Coulomb's Law
Electrostatic force between two charges.
Formula
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Example
Two 1 μC charges 1 m apart repel with F = 9×10⁹·(10⁻⁶)²/1² ≈ 9 mN.
How it works
Coulomb’s law gives the magnitude of the electric force between two point charges, showing that the force grows with the size of the charges and falls off with the square of their separation. The constant k sets the scale in vacuum and is related to the permittivity of free space, which is why electrostatic forces have the strength they do in everyday SI units. The inverse-square dependence comes from the fact that the electric field from a point charge spreads out uniformly over the surface of a sphere, so its intensity drops as 1/r².
When to use it
Use this when finding the force between isolated charged objects, such as small spheres, ions, or idealized point charges in electrostatics. It is also the starting point for analyzing electric fields, superposition of multiple charges, and comparing how force changes when distance or charge changes.
Worked example, step by step
Two charges, +3.0 μC and -2.0 μC, are separated by 0.50 m. Step 1: Write the formula: F = k(q1q2)/r^2 Step 2: Substitute values: F = (8.99×10^9)(3.0×10^-6)(2.0×10^-6)/(0.50)^2 Step 3: Multiply the charges: (3.0×10^-6)(2.0×10^-6) = 6.0×10^-12 Step 4: Square the distance: (0.50)^2 = 0.25 Step 5: Compute the force: F = (8.99×10^9 × 6.0×10^-12) / 0.25 = 0.21576 N Step 6: Final answer: F ≈ 0.216 N Because the charges have opposite signs, the force is attractive.
Common mistakes to avoid
- Forgetting to square the distance r in the denominator
- Using charge units in microcoulombs without converting to coulombs
- Treating the sign of q1q2 as the force magnitude instead of using it to decide attraction vs. repulsion
Did You Know?
The electric force is about 10³⁶ times stronger than gravity — which is why atoms hold together.
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