In simple terms
A friendly intro before the formal notes — no formulas yet.
Electric force between point charges
Cambridge 9702 Paper 4 - Electric force between point charges (18.3). Senpai Corner diagram-backed pilot with premium structure and live visuals.
- 1
The electrostatic force is directly proportional to the product of the magnitudes of the charges ().
- 2
The force is inversely proportional to the square of the distance separating the charges ().
- 3
Charges of the same sign (both positive or both negative) result in a repulsive force.
- 4
Charges of opposite signs (one positive and one negative) result in an attractive force.
What this topic covers
The official Cambridge syllabus points this lesson works through.
- 18.3.1
Understand that, for a point outside a spherical conductor, the charge on the sphere may be considered to be a point charge at its centre
- 18.3.2
Recall and use Coulomb's law for the force between two point charges in free space
Explore the concept
Use the live diagram, PhET or GeoGebra sim, and synced steps — play it, drag controls, or tap a step.
Step-synced diagram — highlights what to look for in the simulation above.
Step 1
The electrostatic force is directly proportional to the product of the magnitudes of the charges ().
9 more simulations for this topic — run them in the Simulations section below
Simulations
Every simulation here runs the real model — try the steps on a card, then check what you see against the notes.
9 simulations · 4 to start with
Start herein this order — each one shows a different piece of the topic
- 3JCN PhysicsStart here · 19702 18.3 · IB D.2
Coulomb's Law 3 Charges
Three-charge Coulomb problem: find the net force on each charge
Why this one: Add a third charge and find the net force on each by adding the two Coulomb forces as vectors.
Try this
- Find the force on each charge from the other two.
- Add the two force vectors to get the net force.
Look for The net force is the vector sum of the separate Coulomb forces.
3JCN Physics Simulation by Thomas Nguyen · CC BY 4.0
- oPhysicsStart here · 29702 18.3 · IB D.2
Coulomb's Law with Two Charged Objects
Two charged objects: set charges and positions; see Coulomb force vectors and magnitudes
Why this one: Watch the force vectors: equal and opposite, repulsive for like charges, attractive for unlike.
Try this
- Double one charge and read the force.
- Double the separation and read it again.
- Make the charges opposite in sign.
Look for The force is proportional to each charge and to 1/r², and the pair of forces are equal and opposite.
Simulation by Tom Walsh, oPhysics.com — made with GeoGebra · Licensed to MarkScheme (site: free for non-profit educational use; applets made with GeoGebra)
- 3JCN PhysicsStart here · 39702 18.3 · 9702 1.3 · 9702 Paper 5
Coulomb's Law for Lab
Coulomb's law for lab: collect force-distance data and fit the inverse square
Why this one: Collect force against distance and fit it to show the inverse-square law.
Try this
- Collect force readings at several separations.
- Plot force against 1/r² and check for a straight line.
Look for Force against 1/r² is a straight line through the origin, confirming the inverse square law.
3JCN Physics Simulation by Thomas Nguyen · CC BY 4.0
- 3JCN PhysicsStart here · 49702 18.3 · IB D.2
Coulomb's Law 4 Charges
Four-charge Coulomb problem in a square arrangement
Why this one: Work out the resultant force on a corner charge of a square of four charges.
Try this
- Find the net force on one corner charge from the other three.
- Compare the contribution of the diagonal charge with the adjacent ones.
Look for The diagonal charge is √2 farther away, so its force is half the size of each adjacent one.
3JCN Physics Simulation by Thomas Nguyen · CC BY 4.0
More simulations5 more on this topic — core ones first
- oPhysicsCore9702 18.3 · IB D.2
Coulomb Forces on Three Charged Objects
Three charged objects: set charges and positions; see each pairwise force and the resultant
Try this
- Place the three charges in a line and look at the resultant on the middle one.
- Move one charge off the line.
- Make one charge negative.
Look for The resultant on each charge is the vector sum of the two pairwise Coulomb forces.
Simulation by Tom Walsh, oPhysics.com — made with GeoGebra · Licensed to MarkScheme (site: free for non-profit educational use; applets made with GeoGebra)
- The Physics ClassroomCore9702 18.3 · IB D.2
Coulomb's Law
Change the charge values and the separation and observe the force
Try this
- Double one charge and read the force.
- Double the separation and read the force.
Look for Force is proportional to q₁q₂ divided by r².
Physics Interactives by The Physics Classroom · Licensed to MarkScheme (site terms otherwise permit linking only)
- SimuPhysicsCore9702 18.3 · IB D.2
Coulomb's Law Sandbox
Place charges anywhere on the canvas and drag them around while the force arrows resize in real time
Try this
- Place two charges and read the force arrows.
- Halve the separation and compare.
- Add a third charge.
Look for Force is proportional to the product of the charges and inversely proportional to the square of the separation.
