Coulomb's Law

Two charged objects push or pull on each other with an electric force. That force grows if either charge is bigger, but it fades very quickly as the charges move apart — doubling the distance between them cuts the force to just one quarter.

F = k · q₁ · q₂ / r²

• F — force (N): the electric push or pull between the two charges
• k — Coulomb's constant (N·m²/C²): a fixed number, about nine times ten to the ninth, that sets the strength of the electric force
• q₁ — first charge (C): the amount of electric charge on the first object
• q₂ — second charge (C): the amount of electric charge on the second object
• r — distance (m): the distance between the centers of the two charges

Two small charges, q₁ = 2 μC and q₂ = 1 μC, sit 0.1 meters apart. What electric force do they exert on each other?

• q₁ = 2 μC
• q₂ = 1 μC
• r = 0.1 m

1. F = k · q₁ · q₂ / r²
2. F = (9×10⁹ · 2×10⁻⁶ · 1×10⁻⁶) / (0.1)²

F = 1.8 N

The same two charges are pulled apart to twice the distance, 0.2 meters. What is the new force?

• 0.9 N
• 0.45 N
• 3.6 N

Keeping r at 0.1 meters, q₁ is doubled to 4 μC while q₂ stays at 1 μC. What is the new force?

• 1.8 N
• 0.9 N
• 3.6 N