times 10^{-6} , \text{C/m}$, length $L = 0.2 , \text{m}$, lies on the x-axis. Calculate the electric field at $(0, 0.1)$ (midpoint perpendicular).

    • (a) $3.59 \times 10^5 \hat{j} , \text{N/C}$
    • (b) $3.60 \times 10^5 \hat{j} , \text{N/C}$
    • (c) $3.61 \times 10^5 \hat{j} , \text{N/C}$
    • (d) $3.62 \times 10^5 \hat{j} , \text{N/C}$

  20. Two charges $q_1 = +6 , \mu\text{C}$ and $q_2 = -3 , \mu\text{C}$ are separated by $r = 0.2 , \text{m}$ in vacuum. Calculate the force magnitude.

    • (a) $4.03 , \text{N}$
    • (b) $4.04 , \text{N}$
    • (c) $4.05 , \text{N}$
    • (d) $4.06 , \text{N}$

  21. Charges $q_1 = +4 , \mu\text{C}$ at $(0.3, 0)$, $q_2 = -4 , \mu\text{C}$ at $(0, 0)$. Calculate the force vector on $q_1$.

    • (a) $-1.599 \hat{i} , \text{N}$
    • (b) $-1.600 \hat{i} , \text{N}$
    • (c) $-1.601 \hat{i} , \text{N}$
    • (d) $-1.602 \hat{i} , \text{N}$

  22. Charges $q_1 = +q$ at $(0, 0)$, $q_2 = +q$ at $(a, 0)$, $q_3 = -2q$ at $(x, 0)$. Find $x$ for equilibrium of $q_3$.

    • (a) $0.41a$
    • (b) $0.42a$
    • (c) $0.43a$
    • (d) $0.44a$

  23. Calculate the electric field at $(0.1, 0.1)$ due to $q = +3 , \mu\text{C}$ at $(0, 0)$.

    • (a) $1.90 \times 10^5 (\hat{i} + \hat{j}) , \text{N/C}$
    • (b) $1.91 \times 10^5 (\hat{i} + \hat{j}) , \text{N/C}$
    • (c) $1.92 \times 10^5 (\hat{i} + \hat{j}) , \text{N/C}$
    • (d) $1.93 \times 10^5 (\hat{i} + \hat{j}) , \text{N/C}$

  24. A ring of charge (radius $R = 0.05 , \text{m}$, total charge $Q = 2 , \mu\text{C}$) lies in the xy-plane. Calculate the electric field at $z = 0.05 , \text{m}$.

    • (a) $1.27 \times 10^6 , \text{N/C}$
    • (b) $1.28 \times 10^6 , \text{N/C}$
    • (c) $1.29 \times 10^6 , \text{N/C}$
    • (d) $1.30 \times 10^6 , \text{N/C}$

  25. Two charges $q_1 = +1 , \mu\text{C}$ and $q_2 = -2 , \mu\text{C}$ are separated by $r = 0.1 , \text{m}$ in vacuum. Calculate the force magnitude.

    • (a) $1.79 , \text{N}$
    • (b) $1.80 , \text{N}$
    • (c) $1.81 , \text{N}$
    • (d) $1.82 , \text{N}$

  26. Charges $q_1 = +5 , \mu\text{C}$ at $(0, 0)$, $q_2 = -2 , \mu\text{C}$ at $(0.2, 0.2)$, $q_3 = +3 , \mu\text{C}$ at $(0.2, 0)$. Calculate the net force on $q_1$ (magnitude).

