Coulomb's Law Calculator
Find the electric force between two charges. Enter their size, how far apart they are, and see if they attract or repel.
F = k × |q₁q₂| / r²
Use scientific notation (e.g., 1e-6 for 1 μC)
Default: 8.987551787×10⁹ N⋅m²/C²
About Coulomb's Law:
Coulomb's Law describes the electrostatic force between two charged particles. The force is proportional to the product of the charges and inversely proportional to the square of the distance between them.
How the Coulomb's Law Calculator Works
Enter the magnitudes of both charges (q₁ and q₂) and the distance between them. Charges can be positive or negative. The calculator accepts values in coulombs, microcoulombs, nanocoulombs, or elementary charge units.
The calculator applies Coulomb's Law: F = k|q₁q₂|/r², where k is Coulomb's constant (8.99 × 10⁹ N⋅m²/C²), q₁ and q₂ are the charges, and r is the separation distance. The force direction (attractive or repulsive) is determined by the charge signs.
Results show the force magnitude in newtons and indicate whether the force is attractive (opposite charges) or repulsive (like charges). A diagram shows the charges with force vectors. Electric field at each charge location is also calculated.
When You'd Actually Use This
Physics homework problems
Solve electrostatics problems. Calculate forces between point charges, find equilibrium positions, or analyze charge configurations.
Atomic structure analysis
Calculate electron-proton attraction in atoms. The electrostatic force binds electrons to nuclei. Compare to gravitational force (electrostatic is 10³⁹ times stronger).
Electrostatic precipitator design
Design air pollution control devices. Charged plates attract and capture particles. Calculate forces on charged dust particles.
Particle accelerator physics
Analyze charged particle interactions. Beam dynamics depend on electrostatic repulsion between particles in the beam.
Static electricity analysis
Understand static cling and shocks. Calculate forces between charged objects. Explain why charged balloons stick to walls.
Molecular bonding estimation
Estimate ionic bond strength. Electrostatic attraction between Na⁺ and Cl⁻ holds salt crystals together. Calculate bond energies.
What to Know Before Using
Force follows inverse-square law.Double the distance, force drops to 1/4. Triple the distance, force drops to 1/9. This is the same mathematical form as gravity.
Like charges repel, opposites attract.Positive-positive or negative-negative: repulsion. Positive-negative: attraction. The calculator determines this from charge signs.
Coulomb's law applies to point charges.For extended objects, integrate over the charge distribution. Spherical charge distributions act like point charges at their center.
Force pairs are equal and opposite.Charge 1 exerts force F on charge 2. Charge 2 exerts force -F on charge 1. Newton's third law holds for electrostatic forces.
Pro tip: For multiple charges, use superposition. Calculate the force from each charge separately, then add the force vectors. Net force is the vector sum of all individual forces.
Common Questions
What's Coulomb's constant?
k = 8.99 × 10⁹ N⋅m²/C². It's related to the permittivity of free space: k = 1/(4πε₀). Determines the strength of electrostatic interactions.
How strong is the electrostatic force?
Extremely strong. Two 1 C charges 1 m apart exert 9 billion newtons of force. Typical static charges are microcoulombs, giving more modest forces.
What's an elementary charge?
e = 1.602 × 10⁻¹⁹ C. The charge of one proton (positive) or electron (negative). All charges are integer multiples of e.
Does the medium affect the force?
Yes. In a material, F = k|q₁q₂|/(εᵣr²), where εᵣ is relative permittivity. Water (εᵣ ≈ 80) reduces the force by 80× compared to vacuum.
How does this compare to gravity?
Electrostatic force is vastly stronger. Between proton and electron, electrostatic force is ~10³⁹ times stronger than gravitational attraction.
Can charges be fractional?
Quarks have fractional charges (±1/3 e, ±2/3 e), but they're never found isolated. All observable particles have integer multiples of e.
What's the electric field?
E = F/q = kQ/r². Force per unit charge. Electric field exists around any charge. Other charges feel force F = qE in the field.
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