Teaching guide for the module

Electrostatics: Coulomb's Law and electric field: Teacher's Guide

Teaching guide for the Electrostatics simulator: explain in class Coulomb's Law between point charges, the electric field generated by a source charge, field lines and interactive exploration with a draggable test charge. Designed for physics teachers.

Module: Electrostatics · Two tabs: Coulomb's Law · Electric Field

Physical phenomenon

Electrostatics studies the interactions between stationary electric charges. The fundamental law, discovered by Charles-Augustin de Coulomb, states that two point charges $q_{1}$ and $q_{2}$ at distance $r$ exert a force on each other directed along the line joining them, with magnitude:

$F = k \cdot \frac{∣ q _{1} \cdot q _{2} ∣}{r ^{2}}, k \approx 8.99 \cdot 1 0^{9} N \cdot m^{2} / C^{2}$

The force is repulsive if the charges have the same sign, attractive if they have opposite signs. The $1/ r^{2}$ dependence is the same as Newton's law of gravitation, one of the deepest parallels in classical physics.

The electric field $E$ generalises the concept of electric force independently of the test charge. A charge $Q$ generates in the surrounding space a field:

$E (P) = k \cdot \frac{Q}{r ^{2}} \cdot \overset{r}{^}$

where $\overset{r}{^}$ is the unit vector from $Q$ to point $P$ . Any test charge $q_{0}$ placed at $P$ feels a force $F = q_{0} \cdot E$ . The field is therefore a property of space, "carved" by the source charges.

Field lines are curves tangent at each point to $E$ : they leave positive charges and enter negative ones, and their density is proportional to the field strength.

Key concepts

Charge quantisation: electric charge is an integer multiple of the elementary charge $e \approx 1.602 \cdot 1 0^{- 19} C$ .
Charge conservation: the total charge of an isolated system does not change.
Central force: the Coulomb force acts along the line joining the two charges.
Inverse-square law: doubling the distance reduces the force to a quarter.
Electric field vs electric force: the field is "of the place", the force concerns a specific charge placed there.
Superposition: the field produced by several charges is the vector sum of the fields produced by each.
Field lines: visual tool: they give direction and intensity of the field at a glance.

How to use it in the classroom

Opening: Coulomb's Law tab. Place two charges of the same sign and observe that the force arrows point away from each other (repulsion). Change the sign of one of them: arrows reverse (attraction). Have students compute $F$ with simple values (e.g. $q_{1} = q_{2} = + 1 nC$ , $r = 10 cm$ ) before reading the KPI.

Development: $1/ r^{2}$ dependence. Keep the charges fixed and vary only the distance. Have them double $r$ and observe that $F$ drops to a quarter. Have them compute mentally what would happen at tripled $r$ , halved $r$ . This is the moment to fix the non-linearity of the law: distance has a much "more violent" effect than simple inverse proportionality.

Deeper exploration: Electric Field tab. Switch to the electric field tab. The $7 \times 7$ grid of vectors shows the field produced by the source charge $Q$ . Drag the test charge $q_{0}$ to different points and observe the force arrow $F = q_{0} E$ , always aligned with the local field vector, modulated by the sign and value of $q_{0}$ . Highlight that the field "exists" even where $q_{0}$ is not: it is a property of space, not of the test charge.

Closing: varying $Q$ . Increase and decrease the source charge: the entire vector grid "breathes" coherently, length and opacity scaling proportionally. This is the moment to clarify that the field depends only on the sources, not on the test charge.

Real-world examples

Electrostatic rubbing. A plastic rod rubbed on a cloth acquires a negative charge and attracts small pieces of paper, everyday Coulomb's Law.
Photocopiers and laser printers. They use an electrostatically charged drum to attract toner only at points corresponding to dark areas of the image.
Electrostatic painting. Paint droplets are charged and attracted by the object to be painted, connected to opposite polarity: uniform coating with little waste.
Lightning rod. Concentrates field lines at its tip, facilitating controlled discharge of atmospheric charges to ground.
Cathode-ray tube TV (historical). An electric field accelerates and deflects a beam of electrons towards the fluorescent screen, direct application of $F = q E$ .

Classroom discussion questions

Two equal positive charges are initially at distance $r$ . If the distance becomes $2 r$ , by how much does the force between them decrease?
A test charge $+ q_{0}$ at a point feels a force of 5 N. If I replace it with $- 2 q_{0}$ at the same point, what is the new force in magnitude and direction?
What does it mean that "the field exists even without a test charge"? Why do we even talk about it then?
Three identical charges at the vertices of an equilateral triangle: what is the resultant force at the geometric centre?
Why do the Coulomb force and gravity have the same mathematical form but completely different scales?

Related modules

Forces & Vectors: the Coulomb force is a vector: it adds via the parallelogram rule and decomposes into Cartesian components.
Magnetic Force & Motor: the magnetic field is the "dual" of the electric field: same vector representation logic, but generated by moving charges.