Coulomb's Law
Electrostatic force between two point charges.
Formula
Variables
Example
Like charges repel and opposite charges attract, with force dropping as 1/r².
How it works
Coulomb's Law gives the size of the electric force between two point charges. The force becomes stronger when either charge is larger, and it weakens rapidly as the charges are moved farther apart because the effect spreads out over a larger spherical area, giving the inverse-square relationship. The constant k sets the scale of electric interaction in SI units and comes from the measured strength of electrostatic forces in vacuum.
When to use it
Use this formula whenever you need the force between two stationary point charges, or when charged objects can be approximated as point charges. It is common in electrostatics problems involving attraction/repulsion, charge separation, and force balance.
Worked example, step by step
A +3.0 μC charge and a -2.0 μC charge are 0.50 m apart. Find the magnitude of the force. F = k(q1q2)/r^2 F = (8.99×10^9) × [(3.0×10^-6)(2.0×10^-6)] / (0.50)^2 F = (8.99×10^9) × (6.0×10^-12) / 0.25 F = 0.05394 / 0.25 F = 0.216 N Since the charges are opposite, the force is attractive. Final answer: 0.22 N attractive
Common mistakes to avoid
- Forgetting to convert microcoulombs or nanocoulombs into coulombs before calculating
- Using the sign of the charges in the arithmetic instead of reporting force direction separately
- Using the formula for extended objects without checking whether the point-charge approximation is valid
Did You Know?
Coulomb measured the incredibly tiny electric force using a delicate torsion balance he built himself.
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