    • (a) $1.58 , \text{N}$
    • (b) $1.59 , \text{N}$
    • (c) $1.60 , \text{N}$
    • (d) $1.61 , \text{N}$

  27. Calculate the electric field at $(0, 0.2)$ due to $q = -7 , \mu\text{C}$ at $(0, 0)$.

    • (a) $-1.574 \times 10^6 \hat{j} , \text{N/C}$
    • (b) $-1.575 \times 10^6 \hat{j} , \text{N/C}$
    • (c) $-1.576 \times 10^6 \hat{j} , \text{N/C}$
    • (d) $-1.577 \times 10^6 \hat{j} , \text{N/C}$

  28. A charge of $+15 , \mu\text{C}$ is created by removing electrons. How many electrons were removed? ($e = 1.6 \times 10^{-19} , \text{C}$)

    • (a) $9.37 \times 10^{13}$
    • (b) $9.38 \times 10^{13}$
    • (c) $9.39 \times 10^{13}$
    • (d) $9.40 \times 10^{13}$

  29. Charges $q_1 = +q$ at $(0, 0)$, $q_2 = +9q$ at $(a, 0)$. Where should $q_3 = -q$ be placed for equilibrium?

    • (a) $x = 0.24a$
    • (b) $x = 0.25a$
    • (c) $x = 0.26a$
    • (d) $x = 0.27a$

  30. Two charges $q_1 = +3 , \mu\text{C}$ and $q_2 = -6 , \mu\text{C}$ are separated by $r = 0.3 , \text{m}$ in a medium ($\epsilon_r = 2$). Calculate the force magnitude.

    • (a) $1.79 , \text{N}$
    • (b) $1.80 , \text{N}$
    • (c) $1.81 , \text{N}$
    • (d) $1.82 , \text{N}$

  31. In a rocket ion engine, charges $q_1 = +2 , \mu\text{C}$ at $(0, 0)$, $q_2 = -3 , \mu\text{C}$ at $(0.1, 0)$ steer a particle $q_3 = +1 , \mu\text{C}$ at $(0, 0.1)$. Calculate the net force on $q_3$ (magnitude).

    • (a) $2.47 , \text{N}$
    • (b) $2.48 , \text{N}$
    • (c) $2.49 , \text{N}$
    • (d) $2.50 , \text{N}$

  32. Calculate the electric field at $(-0.2, 0)$ due to $q = +5 , \mu\text{C}$ at $(0, 0)$.

    • (a) $1.124 \times 10^6 \hat{i} , \text{N/C}$
    • (b) $1.125 \times 10^6 \hat{i} , \text{N/C}$
    • (c) $1.126 \times 10^6 \hat{i} , \text{N/C}$
    • (d) $1.127 \times 10^6 \hat{i} , \text{N/C}$

  33. A ring of charge (radius $R = 0.2 , \text{m}$, total charge $Q = 10 , \mu\text{C}$) lies in the xy-plane. Calculate the electric field at $z = 0.2 , \text{m}$.

    • (a) $1.99 \times 10^6 , \text{N/C}$
    • (b) $2.00 \times 10^6 , \text{N/C}$
    • (c) $2.01 \times 10^6 , \text{N/C}$
    • (d) $2.02 \times 10^6 , \text{N/C}$

  34. Charges $q_1 = +q$ at $(0, 0)$, $q_2 = +q$ at $(0, a)$, $q_3 = -q$ at $(x, 0)$. Find $x$ for equilibrium of $q_3$.

    • (a) $0.40a$
    • (b) $0.41a$
    • (c) $0.42a$
    • (d) $0.43a$

  35. Charges $q_1 = +4 , \mu\text{C}$ at $(0.2, 0.2)$, $q_2 = -2 , \mu\text{C}$ at $(0, 0)$. Calculate the force on $q_1$ (magnitude).

    • (a) $0.449 , \text{N}$
    • (b) $0.450 , \text{N}$
    • (c) $0.451 , \text{N}$
    • (d) $0.452 , \text{N}$

