The formula
F = (1 / 4πε₀ε_r) × (q₁ × q₂) / r² ≈ 9 × 10⁹ × q₁q₂ / r² in air
- F
- force between the charges (newtons)
- q₁, q₂
- the two point charges (coulombs)
- r
- separation between them (metres)
- ε_r
- relative permittivity of the medium (1 for air/vacuum)
Worked example
Two 1 µC charges 10 cm apart in air.
- F = 9 × 10⁹ × (1 × 10⁻⁶ × 1 × 10⁻⁶) / (0.1)²
- F = 9 × 10⁹ × 10⁻¹² / 0.01
- F = 9 × 10⁻³ / 0.01
F = 0.9 N, repulsive since both charges have the same sign.
Where you'll use it
Electrostatics questions, and the physical basis of capacitance. Immersing the charges in a dielectric with ε_r = 4 quarters the force, which is exactly why dielectrics increase a capacitor's value.