Find the electrostatic force between two point charges from F = kq₁q₂/r², with the charges in coulombs and the separation in metres.
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From the article Coulomb's Law — Electrostatic Force Problems Solved.
Question: Two point charges q₁ = +2 μC and q₂ = +3 μC are 30 cm apart in air. Find the force between them.
Step 1 — convert to SI. q₁ = 2 × 10⁻⁶ C, q₂ = 3 × 10⁻⁶ C, r = 30 cm = 0.30 m
Step 2 — square the distance. r² = (0.30)² = 0.09 m²
Step 3 — multiply the charges. q₁q₂ = (2 × 10⁻⁶)(3 × 10⁻⁶) = 6 × 10⁻¹² C²
Step 4 — put it together (using k = 9 × 10⁹):
F = (9 × 10⁹ × 6 × 10⁻¹²) / 0.09 = 0.054 / 0.09 = 0.60 N
Step 5 — state the direction. Both charges are positive, so the force is repulsive, along the line joining them.
Cross-check with the precise constant: k = 8.988 × 10⁹ gives 0.05393/0.09 = 0.599 N — the same to two significant figures ✔
Worked in full in Coulomb's Law — Electrostatic Force Problems Solved.
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