Conceptual Problems

  1. What does Coulomb’s law describe?
  • (a) Magnetic force between charges
  • (b) Electric force between point charges
  • (c) Gravitational force
  • (d) Nuclear force
  1. What is the direction of the force between two positive charges?
  • (a) Attractive
  • (b) Repulsive
  • (c) No force
  • (d) Perpendicular
  1. What does the superposition principle state?
  • (a) Forces are scalar quantities
  • (b) Net force is the vector sum of individual forces
  • (c) Forces cancel out
  • (d) Forces are independent of distance
  1. What happens to the force in a medium with $\epsilon_r > 1$?
  • (a) Increases
  • (b) Decreases
  • (c) Remains the same
  • (d) Becomes zero
  1. What is the unit of electric charge in SI units?
  • (a) Coulomb
  • (b) Newton
  • (c) Joule
  • (d) Volt
  1. What does a zero net force on a charge indicate?
  • (a) No other charges present
  • (b) Charge is in equilibrium
  • (c) Charge is moving
  • (d) Charge is neutral
  1. What does the electric field represent?
  • (a) Force per unit mass
  • (b) Force per unit charge
  • (c) Energy per unit charge
  • (d) Charge per unit area
  1. What is the physical significance of $k \frac{q}{r^2}$?
  • (a) Electric force
  • (b) Electric field magnitude
  • (c) Electric potential
  • (d) Charge density
  1. What does charge quantization imply?
  • (a) Charge is continuous
  • (b) Charge is discrete, $q = n e$
  • (c) Charge is zero
  • (d) Charge is infinite
  1. What is the dimension of electric force?
  • (a) $[\text{M} \text{L} \text{T}^{-2}]$
  • (b) $[\text{M} \text{L}^2 \text{T}^{-2}]$
  • (c) $[\text{L} \text{T}^{-2}]$
    - (d) $[\text{M} \text{L}^2 \text{T}^{-1}]$
  1. What does a negative force magnitude in Coulomb’s law indicate?
  • (a) Repulsive force
  • (b) Attractive force
  • (c) No force
  • (d) Perpendicular force
  1. What is the significance of $\epsilon_0$ in Coulomb’s law?
  • (a) Permittivity of free space
  • (b) Permittivity of medium
  • (c) Charge density
  • (d) Electric field
  1. What happens to the force if the distance between charges doubles?
  • (a) Increases by 4
  • (b) Decreases by 4
  • (c) Doubles
  • (d) Halves
  1. What does the electric field direction indicate for a positive charge?
  • (a) Points inward
  • (b) Points outward
  • (c) Points perpendicular
  • (d) No direction
  1. How does Coulomb’s law apply to ion propulsion in rockets?
  • (a) Calculates magnetic forces
  • (b) Determines electric forces for steering charged particles
  • (c) Reduces charge
  • (d) Increases distance

