04 // Interactive Formula Compendium // PHYSICSF = k_e · |q₁ · q₂| / r², where k_e = 1 / (4π ε₀)
Coulomb's Law of Electrostatic Force & Electric Field Potential Sheet
Coulomb's Law states that the electrostatic force between two point charges q₁ and q₂ separated by distance r is F = k_e |q₁ q₂| / r² (repulsive for like signs, attractive for opposite signs), where k_e = 1/(4πε₀) ≈ 8.98755 × 10⁹ N·m²/C².
Formula Reference
Main Formula
F = k_e · |q₁ · q₂| / r², where k_e = 1 / (4π ε₀)
Rearranged Forms
E = F / q₀ = k_e · |Q| / r² (Point-Charge Electric Field in N/C or V/m)
V = k_e · Q / r, U_e = k_e · (q₁ · q₂) / r (Electric Potential & Energy)
k_e = 8.98755 × 10⁹ N·m²/C², ε₀ = 8.85419 × 10⁻¹² F/m
Variables & Units
| Symbol | Name | Unit |
|---|---|---|
| F | Electrostatic Force Magnitude (F) | N |
| q1_uC | Point Charge |q₁| (microcoulombs, μC) | μC |
| q2_uC | Point Charge |q₂| (microcoulombs, μC) | μC |
| r | Separation Distance (r) | m |
Inputs & Parameters
[μC]
[μC]
[m]
Calculated Result (Electrostatic Force Magnitude (F))
F =0.998617N
Formula Notes & Background
- Start with Gauss's Law ∮ E · dA = Q_enc / ε₀ over a concentric spherical surface of area 4πr² around point charge Q.
- By spherical symmetry, E(4πr²) = Q / ε₀ ⇒ E = Q / (4πε₀ r²) = k_e Q / r².
- Placing a second charge q₂ in field E produces the Lorentz electrostatic force F = q₂ E = k_e q₁ q₂ / r².
Step-by-Step Examples
#1: Calculate the electrostatic force between q₁ = +5.0 μC and q₂ = −2.0 μC separated by r = 0.30 m in air.
|q₁| = 5 × 10⁻⁶ C|q₂| = 2 × 10⁻⁶ Cr = 0.30 m
F = (8.98755×10⁹ × 5×10⁻⁶ × 2×10⁻⁶) / (0.30)² = 0.089876 / 0.09
→ F = 0.9986 N (attractive since signs are opposite)
#2: Compare the electrostatic attraction vs. gravitational attraction between a proton and electron in a hydrogen atom (r = 5.29 × 10⁻¹¹ m).
|e| = 1.602 × 10⁻¹⁹ Cm_p = 1.673 × 10⁻²⁷ kgm_e = 9.109 × 10⁻³¹ kg
F_e / F_g = (k_e e²) / (G m_p m_e) = 2.307×10⁻²⁸ / 1.017×10⁻⁶⁷
→ F_e / F_g ≈ 2.27 × 10³⁹ (electrostatics is 39 orders of magnitude stronger!)
Was this tool helpful?
Frequently Asked Questions
How does placing charges in water or a dielectric (relative permittivity ε_r) affect Coulomb's force?+
Dielectric polarization screens the charges, reducing the electrostatic force by a factor of ε_r: F = F_vacuum / ε_r (for water, ε_r ≈ 80, weakening ionic bonds 80-fold).
What is the Principle of Superposition for multiple point charges?+
The net force on any charge is the vector sum of the individual Coulomb forces exerted by every other charge independently: F_net = Σ F_i.
How is electric potential V related to electric field E?+
Electric field is the negative spatial gradient of electric potential: E = −∇V (or E_r = −dV/dr).