Where can I learn Electric potential for Cambridge 9702?

This free lesson on MarkScheme covers syllabus point 18.5 (Electric potential) for Cambridge A-Level Physics. It includes visual revision, key points, and links to real past-paper questions with mark-scheme marking at markscheme.app/courses/9702/18-5-electric-potential.

Is Electric potential (18.5) on 9702 free to study?

Yes. The Physics 9702 course on MarkScheme is 100% free — including premium visual lessons, exam tips, and past-paper marking. No paywall for Electric potential.

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18.5Physics25 min readPREMIUM

Electric potential

Welcome to the world of electric potential! This fundamental concept helps us understand the energy associated with charges within an electric field. Unlike electric field strength, which is a vector, electric potential is a scalar quantity, meaning it only has magnitude. This makes calculations simpler, but understanding its nature is crucial for mastering electromagnetism. This pilot aligns with Senpai Corner A Level notes (2025–2027) for topic 18.5.

BY THE END, YOU CAN…

exam checklist — tick these off

1Define absolute electric potential and electric potential energy.
2Calculate electric potential and potential energy for point charges.
3Understand equipotential lines and their relationship with electric field lines.
4Calculate the work done when a charge moves between two points of different potential.

STUDY MODE

READING

TYPEFACE

Literata — a reading serif made for e-books; set like a textbook, sits well beside maths.

SIZE

AIRY SPACING

Wider letter and line spacing. The one change with solid evidence for readers who lose their place — worth a try whoever you are.

Pick whatever reads fastest for you — it differs from person to person, by up to a third.

EXPLAIN SIMPLER

The same notes in plain English — no jargon. Key points and exam tips stay.

DIAGRAM NOTES

A small sketch beside each block of notes.

In simple terms

A friendly intro before the formal notes — no formulas yet.

Electric potential

Cambridge 9702 Paper 4 — Electric potential (18.5). Senpai Corner diagram-backed pilot with premium structure and live visuals.

1
18.5 Electric potential.
2
Electric potential is defined as the work done per unit positive charge in bringing a small test charge from infinity to a defined point.
3
Electric potential is a scalar quantity.
4
Although electric potential (V) is a scalar quantity it can have a negative or positive sign.

What this topic covers

The official Cambridge syllabus points this lesson works through.

18.5.1
Define electric potential at a point as the work done per unit positive charge in bringing a small test charge from infinity to the point
18.5.2
Recall and use the fact that the electric field at a point is equal to the negative of potential gradient at that point
18.5.3
Use $V = Q/(4\pi ε_0r)$ for the electric potential in the field due to a point charge
18.5.4
Understand how the concept of electric potential leads to the electric potential energy of two point charges and use $E_p = Qq/(4\pi ε_0r)$

Explore the concept

Use the live diagram, PhET or GeoGebra sim, and synced steps — play it, drag controls, or tap a step.

Figure PhET simulation1 / 4

Loading simulation…

Fetching from PhET…

Charges and Fields

E ∝ 1/r² from a point charge; field lines run from + to −, perpendicular to equipotentials.

If the embed does not load, use Open on PhET.

Simulation by PhET Interactive Simulations, University of Colorado Boulder · Licensed to MarkScheme (public licence CC BY-NC 4.0 since 2026-03-30)

Step-synced diagram — highlights what to look for in the simulation above.

Step 1

18.5 Electric potential.

10 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.