Derivation Problems

  1. Derive the vector form of Coulomb’s law $\vec{F}{1,2} = k \frac{q_1 q_2}{r^2} \hat{r}{12}$.

  2. Derive the force in a medium $F_{\text{medium}} = \frac{F_{\text{vacuum}}}{\epsilon_r}$.

  3. Derive the electric field from Coulomb’s law $\vec{E} = k \frac{q}{r^2} \hat{r}$.

  4. Derive the equilibrium position for a charge between two like charges.

  5. Derive the net force on a charge due to multiple charges using the superposition principle.

  6. Derive the electric field on the axis of a ring of charge.

  7. Derive the force components in 2D for two charges.

  8. Derive the charge quantization relation $q = n e$.

  9. Derive the electric field due to a line charge at a perpendicular distance.

  10. Derive the net electric field at a point due to multiple charges.

  11. Derive the force magnitude in Coulomb’s law $F = k \frac{|q_1 q_2|}{r^2}$.

  12. Derive the equilibrium position for a charge in a non-linear arrangement.

  13. Derive the relation between $k$ and $\epsilon_0$ in Coulomb’s law.

  14. Derive the superposition principle for electric fields.

  15. Derive the force on a charge in a triangular arrangement of charges.

NEET-style Conceptual Problems

  1. What is the unit of electric field in SI units?
  • (a) $\text{N/C}$
  • (b) $\text{J}$
  • (c) $\text{m/s}$
  • (d) $\text{Pa}$
  1. What does a positive electric field direction indicate for a negative charge?
  • (a) Points away from the charge
  • (b) Points toward the charge
  • (c) No direction
  • (d) Perpendicular
  1. Which principle allows the calculation of net force from multiple charges?
  • (a) Quantization
  • (b) Superposition
  • (c) Conservation
  • (d) Equilibrium
  1. What happens to the force if the charges are doubled?
  • (a) Doubles
  • (b) Halves
  • (c) Quadruples
  • (d) Remains the same
  1. What is the dimension of Coulomb’s constant $k$?
  • (a) $[\text{M} \text{L}^3 \text{T}^{-4} \text{A}^{-2}]$
  • (b) $[\text{M} \text{L} \text{T}^{-1}]$
  • (c) $[\text{L} \text{T}^{-2}]$
  • (d) $[\text{M} \text{L}^2 \text{T}^{-1}]$
  1. What does the permittivity of free space $\epsilon_0$ represent?
  • (a) Charge density
  • (b) Medium’s resistance to electric fields
  • (c) Ability of vacuum to permit electric fields
  • (d) Electric field strength
  1. What is the role of vector addition in Coulomb’s law?
  • (a) Determines magnitude only
  • (b) Determines net force direction and magnitude
  • (c) Reduces force
  • (d) Increases distance
  1. What happens to the electric field if the distance from the charge triples?
  • (a) Increases by 9
  • (b) Decreases by 9
  • (c) Triples
  • (d) Decreases by 3
  1. Why does a medium reduce the force between charges?
  • (a) Increases distance
  • (b) Reduces permittivity
  • (c) Polarization reduces effective field
  • (d) Increases charge
  1. What is the unit of force in Coulomb’s law?
  • (a) $\text{N}$
  • (b) $\text{J}$
  • (c) $\text{C}$
  • (d) $\text{V}$
  1. What does a constant $k = \frac{1}{4 \pi \epsilon_0}$ indicate?
  • (a) Charge quantization
  • (b) Relation between force and permittivity
  • (c) Electric field
  • (d) Potential energy
  1. Which type of force does Coulomb’s law describe?
  • (a) Magnetic
  • (b) Electric
  • (c) Gravitational
  • (d) Frictional
  1. What is the direction of the electric field due to a negative charge?
  • (a) Outward
  • (b) Inward
  • (c) Perpendicular
  • (d) Random
  1. What does a pseudo-force do in a non-inertial frame for charged particles?
  • (a) Affects perceived electric force
  • (b) Affects charge magnitude
  • (c) Creates magnetic fields
  • (d) Reduces field strength
  1. What is the dimension of electric charge?
  • (a) $[\text{A} \text{T}]$
  • (b) $[\text{M} \text{L} \text{T}^{-1}]$
  • (c) $[\text{L} \text{T}^{-2}]$
  • (d) $[\text{M} \text{L}^2 \text{T}^{-1}]$
  1. What is the role of Coulomb’s law in rocket ion propulsion?
  • (a) Increases charge
  • (b) Calculates forces for steering charged particles
  • (c) Reduces field
  • (d) Increases distance
  1. What happens to the force if $\epsilon_r$ increases?
  • (a) Increases
  • (b) Decreases
  • (c) Remains constant
  • (d) Becomes zero
  1. Why does the force follow an inverse square law?
  • (a) Due to charge quantization
  • (b) Due to spherical symmetry of field
  • (c) Due to medium effects
  • (d) Due to vector addition
  1. What is the significance of $k \frac{q_1 q_2}{r^2} \hat{r}_{12}$?
  • (a) Scalar force
  • (b) Vector electric force
  • (c) Electric field
  • (d) Potential energy
  1. What is the unit of $\epsilon_0$?
  • (a) $\text{C}^2/\text{N·m}^2$
  • (b) $\text{N·m}^2/\text{C}^2$
  • (c) $\text{J}$
  • (d) $\text{V}$
  1. What does a zero electric field at a point indicate?
  • (a) No charges present
  • (b) Net field cancels out
  • (c) Maximum force
  • (d) No charge movement
  1. What is the physical significance of $q = n e$?
  • (a) Charge conservation
  • (b) Charge quantization
  • (c) Force calculation
  • (d) Field strength
  1. Why does the electric field point away from a positive charge?
  • (a) Due to repulsion of a positive test charge
  • (b) Due to attraction
  • (c) Due to medium effects
  • (d) Due to charge quantization
  1. What is the dimension of electric field?
  • (a) $[\text{M} \text{L} \text{T}^{-3} \text{A}^{-1}]$
  • (b) $[\text{M} \text{L} \text{T}^{-1}]$
  • (c) $[\text{L} \text{T}^{-2}]$
  • (d) $[\text{M} \text{L}^2 \text{T}^{-1}]$
  1. How does superposition help in ion propulsion systems?
  • (a) Reduces charge
  • (b) Calculates net force for particle steering
  • (c) Increases field
  • (d) Decreases distance
  1. What is the role of distance in Coulomb’s law?
  • (a) Linear dependence
  • (b) Inverse square dependence
  • (c) No dependence
  • (d) Exponential dependence
  1. What does a high $\epsilon_r$ indicate?
  • (a) Stronger force
  • (b) Weaker force in the medium
  • (c) No effect on force
  • (d) Increased charge
  1. What is the physical significance of $\frac{1}{4 \pi \epsilon_0}$?
  • (a) Electric field
  • (b) Coulomb’s constant
  • (c) Charge density
  • (d) Potential energy
  1. What is the dimension of $\vec{r}_{12}$ in Coulomb’s law?
  • (a) $[\text{L}]$
  • (b) $[\text{M} \text{L} \text{T}^{-1}]$
  • (c) $[\text{L} \text{T}^{-2}]$
  • (d) $[\text{M} \text{L}^2 \text{T}^{-1}]$
  1. Why does the force depend on the product of charges?
  • (a) Due to linear nature of electric forces
  • (b) Due to inverse square law
  • (c) Due to charge quantization
  • (d) Due to medium effects

