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Coulomb's Law Calculator

Find the electrostatic force between two point charges with F = k q₁ q₂ / r² — or solve for a charge or the separation. Uses Coulomb's constant k = 8.988×10⁹ N·m²/C².

 

Formula

$$ F = k\,\dfrac{q_1 q_2}{r^{2}} \qquad r = \sqrt{\dfrac{k\,q_1 q_2}{F}} \qquad q_1 = \dfrac{F\,r^{2}}{k\,q_2} $$
k = 8.988×10⁹ N·m²/C²

Worked example

Two 1 µC charges 1 cm apart repel with \( F = (8.988\times10^{9})(10^{-6})(10^{-6})/(0.01)^2 \approx 90\ \text{N} \). A positive result means repulsion (like charges); a negative product means attraction.

How it works

Coulomb's law gives the force between two point charges: F = k q₁ q₂ / r², where k = 8.988×10⁹ N·m²/C², charges are in coulombs and separation in metres. Like Newton's gravity, it follows an inverse-square law.

If both charges have the same sign the force is repulsive (positive); opposite signs give an attractive (negative) force. When solving for a charge or distance this calculator uses the magnitudes; interpret the sign from whether the charges are alike or opposite.

Frequently asked questions

What is Coulomb's law?

Coulomb's law states the electric force between two point charges is F = k q₁q₂/r² — proportional to the product of the charges and inversely proportional to the square of the distance between them.

What is the value of Coulomb's constant?

k ≈ 8.988×10⁹ N·m²/C², often rounded to 9×10⁹. It equals 1/(4πε₀), where ε₀ is the permittivity of free space.

How do you know if the force is attractive or repulsive?

Like charges (both + or both −) repel; opposite charges attract. The sign of the product q₁q₂ tells you: positive means repulsion, negative means attraction.

How is Coulomb's law similar to gravity?

Both are inverse-square laws with the same 1/r² form. Coulomb's law can be attractive or repulsive, while gravity is always attractive and vastly weaker.

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