10 simulations · 5 to start with

Start herein this order — each one shows a different piece of the topic

The Physics ClassroomStart here · 19702 18.5 · IB D.2
Electrostatics Landscapes
Place two charges on the conductive paper, tap Start and watch the potential landscape form
Why this one: Watch the potential form a hill around a positive charge and a well around a negative one.
Try this
1. Place two charges and tap Start.
2. Trace an equipotential line.
3. Change one charge and compare.
Look for Equipotentials cross field lines at right angles.
Open on The Physics Classroom
Physics Interactives by The Physics Classroom · Licensed to MarkScheme (site terms otherwise permit linking only)
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: Follow V against r: constant inside a shell, falling as 1/r outside — while E falls as 1/r².
Try this
1. Probe the field inside the inner shell.
2. Probe between the shells.
3. Probe outside the outer shell.
Look for The field is zero inside a charged shell and the potential is constant there.
Open on The Physics Classroom
Physics Interactives by The Physics Classroom · Licensed to MarkScheme (site terms otherwise permit linking only)
3JCN PhysicsStart here · 39702 18.5 · IB D.2
Equipotential Surfaces 2 Points
Equipotential surfaces around two point charges
Why this one: See the equipotentials around two charges bunch up where the field is strongest.
Try this
1. Look at the equipotential surfaces close to each charge.
2. Follow a surface out to where the two charges' influence merges.
Look for Near each charge the equipotentials are spheres; farther out they merge into one surface around both.
Open on 3JCN Physics
3JCN Physics Simulation by Thomas Nguyen · CC BY 4.0
oPhysicsStart here · 49702 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
Why this one: Plot equipotentials and field lines together: they cross at right angles, closest where the field is strongest.
Try this
1. Set two equal positive charges and plot the equipotentials.
2. Make one charge negative.
3. Move one charge further away.
Look for Field lines cross equipotentials at right angles and the field is strongest where equipotentials are closest.
Open on oPhysics
Simulation by Tom Walsh, oPhysics.com — made with GeoGebra · Licensed to MarkScheme (site: free for non-profit educational use; applets made with GeoGebra)
SimuPhysicsStart here · 59702 18.5 · 9702 13.4 · IB D.2
Potential Energy and Electric Potential
A ball lifted through height contours beside a charge moved through equipotential rings; drag either and change its size
Why this one: Move a charge across equipotential rings and see no work is done along a ring.
Try this
1. Drag the ball up and read the energy and gh.
2. Drag the charge out and read the energy and V.
3. Place 1 C, 2 C and 3 C at the same point.
Look for Stored energy scales with mass or charge, while gh and V do not.
Open on SimuPhysicsRuns on their site
SimuPhysics by Mohamed Abdelsalam · Licensed to MarkScheme (site publishes no licence; served with frame-ancestors self)

More simulations5 more on this topic — core ones first

oPhysicsCore9702 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
Try this
1. Drag a +1 nC and a −1 nC charge near each other.
2. Replace the negative charge with a second positive one.
3. Move the charges apart and watch the potential map.
Look for Field lines run from positive to negative and cross equipotentials at right angles.
Open on oPhysics
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 18.5 · 9702 18.1 · 9702 18.4
Electric Field & Equipotential Mapping
Probe a 3D field and plot equipotential lines around configured charges
Try this
1. Probe the field around the configured charges and plot a few equipotential lines.
2. Compare the direction of the field with the equipotentials where they cross.
3. Note where the equipotentials are closest together.
Look for Field lines cross equipotentials at right angles, and closely spaced equipotentials mark a strong field.
Open on 3JCN Physics
3JCN Physics Simulation by Thomas Nguyen · CC BY 4.0
3JCN PhysicsCore9702 18.5 · 9702 18.2 · IB D.2
Equipotential Surfaces Capacitor
Equipotential surfaces between capacitor plates
Try this
1. Look at the spacing of the equipotential surfaces between the plates.
2. Compare the equipotentials near the plate edges with those in the middle.
Look for Between the plates the equipotentials are evenly spaced planes, showing a uniform field.
Open on 3JCN Physics
3JCN Physics Simulation by Thomas Nguyen · CC BY 4.0
3JCN PhysicsCore9702 18.5 · IB D.2
Equipotential Surfaces Point & Plate
Equipotentials between a point charge and a plate
Try this
1. Look at the equipotentials near the point charge and near the plate.
2. Follow the field direction between them.
Look for Equipotentials are spherical near the point and flat near the plate, with the field always perpendicular to them.
Open on 3JCN Physics
3JCN Physics Simulation by Thomas Nguyen · CC BY 4.0
3JCN PhysicsCore9702 18.5 · IB D.2
Equipotential Surfaces Point & Shell
Equipotentials between a point charge and a conducting shell
Try this
1. Look at the equipotentials between the point charge and the shell.
2. Compare the potential across the conducting shell itself.
Look for A conductor is an equipotential, so no potential difference exists across the shell.
Open on 3JCN Physics
3JCN Physics Simulation by Thomas Nguyen · CC BY 4.0

Key formulas

Tap any symbol to reveal exactly what it means and its units.