NEET-style Numerical Problems

  1. Two charges $q_1 = +2 , \mu\text{C}$ and $q_2 = -4 , \mu\text{C}$ are separated by $r = 0.1 , \text{m}$ in vacuum. What is the force magnitude?
  • (a) $7.19 , \text{N}$
  • (b) $7.20 , \text{N}$
  • (c) $7.21 , \text{N}$
  • (d) $7.22 , \text{N}$
  1. Charges $q_1 = +3 , \mu\text{C}$ at $(0, 0)$, $q_2 = -3 , \mu\text{C}$ at $(0.2, 0)$. What is the force on $q_1$ (magnitude)?
  • (a) $2.02 , \text{N}$
  • (b) $2.03 , \text{N}$
  • (c) $2.04 , \text{N}$
  • (d) $2.05 , \text{N}$
  1. Calculate the electric field at $(0, 0.3)$ due to $q = +5 , \mu\text{C}$ at $(0, 0)$.
  • (a) $4.99 \times 10^5 \hat{j} , \text{N/C}$
  • (b) $5.00 \times 10^5 \hat{j} , \text{N/C}$
  • (c) $5.01 \times 10^5 \hat{j} , \text{N/C}$
  • (d) $5.02 \times 10^5 \hat{j} , \text{N/C}$
  1. A charge of $+12 , \mu\text{C}$ is created by removing electrons. How many electrons were removed? ($e = 1.6 \times 10^{-19} , \text{C}$)
  • (a) $7.49 \times 10^{13}$
  • (b) $7.50 \times 10^{13}$
  • (c) $7.51 \times 10^{13}$
  • (d) $7.52 \times 10^{13}$
  1. Charges $q_1 = +q$ at $(0, 0)$, $q_2 = +q$ at $(a, 0)$, $q_3 = -q$ at $(x, 0)$. Where is $q_3$ in equilibrium?
    - (a) $x = 0.49a$
    - (b) $x = 0.50a$
    - (c) $x = 0.51a$
    - (d) $x = 0.52a$

Back to Chapter

Return to Coulomb’s Law Chapter