1. Coulomb's Law
Coulomb's law gives the electrostatic force between two point charges. For two charges q₁ and q₂ separated by distance r:
F = k |q₁q₂| / r²
where:
  • q₁, q₂ = magnitudes of charges
  • r = separation between charges
  • k = Coulomb constant
In vacuum:
k = 1/(4πε₀) ≈ 9 × 10⁹ N m²/C²
2. Vector Form of Coulomb's Law
The vector form gives both the magnitude and direction of the electrostatic force.
F⃗₁₂ = k(q₁q₂/r²) r̂₁₂
Here:
  • F⃗₁₂ = force exerted by q₁ on q₂
  • r̂₁₂ = unit vector directed from q₁ towards q₂
The sign of q₁q₂ determines whether the force is attractive or repulsive.
🔴 Like charges: Repel each other.
🔵 Unlike charges: Attract each other.

The force always acts along the line joining the two charges.
3. ⚡ Practical Coulomb's Law Simulator
Interactive Two-Charge Experiment
q₁ = 5 μC
q₂ = -5 μC
r = 5 m
+
−
Live Result:
Force magnitude: 0 N
Nature: Attractive
Direction: Towards each other
4. Superposition Principle
When several charges act on a charge, the total electrostatic force is the vector sum of all individual forces.
F⃗net = F⃗₁ + F⃗₂ + F⃗₃ + ...
For n charges:
F⃗ = Σ F⃗ᵢ
Each force is calculated independently using Coulomb's law.
Practical Example: Suppose a charge q is acted upon by three charges.

The individual forces are:
F⃗₁, F⃗₂, F⃗₃
The resultant force is:
F⃗net = F⃗₁ + F⃗₂ + F⃗₃
The forces must be added as vectors, not ordinary scalar numbers.
5. Superposition – One Dimensional Example
Suppose a test charge q is placed between two charges. If one charge produces a force of 10 N towards the right and another produces 6 N towards the left:
Fnet = 10 − 6 = 4 N
Therefore:
Net force = 4 N towards the right
6. Vector Example – Perpendicular Forces
Suppose two forces act at right angles:
F₁ = 3 N     F₂ = 4 N
The resultant magnitude is:
F = √(F₁² + F₂²)
F = √(3² + 4²) = 5 N
Resultant force = 5 N
7. JEE Quick Rules
Condition Result
q₁q₂ > 0 Repulsive force
q₁q₂ < 0 Attractive force
Distance doubles Force becomes F/4
Distance triples Force becomes F/9
One charge doubles Force doubles
Both charges double Force becomes 4F
Several charges Use vector superposition
🔥 Golden Rule:

First calculate every individual Coulomb force separately → determine its direction → then add all forces vectorially.
8. 📝 30 MCQs with Solutions
1. Coulomb's law describes the force between:
A. Two masses
B. Two electric charges
C. Two magnetic poles only
D. Two neutral bodies
Answer: B. Two electric charges
2. Coulomb force varies with distance as:
A. r
B. r²
C. 1/r
D. 1/r²
Answer: D. 1/r²
3. If the distance between two charges is doubled, force becomes:
A. 2F
B. F/2
C. F/4
D. 4F
Answer: C. F/4
4. If both charges are doubled, Coulomb force becomes:
A. F
B. 2F
C. 4F
D. F/4
Answer: C. 4F
5. Like charges:
A. Attract
B. Repel
C. Have no force
D. Always rotate
Answer: B. Repel
6. Unlike charges:
A. Repel
B. Attract
C. Have zero force
D. Have equal charge
Answer: B. Attract
7. Coulomb's constant in vacuum is approximately:
A. 9 × 10⁹
B. 9 × 10⁶
C. 3 × 10⁸
D. 6.67 × 10⁻¹¹
Answer: A. 9 × 10⁹ N m²/C²
8. Coulomb force is a:
A. Scalar quantity
B. Vector quantity
C. Dimensionless quantity
D. Constant quantity
Answer: B. Vector quantity
9. The vector form of Coulomb's law contains:
A. Only magnitude
B. Only direction
C. Magnitude and direction
D. Neither
Answer: C. Magnitude and direction
10. The unit vector in Coulomb's law specifies:
A. Charge
B. Direction
C. Mass
D. Energy
Answer: B. Direction
11. The net force due to multiple charges is obtained using:
A. Multiplication
B. Vector addition
C. Division
D. Scalar subtraction only
Answer: B. Vector addition
12. The superposition principle states that total force is:
A. Product of forces
B. Sum of individual forces
C. Average of forces
D. Difference of charges
Answer: B. Sum of individual forces
13. If F₁ = 3 N and F₂ = 4 N act perpendicular to each other, resultant force is:
A. 1 N
B. 5 N
C. 7 N
D. 12 N
Answer: B. 5 N
14. If two equal forces act in opposite directions, resultant is:
A. 2F
B. F
C. Zero
D. F²
Answer: C. Zero
15. If q₁q₂ is positive, the force is:
A. Attractive
B. Repulsive
C. Zero
D. Random
Answer: B. Repulsive
16. If q₁q₂ is negative, the force is:
A. Repulsive
B. Attractive
C. Zero
D. Infinite
Answer: B. Attractive
17. If one charge becomes three times, force becomes:
A. F/3
B. 3F
C. 9F
D. F
Answer: B. 3F
18. If distance becomes three times, force becomes:
A. 3F
B. F/3
C. F/9
D. 9F
Answer: C. F/9
19. Coulomb force acts along:
A. Perpendicular to the line joining charges
B. Line joining the charges
C. Circular path
D. Random direction
Answer: B. Line joining the charges
20. The SI unit of electric charge is:
A. Newton
B. Joule
C. Coulomb
D. Volt
Answer: C. Coulomb
21. The SI unit of Coulomb force is:
A. Coulomb
B. Newton
C. Volt
D. Joule
Answer: B. Newton
22. If one charge is zero, Coulomb force is:
A. Maximum
B. Zero
C. Infinite
D. Negative
Answer: B. Zero
23. The force exerted by q₁ on q₂ is equal and opposite to:
A. Gravitational force
B. Force exerted by q₂ on q₁
C. Electric field
D. Potential
Answer: B. Force exerted by q₂ on q₁
24. The principle used to calculate force due to three or more charges is:
A. Bernoulli principle
B. Superposition principle
C. Archimedes principle
D. Doppler principle
Answer: B. Superposition principle
25. For two forces acting in the same direction, resultant is:
A. F₁ − F₂
B. F₁ + F₂
C. F₁F₂
D. F₁/F₂
Answer: B. F₁ + F₂
26. For two opposite forces, resultant magnitude is:
A. F₁ + F₂
B. |F₁ − F₂|
C. F₁F₂
D. F₁² + F₂²
Answer: B. |F₁ − F₂|
27. Coulomb's law is analogous to:
A. Newton's law of gravitation
B. Ohm's law
C. Faraday's law
D. Hooke's law only
Answer: A. Newton's law of gravitation
28. In a medium of dielectric constant K, Coulomb force becomes:
A. KF
B. F/K
C. K²F
D. F
Answer: B. F/K
29. The force between charges decreases rapidly with:
A. Charge
B. Distance
C. Mass
D. Time
Answer: B. Distance
30. Which is the correct superposition relation?
A. F = F₁F₂F₃
B. F⃗ = ΣF⃗ᵢ
C. F = F₁/F₂
D. F = F₁² + F₂² always
Answer: B. F⃗ = ΣF⃗ᵢ
9. ⭐ Exam Revision Summary
Coulomb's Law: F = k|q₁q₂|/r²

Vector Form: F⃗ = k(q₁q₂/r²)r̂

Superposition: F⃗net = ΣF⃗ᵢ

Like charges → Repulsion ⚡
Unlike charges → Attraction ⚡
Multiple charges → Add forces vectorially 🧭
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