KEY RELATION

$V = \frac{W}{Q}$

Tap a symbol — great for exam definitions

KEY RELATION

$V = \frac{1}{4\pi\epsilon_0} \frac{Q}{r}$

Tap a symbol — great for exam definitions

KEY RELATION

$U = \frac{Q_1Q_2}{4\pi\epsilon_0 r}$

Tap a symbol — great for exam definitions

KEY RELATION

$W = Q\Delta V$

Tap a symbol — great for exam definitions

KEY RELATION

$E = \frac{\Delta V}{d}$

Tap a symbol — great for exam definitions

Full topic notes

Formal explanation with the rigour you need for the exam.

What is Electric Potential?

Electric potential ( $V$ ) at any point in an electric field is fundamentally defined as the amount of work done per unit positive test charge. This work is performed by an external force to slowly move a tiny positive test charge from an infinitely distant point (where potential is considered zero) to the specific point you're interested in, without causing any acceleration. Think of it as the electric potential energy that each coulomb of charge would possess at that location.

$V = \frac{W}{Q}$

18.5 Electric potential.
Electric potential is defined as the work done per unit positive charge in bringing a small test charge from infinity to a defined point.
Electric potential is a scalar quantity.
Although electric potential (V) is a scalar quantity it can have a negative or positive sign.
The electric potential in the field due to a point charge is defined as: 𝑉 = 𝑄 4𝜋𝜀 0 𝑟.
Here Q is the point charge producing the charge (C).

Not clear?

Electric Potential from a Point Charge

For an isolated point charge, the electric field it creates is radial. The electric potential at a distance $r$ from this charge depends directly on the charge's magnitude and inversely on the distance. This formula describes the absolute potential created by a single point charge in a vacuum or air.

$V = \frac{1}{4\pi\epsilon_0} \frac{Q}{r}$

$Q$ is the source charge creating the potential.
$\\epsilon_0$ is the permittivity of free space.
The sign of $V$ is the same as the sign of $Q$ .
Potential is highest (most positive or least negative) near the charge.
Potential decreases with distance, approaching zero at infinity.

Not clear?

Electric Potential Energy

While electric potential is energy per unit charge, electric potential energy ( $U$ ) is the total work done to bring a specific charge from infinity to a point in an electric field. If you have two point charges, $Q_1$ and $Q_2$ , separated by a distance $r$ , this formula gives the potential energy stored in their configuration. It's the work required to assemble them from infinite separation.

$U = \frac{Q_1Q_2}{4\pi\epsilon_0 r}$

Represents the work done to assemble a system of charges.
Positive $U$ means work was done on the system (charges repel).
Negative $U$ means the field did work (charges attract).
Units are Joules (J).

Not clear?

Work Done by a Charge Moving Through Potential Difference

When a charge moves from one point to another within an electric field, if there's a difference in electric potential between these points, work will be done either by the field or on the charge. The amount of work done depends on the charge's magnitude and the potential difference it traverses.

$W = Q\Delta V$

$W$ is work done, $Q$ is the charge, $\Delta V$ is potential difference.
If $W$ is positive, work is done on the charge (its energy increases).
If $W$ is negative, work is done by the field (its energy decreases).
Positive charges naturally move from higher to lower potential.

Not clear?

Equipotential Lines and Electric Fields

Equipotential lines (or surfaces in 3D) are incredibly useful visual tools. They represent all the points in an electric field that share the exact same electric potential. Imagine contour lines on a map, but for electrical 'height'. A crucial property is that if a charge moves along an equipotential line, no work is done by the electric field, because there's no change in potential energy ( $\Delta V = 0$ ).

