⚡Coulomb's Law
The Electric Force
Coulomb's Law gives the force between two point charges:
F = k × |q₁| × |q₂| / r²
Where: - k = 9×10⁹ N·m²/C² (Coulomb's constant, or k = 1/4πε₀) - q₁, q₂ = charges in Coulombs - r = distance between charges in meters
The force is: - Attractive if charges have opposite signs - Repulsive if charges have the same sign - Along the line connecting the two charges
Compare to gravity: F_g = Gm₁m₂/r². Same mathematical form! But the electric force is enormously stronger than gravity.
Superposition Principle
When multiple charges are present, the net force on a charge is the vector sum of all individual forces:
F_net = F₁ + F₂ + F₃ + ...
You calculate each force separately using Coulomb's law, then add them as vectors (with direction!).
This is the superposition principle — charges don't "interfere" with each other's forces.
✏️ Worked Example
Problem: Find the force between q₁ = +2 μC and q₂ = −3 μC separated by 0.3 m.
📐 Key Equations
Coulomb's Law
F = (k|q_1||q_2|)/(r²)k = 9 × 10^9 N·m²/C²⚠️ Common Mistakes
Misconception: The electric force between two charges is proportional to r, not 1/r².
✓ Correct thinking: Coulomb's law is an inverse-square law: F ∝ 1/r². Doubling the separation reduces the force by a factor of 4.
Why: Students often mix up the linear gravitational formula (F = mg) with the distance-dependent form. The 1/r² dependence is fundamental to both Coulomb and gravitational forces.
Misconception: When finding the net force on a charge from multiple other charges, just add the magnitudes.
✓ Correct thinking: Electric forces are vectors. You must add them using components, accounting for both magnitude and direction.
Why: Two equal forces pointing in opposite directions cancel to zero — you would get the wrong answer by adding magnitudes.
Misconception: A larger charge always exerts more force than a smaller one.
✓ Correct thinking: The force depends on the product of BOTH charges divided by r². A tiny charge very close can exert more force than a large charge far away.
Why: F = k|q₁||q₂|/r². The r² term can dominate: halving distance quadruples force, regardless of charge sizes.
📝 Practice Problems
Try these problems. Check your answer when ready.
Find the electric force between q₁ = +1 μC and q₂ = +1 μC separated by 0.1 m. Is it attractive or repulsive?
F = (k|q_1||q_2|)/(r²)The force between two charges separated by 0.2 m is 4.5 N. If the separation is doubled to 0.4 m, what is the new force?
Find the force between q₁ = +4 μC and q₂ = −2 μC separated by 0.3 m.
Three charges lie on a line: q₁ = +2 μC at x = 0, q₂ = −2 μC at x = 0.3 m, q₃ = +2 μC at x = 0.6 m. Find the net force on q₂.
Two equal charges q are separated by 0.5 m and repel each other with 0.36 N. Find q.
F = (kq²)/(r²)q₁ = +3 μC is at the origin. q₂ = +3 μC is at (0.4 m, 0). A third charge q₃ = −1 μC is at (0.2 m, 0.2 m). Find the net force on q₃ (magnitude and direction).
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