In simple terms
A friendly intro before the formal notes — no formulas yet.
Electric field of a point charge
Cambridge 9702 Paper 4 — Electric field of a point charge (18.4). Senpai Corner diagram-backed pilot with premium structure and live visuals.
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An electric field is a vector field created by electric charges.
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Field lines represent the path a positive test charge would take.
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Field lines point away from positive charges and towards negative charges.
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The density of field lines indicates the strength of the field.
What this topic covers
The official Cambridge syllabus points this lesson works through.
- 18.4.1
Recall and use for the electric field strength due to a point charge 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.
An isolated point charge creates a radial…
An isolated point charge creates a radial electric field.
7 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.
7 simulations · 4 to start with
Start herein this order — each one shows a different piece of the topic
- 3JCN PhysicsStart here · 19702 18.1 · 9702 18.4 · IB D.2
Electric Field of a Spherical Shell
Electric field inside and outside a charged spherical shell
Why this one: Outside a charged sphere the field is exactly that of a point charge at its centre; inside it is zero.
Try this
- Read E inside the shell.
- Read E just outside the shell and then at twice the radius.
Look for E is zero inside the shell and falls as 1/r² outside, as if the charge were at the centre.
3JCN Physics Simulation by Thomas Nguyen · CC BY 4.0
- The Physics ClassroomStart here · 29702 18.4 · 9702 18.5 · IB D.2
Electric Two-Shell Analysis
Two concentric charged shells: see how field strength and potential vary inside the inner shell, between the shells and outside
Why this one: Read E and V against r through two shells and see where each is constant, zero or 1/r².
Try this
- Probe the field inside the inner shell.
- Probe between the shells.
- Probe outside the outer shell.
Look for The field is zero inside a charged shell and the potential is constant there.
Physics Interactives by The Physics Classroom · Licensed to MarkScheme (site terms otherwise permit linking only)
- The Physics ClassroomStart here · 39702 18.1 · 9702 18.4 · IB D.2
3D Electric Field Mapping
Drag source charges onto the workspace, see the lines of force, and tap any point for the field vector; 3D view
Why this one: Tap a point between two charges and read the resultant field — superposition as vectors.
Try this
- Place a charge and tap a point to read the field.
- Double the distance and read it again.
- Add a second charge.
Look for Field strength falls as 1 divided by r² from a point charge.
Physics Interactives by The Physics Classroom · Licensed to MarkScheme (site terms otherwise permit linking only)
- oPhysicsStart here · 49702 18.1 · 9702 18.5 · 9702 18.4
Electric Field & Potential
Drag +1 nC / -1 nC point charges; see field lines and the electric potential map update
Why this one: Drag two charges around and watch the field lines and the potential map update together.
Try this
- Drag a +1 nC and a −1 nC charge near each other.
- Replace the negative charge with a second positive one.
- Move the charges apart and watch the potential map.
Look for Field lines run from positive to negative and cross equipotentials at right angles.
Simulation by Tom Walsh, oPhysics.com — made with GeoGebra · Licensed to MarkScheme (site: free for non-profit educational use; applets made with GeoGebra)
More simulations3 more on this topic — core ones first
- oPhysicsCore9702 18.5 · 9702 18.4 · IB D.2
Equipotentials & Electric Field of Two Charges
Two charges: set charge and position; plot equipotential lines and electric field around them
Try this
- Set two equal positive charges and plot the equipotentials.
- Make one charge negative.
- Move one charge further away.
Look for Field lines cross equipotentials at right angles and the field is strongest where equipotentials are closest.
Simulation by Tom Walsh, oPhysics.com — made with GeoGebra · Licensed to MarkScheme (site: free for non-profit educational use; applets made with GeoGebra)
- 3JCN PhysicsCore9702 18.1 · 9702 18.4 · IB D.2
Electric Field of Charged Particles
Place positive and negative charges; see field lines and field vectors
Try this
- Place one positive charge and look at the field lines.
- Add a negative charge and watch the lines link the two.
- Place two like charges and look for the region where the field vectors cancel.
Look for Field lines start on positive charge and end on negative charge, and are densest where the field is strongest.
3JCN Physics Simulation by Thomas Nguyen · CC BY 4.0
- 3JCN PhysicsCore9702 18.5 · 9702 18.1 · 9702 18.4
Electric Field & Equipotential Mapping
Probe a 3D field and plot equipotential lines around configured charges
Try this
- Probe the field around the configured charges and plot a few equipotential lines.
- Compare the direction of the field with the equipotentials where they cross.
- Note where the equipotentials are closest together.
Look for Field lines cross equipotentials at right angles, and closely spaced equipotentials mark a strong field.
3JCN Physics Simulation by Thomas Nguyen · CC BY 4.0
Key formulas
Tap any symbol to reveal exactly what it means and its units.
Tap a symbol — great for exam definitions
Tap a symbol — great for exam definitions
Tap a symbol — great for exam definitions
Tap a symbol — great for exam definitions
Full topic notes
Formal explanation with the rigour you need for the exam.
What is an Electric Field?