Lines connecting points of equal electric potential.
Electric field lines are always perpendicular to equipotential lines.
No work is done by the electric field when a charge moves along them.
Closer spacing indicates a stronger electric field (steeper potential gradient).
The electric field strength ( $E$ ) is the negative gradient of the potential: $E = -\frac{\Delta V}{\Delta r}$ .

Not clear?

Uniform Electric Fields

A special case is a uniform electric field, typically found between two large, parallel conducting plates with opposite charges. In such a field, the electric field strength is constant in magnitude and direction. This simplifies the relationship between electric field strength and potential difference significantly.

$E = \frac{\Delta V}{d}$

Applies to uniform fields, e.g., between parallel plates.
$d$ is the distance between the plates or points.
Units of E can be V/m, equivalent to N/C.

Not clear?

Worked examples

See the formulas applied — reveal one step at a time, like the exam.

reveal slowly — mark each step

EXAMPLE 1

A point charge of +5.0 nC is located at the origin. Calculate the absolute electric potential at a point 0.20 m away from the charge. (Constant $k = \frac{1}{4\pi\epsilon_0} = 8.99 \times 10^9 \text{ N m}^2 \text{ C}^{-2}$ )

1
Identify knowns: $Q = +5.0 \times 10^{-9} \text{ C}$ (remember nano = $10^{-9}$ ), $r = 0.20 \text{ m}$ , $k = 8.99 \times 10^9 \text{ N m}^2 \text{ C}^{-2}$ .

EXAMPLE 2

A fixed point charge $Q = +2.0 \mu C$ creates an electric field. Calculate the work done by the electric field when a proton (charge $q = +1.60 \times 10^{-19} C$ ) moves from a point A, 0.10 m from $Q$ , to a point B, 0.50 m from $Q$ . (Use $k = 8.99 \times 10^9 \text{ N m}^2 \text{ C}^{-2}$ )

1
Strategy: First, calculate the electric potential at points A and B due to the source charge $Q$ . Then, find the potential difference $\Delta V$ . Finally, use the relationship between work and potential energy to find the work done by the field.

How it all connects

The big idea sits in the middle — tap a linked idea to explore the link.

MAIN IDEAElectric potential

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 potential energy: While electric potential is energy per unit charge, electric potential energy ( $U$ ) is the total work done to bring a specific charge from infinity to a point in an electric field.
Absolute electric potential (V): The work done per unit positive test charge to move it from infinity to a specific point in an electric field without acceleration.
Electric potential energy (U): The work done to bring a positive charge from infinity to a specific point within an electric field.
Equipotential lines: Imaginary lines (or surfaces) connecting points in an electric field that all have the same electric potential.
Electron-volt (eV): A unit of energy equal to the work done on an electron when it moves through a potential difference of one volt. It is the kinetic energy gained by an electron accelerated through 1V. $1 \text{ eV} = 1.60 \times 10^{-19} \text{ J}$ .
electric potential: The electric potential inside a charged hollow conducting sphere is constant everywhere within the sphere and is equal to the potential on its surface.

10Apply

Quick check

Write your answer first, then compare it with the model one — the gap is what you would have lost.

0 of 6 answered

11Understand

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.

Your explanation — no notes

12Remember

Revision flashcards

Guess first, then flip — retrieval beats re-reading.

Your guess — write it before you look

1 / 14 · ← → space

Key takeaways

Review these before you close the topic — retrieval beats re-reading.

close the tab only after these stick

18.5 Electric potential.
Electric potential is defined as the work done per unit positive charge in bringing a small test charge from infinity to a defined point.
Electric potential is a scalar quantity.
Although electric potential (V) is a scalar quantity it can have a negative or positive sign.
The electric potential in the field due to a point charge is defined as: 𝑉 = 𝑄 4𝜋𝜀 0 𝑟.
Here Q is the point charge producing the charge (C).

