Coulomb'ss Law Calculator
Calculate coulomb's law calculator calculate electrostatic force F = ke * |q1 * q2| / r^2 in Newtons from point charges q1, q2 in microcoulombs and separation distance r. Accurate physics formulas and unit conversions for engineers, students & technicians.
Calculate Electrostatic Force (F = k_e · |q_1 · q_2| / r²)
Enter your physical parameters below to compute verified electrostatic metrics.
Calculation Results
Calculated using verified physical methodology: Coulomb's Law Electrostatic Force: F = k_e \cdot \|q_1 \cdot q_2| / r^2
\text{Coulomb Constant: } k_e = 8.98755 \times 10^9 \text{ N}\cdot\text{m}^2/\text{C}^2 = \1 / 4\pi\varepsilon_0
Quick Summary
The Coulomb's Law Calculator evaluates electrostatic force ($F = k_e \cdot \|q_1 \cdot q_2| / r^2$) between two point charges ($q_1, q_2$) at distance ($r$) in Newtons (N), Kilonewtons (kN), and Imperial pounds-force (lbf).
Formula Explanation
Coulomb's Law Electrostatic Force: F = k_e \cdot \|q_1 \cdot q_2| / r^2
\text{Coulomb Constant: } k_e = 8.98755 \times 10^9 \text{ N}\cdot\text{m}^2/\text{C}^2 = \1 / 4\pi\varepsilon_0
How It Works
The Coulomb's Law Calculator converts charges ($q_1, q_2$) from Microcoulombs ($\mu\text{C}$) to Coulombs ($q \times 10^{-6}\text{ C}$). It multiplies Coulomb constant $k_e = 8.98755 \times 10^9\text{ N}\cdot\text{m}^2/\text{C}^2$, $|q_1 \cdot q_2|$, and divides by $r^2$. It outputs force ($F$) in Newtons, vector nature (repulsive vs attractive), and electric field intensity.
Step-by-Step Worked Example
Practical Problem: Calculate the electrostatic force $F$ between two positive point charges $q_1 = +5.0\ \mu\text{C}$ and $q_2 = +10.0\ \mu\text{C}$ separated by distance $r = 0.10\text{ meters}$ (10 cm) in vacuum.
- Step 1: Identify Input Parameters: $q_1 = 5.0 \times 10^{-6}\text{ C}$, $q_2 = 10.0 \times 10^{-6}\text{ C}$, $r = 0.10\text{ m}$.
- Step 2: Calculate Charge Product ($q_1 \cdot q_2$): $5.0\times 10^{-6} \times 10.0\times 10^{-6} = 5.00 \times 10^{-11}\text{ C}^2$.
- Step 3: Calculate Distance Squared ($r^2$): $r^2 = (0.10)^2 = 0.0100\text{ m}^2$.
- Step 4: Apply Coulomb's Law Formula ($F = k_e \cdot \frac{5.0\times 10^{-11}}{0.0100}$): $F = 8.98755 \times 10^9 \times 5.00 \times 10^{-9} = 44.9378\text{ Newtons (N)}$.
- Step 5: Determine Force Direction & Imperial Units: Because both charges are positive (+), the force is **Repulsive** (pushing charges apart). Imperial Force = $44.94 \times 0.224809 = 10.10\text{ lbf}$. Equivalent mass force = $4.58\text{ kg}$.
Real-World Calculation Examples
Scenario 1: Two Positive Lab Charges (+5µC & +10µC @ 10cm)
Parameters: $q_1 = +5\ \mu\text{C}$, $q_2 = +10\ \mu\text{C}$, $r = 0.10\text{ m}$
Result: $F = 44.938\text{ N}$ (Repulsive, 10.10 lbf). Electrostatic repulsion.
Scenario 2: Opposite Charged Electrostatic Plates (+50µC & -50µC @ 5cm)
Parameters: $q_1 = +50\ \mu\text{C}$, $q_2 = -50\ \mu\text{C}$, $r = 0.05\text{ m}$
Result: $F = 8,987.55\text{ N}$ ($8.988\text{ kN}$, Attractive). Strong electrostatic attraction.
Scenario 3: Hydrogen Atom Proton & Electron ($1.6\times 10^{-19}\text{C}$ @ 53 pm)
Parameters: $q_1 = +1.602\times 10^{-19}\text{ C}$, $q_2 = -1.602\times 10^{-19}\text{ C}$, $r = 5.29177\times 10^{-11}\text{ m}$
Result: $F = 8.238 \times 10^{-8}\text{ N}$ (Atomic attraction force).
Scenario 4: Thundercloud Static Charge (+10 Coulombs & -10 C @ 1,000m)
Parameters: $q_1 = +10\text{ C}$, $q_2 = -10\text{ C}$, $r = 1,000\text{ m}$
Result: $F = 898.76\text{ kN}$ (898,755 N, Attractive cloud force).
Key Benefits of Using This Calculator
Inverse-Square Distance Scaling ($r^2$)
Demonstrates how doubling charge separation distance ($r$) reduces electrostatic force to 25% (inverse-square law).
Charge Sign & Vector Direction
Automatically determines whether electrostatic force is Repulsive (like signs) or Attractive (opposite signs).
Multi-Unit Readouts
Outputs force in Newtons (N), Kilonewtons (kN), Imperial pounds-force (lbf), and electric field intensity.
100% Free & Client-Side
Executes locally in your browser with zero latency or web server transmission.
Frequently Asked Questions (FAQ)
What is Coulomb's Law?
Coulomb's Law states that the electrostatic force F between two stationary point charges is directly proportional to the product of their charge magnitudes (|q1 * q2|) and inversely proportional to the square of separation distance r² (F = ke * |q1 * q2| / r²).
What is Coulomb Constant ke?
Coulomb constant ke = 1 / (4 * pi * epsilon0) = 8.98755179 x 10^9 N*m²/C² in vacuum/air, where epsilon0 = 8.854187 x 10^-12 F/m is vacuum permittivity.
What is the fundamental law of electric charges?
Like charges REPEL each other (+ and +, or - and -); Opposite charges ATTRACT each other (+ and -).
What is 1 Coulomb of charge?
1 Coulomb (C) is an enormous quantity of electric charge equal to approximately 6.2415 x 10^18 elementary electron charges (1 e = 1.602176 x 10^-19 C).
How does dielectric medium relative permittivity epsilon_r affect Coulomb force?
In a dielectric medium (e.g. water epsilon_r = 80), electrostatic force is REDUCED by factor epsilon_r: F_medium = F_vacuum / epsilon_r.
How compares Coulomb's Law to Newton's Law of Universal Gravitation?
Both are inverse-square laws (F proportional to 1/r²); however, Coulomb force acts on charges (q1, q2) and can be attractive OR repulsive, whereas gravity acts on masses (m1, m2) and is ALWAYS attractive.
Why is electrostatic force vastly stronger than gravity at atomic scales?
For two protons, electrostatic repulsion is approximately 10^36 times stronger than gravitational attraction!
Who formulated Coulomb's Law?
French physicist Charles-Augustin de Coulomb published the experimental inverse-square law in 1785 using a precision torsion balance.
How converts Microcoulombs (uC) to Coulombs (C)?
Divide Microcoulombs by 1,000,000 (1 uC = 1 x 10^-6 Coulombs).
What is principle of superposition for multiple charges?
The total electrostatic force on a charge due to multiple surrounding charges equals the vector sum of individual Coulomb forces exerted by each charge independently.