Open on SimuPhysicsRuns on their siteSimuPhysics by Mohamed Abdelsalam · Licensed to MarkScheme (site publishes no licence; served with frame-ancestors self)
- 3JCN PhysicsCore9702 18.3 · IB D.2
Coulomb's Law
Change two charges and their separation; read the Coulomb force
Try this
- Double one charge and read the force.
- Double the separation and read the force.
- Give the charges opposite signs and read the direction.
Look for F = kq1q2 / r²: doubling a charge doubles the force and doubling the separation quarters it.
3JCN Physics Simulation by Thomas Nguyen · CC BY 4.0
- PhETJava · best on a laptop9702 18.1 · 18.3 · IB D.2
Electric Field Hockey
Place fixed positive and negative charges to steer a moving puck into the goal using electrostatic force.
Try this
- Place one positive charge behind the puck and start — it is pushed away.
- Add a negative charge near the goal to pull the puck in.
- Turn on the field lines to see where the puck will be pushed.
Look for Force follows the field lines; like charges push, unlike charges pull, and closer charges act more strongly.
Simulation by PhET Interactive Simulations, University of Colorado Boulder · Licensed to MarkScheme (public licence CC BY-NC 4.0 since 2026-03-30)
Key formulas
Tap any symbol to reveal exactly what it means and its units.
Tap a symbol — great for exam definitions
Full topic notes
Formal explanation with the rigour you need for the exam.
Unpacking Coulomb's Law
Coulomb's Law is the cornerstone for understanding how electric charges interact. It specifically describes the electrostatic force that exists between two stationary point charges. For uniformly charged spheres, the charge can be treated as if it were concentrated at the center, allowing the law to be applied to larger objects as well. This force always acts directly along the straight line that connects the centres of these two charges, dictating whether they are drawn together or pushed apart.
The electrostatic force is directly proportional to the product of the magnitudes of the charges ().
The force is inversely proportional to the square of the distance separating the charges ().
Charges of the same sign (both positive or both negative) result in a repulsive force.
Charges of opposite signs (one positive and one negative) result in an attractive force.
For practical calculations, the permittivity of air is typically assumed to be the same as a vacuum.
The Components of Coulomb's Law
Let's break down the formula. and represent the magnitudes of the point charges, measured in Coulombs (C). is the distance separating their centres, in metres (m). The constant term is crucial. Here, is the permittivity of free space, a fundamental physical constant with an approximate value of $8.85 \times 10^{-12} \text{ F m}^{-1}$. The combined constant, $k_e$, is approximately $8.99 \times 10^9 \text{ N m}^2 \text{ C}^{-2}$, which is often used to simplify calculations.
Superposition of Electric Forces
What happens when more than two charges are present? The principle of superposition applies. The net electrostatic force on any one charge is the vector sum of the individual forces exerted on it by all other charges. Each force is calculated independently using Coulomb's Law and then all forces are added together as vectors, taking their directions into account.
Worked examples
See the formulas applied — reveal one step at a time, like the exam.
Two point charges, and , are separated by a distance of $0.20 \text{ m}$ in a vacuum. Calculate the magnitude of the electrostatic force between them and state its nature.
- 1
Identify knowns and state the formula:
Three point charges are placed along the x-axis. Charge is at the origin (), charge is at , and charge is at . Calculate the net electrostatic force on charge .
- 1
Apply the Principle of Superposition:
How it all connects
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Tap a linked idea to see how it connects back to the main topic — that connection is what examiners reward.
Glossary
Key terms for this topic — skim now; the Check step will test them.
- permittivity of free space
Here, is the permittivity of free space, a fundamental physical constant with an approximate value of $8.85 \times 10^{-12} \text{ F m}^{-1}
- nature of the force
Repulsive.
- For charged spheres,
At their geometric center.
Quick check
Write your answer first, then compare it with the model one — the gap is what you would have lost.
Teach it back
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Teach it back
Explain this topic as if teaching a friend. We name the gaps an examiner would still dock.
Revision flashcards
Guess first, then flip — retrieval beats re-reading.
Key takeaways
Review these before you close the topic — retrieval beats re-reading.
The electrostatic force is directly proportional to the product of the magnitudes of the charges ().
The force is inversely proportional to the square of the distance separating the charges ().
Charges of the same sign (both positive or both negative) result in a repulsive force.
Charges of opposite signs (one positive and one negative) result in an attractive force.
For practical calculations, the permittivity of air is typically assumed to be the same as a vacuum.
Practice — then mark it
The whole point: a real Cambridge question, marked mark-by-mark.
Show that the distance y of point P from the centre of sphere Y is equal to 2x.
State Coulomb's law.
Extra simulations & links
PhET, GeoGebra and other curated tools — open in a new tab.
Frequently asked
Checkpoint
One marked question is worth ten re-reads — close the loop before you move on.
Reading it isn’t knowing it — prove it.
Before you move on: do 9702/41 · Q5(c)(i) on paper, snap a photo, and get examiner-style feedback on exactly where you win and lose marks.
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