Practice — then mark it

The whole point: a real Cambridge question, marked mark-by-mark.

Question 1 of 29702/42 · Q5(c)

PhysicsMay/June 2024

(c)

A proton is held at rest on the line joining the centres of the spheres in (b) at the position where x = 0.60 m. The proton is released. Describe and explain, without calculation, the subsequent motion of the proton.

Do it on paper → mark itMARKED MARK-BY-MARK · B1 / M1 / A1 · OFFICIAL SCHEME

9702/42/M/J/24

Question 2 of 29702/42 · Q5(a)

PhysicsMay/June 2024

(a)

Define electric potential at a point.

Do it on paper → mark itMARKED MARK-BY-MARK · B1 / M1 / A1 · OFFICIAL SCHEME

9702/42/M/J/24

Extra simulations & links

PhET, GeoGebra and other curated tools — open in a new tab.

Frequently asked

What is the difference between electric potential and electric potential energy?

Why is electric potential at infinity considered zero?

How can electric potential be negative?

What's the difference between work done 'by the field' and work done 'on the charge'?

Checkpoint

One marked question is worth ten re-reads — close the loop before you move on.

Checkpoint

Reading it isn’t knowing it — prove it.

Before you move on: do 9702/42 · Q5(c) on paper, snap a photo, and get examiner-style feedback on exactly where you win and lose marks.

Attempt & get marked →Takes about a minute · you’ll land back on this lesson

← PREVIOUS18.4 Electric field of a point charge NEXT →19.1 Capacitors and capacitance

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Revise Electric potential for Cambridge 9702 (18.5)

Looking for free Physics 9702 notes on Electric potential? This A-Level lesson covers official syllabus point 18.5 on Paper 4: A Level Structured Questions. Use the visual steps, key terms, and quick checks below — then practise a real 9702 past-paper question with mark-scheme marking. Built for students searching "Electric potential 9702 revision", "9702 18.5 notes", or a free alternative to paid note sites.

Full Physics 9702 course Mark a past paper →9702 subject hub

18.5Physics25 min readPREMIUM

Electric potential

BY THE END, YOU CAN…

exam checklist — tick these off

1Define absolute electric potential and electric potential energy.
2Calculate electric potential and potential energy for point charges.
3Understand equipotential lines and their relationship with electric field lines.
4Calculate the work done when a charge moves between two points of different potential.

STUDY MODE

READING

TYPEFACE

Literata — a reading serif made for e-books; set like a textbook, sits well beside maths.

SIZE

AIRY SPACING

Wider letter and line spacing. The one change with solid evidence for readers who lose their place — worth a try whoever you are.

Pick whatever reads fastest for you — it differs from person to person, by up to a third.

EXPLAIN SIMPLER

The same notes in plain English — no jargon. Key points and exam tips stay.

DIAGRAM NOTES

A small sketch beside each block of notes.

In simple terms

A friendly intro before the formal notes — no formulas yet.

Electric potential

Cambridge 9702 Paper 4 — Electric potential (18.5). Senpai Corner diagram-backed pilot with premium structure and live visuals.

1
18.5 Electric potential.
2
Electric potential is defined as the work done per unit positive charge in bringing a small test charge from infinity to a defined point.
3
Electric potential is a scalar quantity.
4
Although electric potential (V) is a scalar quantity it can have a negative or positive sign.

What this topic covers

The official Cambridge syllabus points this lesson works through.

18.5.1
Define electric potential at a point as the work done per unit positive charge in bringing a small test charge from infinity to the point
18.5.2
Recall and use the fact that the electric field at a point is equal to the negative of potential gradient at that point
18.5.3
Use $V = Q/(4\pi ε_0r)$ for the electric potential in the field due to a point charge
18.5.4
Understand how the concept of electric potential leads to the electric potential energy of two point charges and use $E_p = Qq/(4\pi ε_0r)$

Explore the concept

Use the live diagram, PhET or GeoGebra sim, and synced steps — play it, drag controls, or tap a step.

