Coulomb's Law
Force between two point charges.
Formula
Variables
How it works
Coulomb’s law tells you the size of the electric force between two point charges: like charges repel and opposite charges attract. The force gets stronger when either charge is larger, and it falls off with the square of the distance, which means doubling the separation makes the force one-quarter as big. The constant k sets the scale of electric interaction in vacuum or air, and the inverse-square form comes from how electric influence spreads out uniformly in three-dimensional space.
When to use it
Use this formula when you need the force between two isolated charged objects, especially in electrostatics problems with point charges or objects that can be treated as point charges. It is also the starting point for many problems involving electric fields, charge distributions, and comparisons of how force changes with distance or charge size.
Worked example, step by step
Two point charges are separated by 0.20 m: q1 = +3.0 µC and q2 = -5.0 µC. Step 1: Write Coulomb’s law: F = k(q1q2)/r^2 Step 2: Convert microcoulombs to coulombs: q1 = 3.0 × 10^-6 C, q2 = -5.0 × 10^-6 C Step 3: Substitute values with k = 8.99 × 10^9 N·m^2/C^2 F = (8.99 × 10^9) [(3.0 × 10^-6)(-5.0 × 10^-6)] / (0.20)^2 Step 4: Multiply the charges: (3.0 × 10^-6)(-5.0 × 10^-6) = -1.5 × 10^-11 Step 5: Square the distance: (0.20)^2 = 0.040 Step 6: Compute the force: F = (8.99 × 10^9)(-1.5 × 10^-11) / 0.040 = -3.37 N Final answer: The force has magnitude 3.4 N and is attractive because the charges have opposite signs.
Common mistakes to avoid
- Forgetting to convert microcoulombs, nanocoulombs, or other prefixes into coulombs before calculating
- Using the wrong distance, such as the distance from a charge to a surface instead of the center-to-center separation
- Ignoring the sign of the charges and forgetting that like charges repel while opposite charges attract
Did You Know?
The electric force between two protons is about 10³⁶ times stronger than the gravity between them.
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