Coulomb's Law Formula

Coulomb's law gives the electric force between two point charges.

The Formula

F=k∣q1∣∣q2∣r2F = k\frac{|q_1||q_2|}{r^2} where k≈8.99×109k \approx 8.99 \times 10^9 N m2^2/C2^2.

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 2 μC2\,\mu\text{C} and 3 μC3\,\mu\text{C} separated by 0.50 m exert a force of about 0.220.22 N on each other: F=kq1q2/r2F = kq_1q_2/r^2.

Notation

FF is the force in newtons, q1q_1 and q2q_2 are the charges in coulombs, rr is the separation in metres, kk is Coulomb's constant, and ϵ0\epsilon_0 is the permittivity of free space.

What This Formula Means

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.

Formal View

Coulomb's law in vector form is F⃗12=14πϵ0q1q2r2r^12\vec{F}_{12} = \frac{1}{4\pi\epsilon_0}\frac{q_1 q_2}{r^2}\hat{r}_{12}, where r^12\hat{r}_{12} points from charge 1 to charge 2. The constant k=1/(4πϵ0)≈8.99×109k = 1/(4\pi\epsilon_0) \approx 8.99 \times 10^9 N·m²/C².

Worked Examples

Example 1

medium
Two charges q1=3×10−6 Cq_1 = 3 \times 10^{-6} \text{ C} and q2=5×10−6 Cq_2 = 5 \times 10^{-6} \text{ C} are separated by 0.2 m0.2 \text{ m}. What is the electrostatic force between them? Use k=9×109 N m2/C2k = 9 \times 10^9 \text{ N m}^2/\text{C}^2.

Answer

F=3.375 NF = 3.375 \text{ N}

First step

1
Apply Coulomb's law: F=k∣q1q2∣r2F = k\frac{|q_1 q_2|}{r^2}

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Example 2

hard
Two identical charges experience a force of 0.1 N0.1 \text{ N} when separated by 0.3 m0.3 \text{ m}. What is the magnitude of each charge?

Example 3

medium
Two identical charges 1.5×10−6 C1.5\times 10^{-6}\text{ C} repel with 9 N9\text{ N}. Find the separation. Use k=9×109k = 9\times 10^9.

Common Mistakes

  • Forgetting the inverse-square dependence — halving the distance quadruples the force, not just doubles it. - Fix this by naming the system, checking "Am I using a field or potential to explain how one object influences another across space?", and attaching units or direction to the final statement.
  • 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. - Fix this by naming the system, checking "Am I using a field or potential to explain how one object influences another across space?", and attaching units or direction to the final statement.
  • 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). - Fix this by naming the system, checking "Am I using a field or potential to explain how one object influences another across space?", and attaching units or direction to the final statement.
  • Using coulomb's law from a keyword alone - Signal words like field, charge, magnet only point to a possible model; the system must match too.

Common Mistakes Guide

If this formula feels simple in isolation but keeps breaking during real problems, review the most common errors before you practice again.

Coulomb's Law Mistakes

Why This Formula Matters

Coulomb's Law gives students a way to explain non-contact forces and energy changes. It connects electricity, magnetism, gravitation, induction, motors, generators, and orbital motion through a shared spatial model.

Frequently Asked Questions

What is the Coulomb's Law formula?

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.

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.

What do the symbols mean in the Coulomb's Law formula?

FF is the force in newtons, q1q_1 and q2q_2 are the charges in coulombs, rr is the separation in metres, kk is Coulomb's constant, and ϵ0\epsilon_0 is the permittivity of free space.

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

Coulomb's Law gives students a way to explain non-contact forces and energy changes. It connects electricity, magnetism, gravitation, induction, motors, generators, and orbital motion through a shared spatial model.

What do students get wrong about Coulomb's Law?

Students often know a formula related to coulomb's law but skip the recognition step: Am I using a field or potential to explain how one object influences another across space? That leads to a correct-looking substitution attached to the wrong physical model.

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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