PhysicsSolver360 logoPhysicsSolver360°
Powered by Solver360°

Coulomb's Law Calculator

Calculate the electrostatic force between two point charges with interactive animation

Parameters

Cⓘ
Cⓘ
mⓘ
Show Trail

Controls

xⓘ

Calculated Values

Force Magnitude:
0.90;N0.90;N
k/r² factor:
899000000000.00;N/C2899000000000.00;N/C²

Examples

Two 1 μC charges, 10 cm apart

Like charges — repulsive force magnitude.

  • Force Magnitude: 0.900.90

±1 μC, 20 cm apart

Opposite charges — same magnitude, attractive.

  • Force Magnitude: 0.220.22

Visualization

Coulomb's Law — Electrostatic Force Between Point Charges

Electrostatic force is the mutual force between two stationary point charges. Coulomb's law (1785) states that the magnitude is proportional to |q₁q₂| and inversely proportional to r², where r is the center-to-center distance.

In SI units, F = (1/(4πε₀))·|q₁q₂|/r² with ε₀ ≈ 8.85×10⁻¹² F/m. The Coulomb constant k = 1/(4πε₀) ≈ 8.99×10⁹ N·m²/C². In a dielectric medium, replace ε₀ with ε = κε₀ (κ = relative permittivity).

Direction: like charges repel (force pushes apart along the line joining them); unlike charges attract. Newton's third law: the force on q₁ equals and opposes the force on q₂.

Superposition principle: the net force on a charge from many others is the vector sum of individual Coulomb forces. This is the basis for calculating fields from charge distributions.

Validity: exact for point charges; for spherically symmetric distributions (e.g. uniform shell), use total charge at center when field point is outside. Breaks down at r → 0 for extended bodies.

Comparison with gravity: both are inverse-square central forces, but electrostatic force can be attractive or repulsive and is vastly stronger for elementary charges (e.g. two protons: F_e/F_g ~ 10³⁶).

Key Concepts

  • F = k|q₁q₂|/r² — scalar magnitude
  • k ≈ 8.99×10⁹ N·m²/C²; k = 1/(4πε₀)
  • Vector form: F⃗₁₂ = k q₁q₂/r̂₁₂ r²
  • Inverse square: F → F/4 when r doubles
  • Superposition: F⃗_net = Σ F⃗_i
  • Medium: multiply by 1/κ or use ε = κε₀

Real-World Applications

  • Electrostatic precipitators (dust removal in power plants)
  • Ink-jet printing and paint electrostatic spraying
  • Van de Graaff generator demonstrations
  • Ionic bonding models in chemistry
  • Class 11–12 NCERT/CBSE electrostatics problems
  • Particle accelerator beam focusing (qualitative)

Explore Further

More electricity tools

  • Ohm's Law

    Calculate voltage, current, and resistance in electrical circuits.

  • Capacitance

    Analyze charge storage and electric fields in capacitors.

  • RC Circuits

    Calculate charging and discharging of capacitors in circuits.

  • Power Calculator

    Calculate electrical power, energy consumption, and efficiency.

  • Series Circuit

    Analyze series circuits with total resistance, current, and voltage drops.

  • Parallel Circuit

    Analyze parallel circuits with current division and total resistance.

Physics Equations

Coulomb's Law:
F=k∣q1q2∣r2F = k\frac{|q_1 q_2|}{r^2}
Coulomb Constant:
k=14πε0≈8.99×109k = \frac{1}{4\pi\varepsilon_0} \approx 8.99 \times 10^9

Step-by-Step Solution

See how the main results are calculated.

1

Step 1: Identify Given Quantities

Write down charges and separation with SI units (coulombs, meters).

Result:

q1=0.000001 C,q2=−0.000001 C,r=0.1 mq_1 = 0.000001 \text{ C}, \quad q_2 = -0.000001 \text{ C}, \quad r = 0.1 \text{ m}

Explanation:

Coulomb's law applies to two point charges separated by distance r between their centers. Use SI units throughout.

