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Question

Two point charges \( 6 \times 10^{-7} \, \text{C} \) and \( 9 \times 10^{-7} \, \text{C} \) are 45 cm
apart in air. What is the magnitude of the force between them?

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Explanation

**Independent action of charges** allows total force or field as vector sum. Geometry dictates distances to evaluation point, and resultant follows Σ k q_i/r_i², explaining zero field at symmetric centres for equal charges. Using Coulomb’s law: F = k (|q₁ q₂|/r²) . k = 9 × 10⁹ N·m²/C² , q₁ = 6 × 10⁻⁷ C , q₂ = 9 × 10⁻⁷ C , r = 0.45 m . |q₁ q₂| = 6 × 9 × 10⁻¹⁴ = 54 × 10⁻¹⁴ C² . r² = (0.45)² = 0.2025 m² . F = 9 × 10⁹ × (54 × 10⁻¹⁴/0.2025) = 9 × 10⁹ × 2.667 ×

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