Coulomb's law proportionality constant

Meaning: Coulomb's law says the electrostatic force between two point charges is proportional to the product of the charges and inversely proportional to the square of their separation. The constant k turns that proportionality into an equation that gives force in newtons. Its value is about 8.99 × 10⁹ N·m²/C², usually rounded to 9.0 × 10⁹ on the exam. It is written as 1/(4πε₀), where ε₀ is the permittivity of free space. In a material medium the permittivity is larger, so the force is smaller by the dielectric constant κ.

Equation: F = kq₁q₂/r², with k = 1/(4πε₀). F is the force in N, q₁ and q₂ are the charges in C, r is the separation in m, k is in N·m²/C², and ε₀ = 8.85 × 10⁻¹² C²/(N·m²).

On the MCAT: k is the electric counterpart of G in F = Gm₁m₂/r², but it is far larger, so electric forces dominate gravity between charged particles. Questions ask for ratios, such as doubling r cuts F to one quarter and doubling one charge doubles F, and k cancels. Other direct uses are E = kq/r², V = kq/r and U = kq₁q₂/r.

Common confusion: k is not the dielectric constant κ, which is dimensionless and at least 1. Changing the charges or the distance never changes k. The sign of the force comes from the signs of the charges, not from k, which is positive.