Coulomb's Law

Fields
definition

Also known as: electrostatic force law

Grade 9-12

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Coulomb's law gives the electric force between two point charges. Coulomb's law is the foundation of electrostatics.

Definition

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.

💡 Intuition

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

🎯 Core Idea

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

Example

Two charges of 2\,\mu\text{C} and 3\,\mu\text{C} separated by 0.50 m exert a force of about 0.22 N on each other: F = kq_1q_2/r^2.

Formula

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

Notation

F is the force in newtons, q_1 and q_2 are the charges in coulombs, r is the separation in metres, k is Coulomb's constant, and \epsilon_0 is the permittivity of free space.

🌟 Why It Matters

Coulomb's law is the foundation of electrostatics. It explains how charged particles interact in atoms, electric fields, capacitors, and many devices from photocopiers to particle accelerators. It also gives the starting point for electric field and electric potential calculations.

💭 Hint When Stuck

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.

Formal View

Coulomb's law in vector form is \vec{F}_{12} = \frac{1}{4\pi\epsilon_0}\frac{q_1 q_2}{r^2}\hat{r}_{12}, where \hat{r}_{12} points from charge 1 to charge 2. The constant k = 1/(4\pi\epsilon_0) \approx 8.99 \times 10^9 N·m²/C².

🚧 Common Stuck Point

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

⚠️ Common Mistakes

  • Forgetting the inverse-square dependence — halving the distance quadruples the force, not just doubles it.
  • Using the distance between the surfaces of two charged spheres instead of the distance between their centres — Coulomb's law uses centre-to-centre distance for point charges and uniform spheres.
  • Dropping the sign of the charges and getting the force direction wrong — like charges repel (positive force away) and unlike charges attract (force toward each other).

Common Mistakes Guides

Coulomb's Law

Frequently Asked Questions

What is Coulomb's Law in Physics?

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.

What is the Coulomb's Law formula?

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

When do you use Coulomb's Law?

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.

How Coulomb's Law Connects to Other Ideas

To understand coulomb's law, you should first be comfortable with electric charge and electric field. Once you have a solid grasp of coulomb's law, you can move on to electric potential.

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