Coulomb's Law Formula

The Formula

F = k\frac{|q_1||q_2|}{r^2} where k \approx 8.99 \times 10^9 N m^2/C^2.

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

Quick Example

Two charges of 1 C placed 1 m apart experience a force of about 9 billion newtons — enormous, showing how strong electric forces are.

What This Formula Means

The force between two point charges is proportional to the product of their charges and inversely proportional to the square of the distance between them.

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

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?

Why This Formula Matters

Coulomb's law quantifies the electric force and is the foundation of electrostatics.

Frequently Asked Questions

What is the Coulomb's Law formula?

The force between two point charges is proportional to the product of their charges and inversely proportional to the square of the distance between them.

How do you use the Coulomb's Law formula?

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

Why is the Coulomb's Law formula important in Physics?

Coulomb's law quantifies the electric force and is the foundation of electrostatics.

What do students get wrong about Coulomb's Law?

Like charges repel, unlike charges attract — the sign of the force tells you the direction.

What should I learn before the Coulomb's Law formula?

Before studying the Coulomb's Law formula, you should understand: electric charge, electric field.

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