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Electromagnetism

Coulomb's Law

Coulomb’s law gives the electrostatic force magnitude between point charges.

F = \frac{k ∣ q _{1} q _{2} ∣}{r ^{2}}

Study tools

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Source & review

Difficulty

Intermediate

Read time

5 min

Prerequisites

Basic algebra, consistent units, and the stated model assumptions

Review statusNeeds review

Source

OpenStax, College Physics 2e, §18.3 (Paul Peter Urone and Roger Hinrichs)

OpenFormulaGraph equation reference; FormuLab adaptation details and license are provided below.

Adapted from OpenFormulaGraph, under CC BY 4.0.

FormuLab adapted wording, notation, applicability conditions and topic placement, and expanded the numerical check into a worked example.

Definition

Understanding the core concept

Coulomb’s law gives the electrostatic force magnitude between point charges. Like charges repel and unlike charges attract, with the force along their connecting line.

Variables & Units

Understanding each component

Symbol	Meaning	Units
$F$	Electrostatic force magnitude	$N$
$k$	Coulomb's Constant	$N \cdot m^{2} / C^{2}$
$q_{1}$	Electric charge (first charge)	$C$
$q_{2}$	Electric charge (second charge)	$C$
$r$	Charge separation	$m$

Real-World Applications

Where this formula is used in practice

Point charges

Estimate electrostatic attraction or repulsion.

Separation changes

Compare force as charge separation changes.

Worked Example

Step-by-step calculation with real numbers

Problem

Find the force magnitude between two +1.00 µC point charges separated by 1 m in vacuum.

Given

k = 8990000000 N \cdot m^{2} / C^{2}

q_{1} = 0.000001 C

q_{2} = 0.000001 C

r = 1 m

Solution

F = \frac{k ∣ q _{1} q _{2} ∣}{r ^{2}}

F = \frac{( 8990000000 N \cdot m ^{2} / C ^{2} ) \cdot ∣ ( 0.000001 C ) \cdot ( 0.000001 C ) ∣}{( 1 m ) ^{2}}

F = 0.00899 N

Final Answer

F = 0.00899 N

Formula Guide

Info

DifficultyIntermediate

Read Time5 min

PrerequisitesBasic algebra, consistent units, and the stated model assumptions

Tools

Source & review

StatusNeeds review

Last reviewedPending

Source

OpenStax, College Physics 2e, §18.3 (Paul Peter Urone and Roger Hinrichs)

OpenFormulaGraph equation reference; FormuLab adaptation details and license are provided below.

Adapted from OpenFormulaGraph, under CC BY 4.0.

FormuLab adapted wording, notation, applicability conditions and topic placement, and expanded the numerical check into a worked example.

Assumptions

• Use stationary point charges or spherical charges whose external field has the point-charge form.
• The displayed constant is for vacuum or approximately air; use the medium’s permittivity when necessary.

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Coulomb's Law

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