Coulomb's Law Examples in Physics

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Coulomb's Law.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Physics.

Concept Recap

Coulomb's law gives the electric force between two point charges. The force gets larger when the charges are larger and gets smaller with the square.

Like gravity between masses, but for charges. Double the distance and the force drops to one quarter. Double either charge and the force doubles.

Read the full concept explanation →

How to Use These Examples

  • Read the first worked example with the solution open so the structure is clear.
  • Try the practice problems before revealing each solution.
  • Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Electric force follows an inverse-square law, just like gravity, but can be attractive or repulsive.

Common stuck point: Like charges repel, unlike charges attract — the sign of the force tells you the direction.

Sense of Study hint: When solving a Coulomb's law problem, identify the two charges q_1 and q_2 and the distance r between them. Then substitute into F = kq_1 q_2/r^2. Use the magnitudes for the force size and the signs to determine direction: same-sign charges repel, opposite-sign charges attract.

Common Mistakes to Watch For

Before you work through the examples, skim the mistake guide so you know which shortcuts and sign errors to avoid.

Coulomb's Law Mistakes

Worked Examples

Example 1

medium
Two charges q_1 = 3 \times 10^{-6} \text{ C} and q_2 = 5 \times 10^{-6} \text{ C} are separated by 0.2 \text{ m}. What is the electrostatic force between them? Use k = 9 \times 10^9 \text{ N m}^2/\text{C}^2.

Solution

  1. 1
    Apply Coulomb's law: F = k\frac{|q_1 q_2|}{r^2}
  2. 2
    F = 9 \times 10^9 \times \frac{3 \times 10^{-6} \times 5 \times 10^{-6}}{(0.2)^2}
  3. 3
    F = 9 \times 10^9 \times \frac{15 \times 10^{-12}}{0.04} = 9 \times 10^9 \times 3.75 \times 10^{-10} = 3.375 \text{ N}

Answer

F = 3.375 \text{ N}
Coulomb's law describes the electrostatic force between two point charges. Like gravity, it follows an inverse-square law, but it can be attractive or repulsive depending on the signs of the charges.

Example 2

hard
Two identical charges experience a force of 0.1 \text{ N} when separated by 0.3 \text{ m}. What is the magnitude of each charge?

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

medium
If the distance between two charges is tripled, by what factor does the electrostatic force change?

Example 2

hard
Two charges q_1 = +4 \times 10^{-6} \text{ C} and q_2 = -2 \times 10^{-6} \text{ C} are separated by 0.1 \text{ m}. (a) Calculate the force between them. (b) Is the force attractive or repulsive? Use k = 9 \times 10^9 \text{ N m}^2/\text{C}^2.
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Background Knowledge

These ideas may be useful before you work through the harder examples.

electric chargeelectric field