2

Step 2: Write Coulomb Constant

Use k = 1/(4πε₀) in vacuum.

Equation:

k=14πε0≈8.99×109 N\cdotpm2/C2k = \frac{1}{4\pi\varepsilon_0} \approx 8.99 \times 10^9 \text{ N·m}^2/\text{C}^2

Explanation:

ε₀ ≈ 8.85×10⁻¹² F/m. In a dielectric medium, replace k with k/κ where κ is relative permittivity.

3

Step 3: Compute Charge Product

Multiply magnitudes of the two charges.

Calculation:

∣q1q2∣=∣0.000001×−0.000001∣=1.0000e−12 C2|q_1 q_2| = |0.000001 \times -0.000001| = 1.0000e-12 \text{ C}^2

Result:

∣q1q2∣=1.0000e−12C2|q_1 q_2| = 1.0000e-12 C²

Explanation:

Magnitude formula uses absolute value of product; sign determines attraction vs repulsion separately.

4

Step 4: Square the Distance

Inverse-square law requires r² in the denominator.

Calculation:

r2=(0.1)2=0.010000 m2r^2 = (0.1)^2 = 0.010000 \text{ m}^2

Result:

r2=0.010000m2r² = 0.010000 m²

Explanation:

Doubling distance increases r² by 4×, reducing force to ¼ — characteristic of inverse-square laws.

5

Step 5: Apply Coulomb's Law

Equation:

F=k∣q1q2∣r2F = k\frac{|q_1 q_2|}{r^2}

Calculation:

F=(8.99×109)×1.0000e−120.010000F = (8.99 \times 10^9) \times \frac{1.0000e-12}{0.010000}
F=8.9900e−1 NF = 8.9900e-1 \text{ N}

Result:

F=8.9900e−1NF = 8.9900e-1 N

Explanation:

This is the magnitude of the electrostatic force on each charge (Newton's third law: equal and opposite forces).

6

Step 6: Determine Force Direction

Classify interaction as attractive or repulsive.

Result:

Attractive (unlike charges)

Explanation:

Opposite signs → charges attract along the line joining them.

Frequently Asked Questions (FAQ)

Why inverse-square law?

Field lines from a point charge spread uniformly on a sphere of area 4πr², so field strength E ∝ 1/r² and force F = qE follows the same dependence.

Can Coulomb force be negative?

We usually quote magnitude F = k|q₁q₂|/r². Sign in vector form encodes attraction (opposite signs) vs repulsion (same signs).

What if charges are not point-like?

Use superposition or Gauss's law. For uniform spheres, treat as point charge at center when outside the sphere.

Does Coulomb's law work for moving charges?

Not exactly — moving charges create magnetic fields; electrostatic formula applies when charges are approximately stationary (quasi-static).

How does ε₀ relate to k?

k = 1/(4πε₀). ε₀ is the permittivity of free space, a fundamental constant in Maxwell's equations.

Practice MCQs

  1. If distance between two point charges doubles, the force becomes:
  2. The SI unit of the Coulomb constant k is:
  3. Two positive charges experience a force that is:
  4. Coulomb's law is most accurate when:
  5. Compared to gravity between two protons, electrostatic repulsion is:
  6. In a medium with κ = 4, the force between two charges compared to vacuum is:

Related Calculators

These tools connect to the same physics concepts used in this calculator.

Voltage DividerFind output voltage and current in resistive potential divider circuits.Wheatstone BridgeCheck bridge balance and calculate unknown resistance from ratio arms.ResistivityCalculate wire resistance from resistivity, length, and cross-sectional area.Capacitor EnergyFind stored charge and energy U = ½CV² with charging animation.Magnetic FieldCalculate magnetic field strength, magnetic force, and magnetic flux using Ampere's Law.Related Magnetism topic.Error PropagationCombine measurement uncertainties for sums, products, quotients, and powers in experimental formulas.Related Measurement & Uncertainty topic.Wave PropertiesCalculate wavelength, frequency, amplitude, and wave velocity.Related Waves topic.