An electric field is a region in space around a charged object where another charged particle would experience a non-contact electrostatic force. We often use the concept of a 'point charge' – an idealised, infinitesimally small charge – to simplify calculations and understand fundamental principles. These fields are radial, meaning they spread outwards from positive charges and converge inwards towards negative charges.
An electric field is a vector field created by electric charges.
Field lines represent the path a positive test charge would take.
Field lines point away from positive charges and towards negative charges.
The density of field lines indicates the strength of the field.
Coulomb's Law: Force Between Point Charges
Before we look at field strength, let's remember Coulomb's Law, which describes the electrostatic force between two point charges. This law is crucial because the electric field itself is defined by the force it exerts. The force is proportional to the product of the charges and inversely proportional to the square of their separation.
is the electrostatic force (N).
are the magnitudes of the point charges (C).
is the distance between the charges (m).
is the permittivity of free space ().
Like charges repel, opposite charges attract.
Electric Field Strength (E)
The electric field strength (E) at a point is defined as the force experienced per unit positive test charge placed at that point. It's a vector quantity, with its direction being the same as the force on a positive test charge. For a single point charge, E decreases rapidly with distance.
is electric field strength (N C^{-1} or V m^{-1}).
is the magnitude of the source point charge (C).
is the distance from the point charge (m).
E follows an inverse square law: .
Electric Potential (V)
While electric field strength describes the force, electric potential (V) describes the energy 'landscape'. It's defined as the work done per unit positive test charge to bring it from infinity (where V=0) to a specific point within the field. Potential is a scalar quantity, meaning it has magnitude but no direction, and its sign matches the source charge.
is electric potential (V or J C^{-1}).
is the source point charge (C).
is the distance from the point charge (m).
Positive charges create positive potentials; negative charges create negative potentials.
V decreases with distance, , approaching zero at infinity.
The Principle of Superposition
When more than one charge is present, the total electric field and total electric potential at a point are found by summing the contributions from each charge individually. This is known as the Principle of Superposition.
For Electric Potential (V): Since potential is a scalar, the total potential is the simple algebraic sum of the individual potentials. Be sure to include the signs (+ or -) of the charges.
For Electric Field Strength (E): Since field strength is a vector, the total field is the vector sum of the individual fields. You must consider both magnitude and direction for each field vector. (vector addition).
Equipotential Lines and Surfaces
Just as contour lines on a map show points of equal height, equipotential lines (or surfaces in 3D) show points of equal electric potential. For a point charge, these are concentric circles. A key property is that no work is done by the electric field when a charge moves along an equipotential line.
Connect points of identical electric potential.
Always perpendicular to electric field lines.
No work done moving a charge along them.
Closer spacing indicates a stronger field (steeper potential gradient).
Connecting E and V: The Potential Gradient
There's a fundamental relationship between electric field strength and electric potential. The electric field strength is essentially the rate at which the potential changes with distance – known as the potential gradient. The field points in the direction of decreasing potential, like a ball rolling down a hill.
Electric field strength is the magnitude of the potential gradient.
This means is the magnitude of the slope of a against graph.
Units: (which is equivalent to ).
The negative sign (often omitted for magnitude) indicates E points from high to low potential.
Worked examples
See the formulas applied — reveal one step at a time, like the exam.
A point charge of +5.0 nC is placed in a vacuum. Calculate the electric field strength and the electric potential at a point 15 cm away from the charge. (Take )
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Convert units:
Two point charges, and , are placed on a line 10.0 cm apart in a vacuum. is at and is at m. Point P is located on the line between them, at a distance of 6.0 cm from . Calculate: (a) The net electric potential at P. (b) The net electric field strength at P. (Take )
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Identify charges and distances:
How it all connects
The big idea sits in the middle — tap a linked idea to explore the link.
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.
- electric field
An electric field is a region in space around a charged object where another charged particle would experience a non-contact electrostatic force.
- Coulomb's Law
Before we look at field strength, let's remember Coulomb's Law, which describes the electrostatic force between two point charges.
- electric field strength (E)
The electric field strength (E) at a point is defined as the force experienced per unit positive test charge placed at that point. It's a vector quantity, with its direction being the same as the force on a positive test charge.
- electric potential (V)
While electric field strength describes the force, electric potential (V) describes the energy 'landscape'.
- equipotential lines
Just as contour lines on a map show points of equal height, equipotential lines (or surfaces in 3D) show points of equal electric potential.
Quick check
Write your answer first, then compare it with the model one — the gap is what you would have lost.
Teach it back
If you can explain it simply, you own it — gaps here are marks you’d lose.
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.
An electric field is a vector field created by electric charges.
Field lines represent the path a positive test charge would take.
Field lines point away from positive charges and towards negative charges.
The density of field lines indicates the strength of the field.
Practice — then mark it
The whole point: a real Cambridge question, marked mark-by-mark.
Determine an expression, in terms of Q, x and ɛ₀, for the resultant electric field strength E at point P due to the two spheres.
Extra simulations & links
PhET, GeoGebra and other curated tools — open in a new tab.
Frequently asked
Checkpoint
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Reading it isn’t knowing it — prove it.
Before you move on: do 9702/41 · Q5(c)(iii) on paper, snap a photo, and get examiner-style feedback on exactly where you win and lose marks.
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