Figure PhET simulation1 / 4

Loading simulation…

Fetching from PhET…

Charges and Fields

E ∝ 1/r² from a point charge; field lines run from + to −, perpendicular to equipotentials.

If the embed does not load, use Open on PhET.

Simulation by PhET Interactive Simulations, University of Colorado Boulder · Licensed to MarkScheme (public licence CC BY-NC 4.0 since 2026-03-30)

Step-synced diagram — highlights what to look for in the simulation above.

Step 1

18.5 Electric potential.

10 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.

10 simulations · 5 to start with

Start herein this order — each one shows a different piece of the topic

The Physics ClassroomStart here · 19702 18.5 · IB D.2
Electrostatics Landscapes
Place two charges on the conductive paper, tap Start and watch the potential landscape form
Why this one: Watch the potential form a hill around a positive charge and a well around a negative one.
Try this
1. Place two charges and tap Start.
2. Trace an equipotential line.
3. Change one charge and compare.
Look for Equipotentials cross field lines at right angles.
Open on The Physics Classroom
Physics Interactives by The Physics Classroom · Licensed to MarkScheme (site terms otherwise permit linking only)
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: Follow V against r: constant inside a shell, falling as 1/r outside — while E falls as 1/r².
Try this
1. Probe the field inside the inner shell.
2. Probe between the shells.
3. Probe outside the outer shell.
Look for The field is zero inside a charged shell and the potential is constant there.
Open on The Physics Classroom
Physics Interactives by The Physics Classroom · Licensed to MarkScheme (site terms otherwise permit linking only)
3JCN PhysicsStart here · 39702 18.5 · IB D.2
Equipotential Surfaces 2 Points
Equipotential surfaces around two point charges
Why this one: See the equipotentials around two charges bunch up where the field is strongest.
Try this
1. Look at the equipotential surfaces close to each charge.
2. Follow a surface out to where the two charges' influence merges.
Look for Near each charge the equipotentials are spheres; farther out they merge into one surface around both.
Open on 3JCN Physics
3JCN Physics Simulation by Thomas Nguyen · CC BY 4.0
oPhysicsStart here · 49702 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
Why this one: Plot equipotentials and field lines together: they cross at right angles, closest where the field is strongest.
Try this
1. Set two equal positive charges and plot the equipotentials.
2. Make one charge negative.
3. Move one charge further away.
Look for Field lines cross equipotentials at right angles and the field is strongest where equipotentials are closest.
Open on oPhysics
Simulation by Tom Walsh, oPhysics.com — made with GeoGebra · Licensed to MarkScheme (site: free for non-profit educational use; applets made with GeoGebra)
SimuPhysicsStart here · 59702 18.5 · 9702 13.4 · IB D.2
Potential Energy and Electric Potential
A ball lifted through height contours beside a charge moved through equipotential rings; drag either and change its size
Why this one: Move a charge across equipotential rings and see no work is done along a ring.
Try this
1. Drag the ball up and read the energy and gh.
2. Drag the charge out and read the energy and V.
3. Place 1 C, 2 C and 3 C at the same point.
Look for Stored energy scales with mass or charge, while gh and V do not.
Open on SimuPhysicsRuns on their site
SimuPhysics by Mohamed Abdelsalam · Licensed to MarkScheme (site publishes no licence; served with frame-ancestors self)

More simulations5 more on this topic — core ones first

oPhysicsCore9702 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
Try this
1. Drag a +1 nC and a −1 nC charge near each other.
2. Replace the negative charge with a second positive one.
3. Move the charges apart and watch the potential map.
Look for Field lines run from positive to negative and cross equipotentials at right angles.
Open on oPhysics
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 18.5 · 9702 18.1 · 9702 18.4
Electric Field & Equipotential Mapping
Probe a 3D field and plot equipotential lines around configured charges
Try this
1. Probe the field around the configured charges and plot a few equipotential lines.
2. Compare the direction of the field with the equipotentials where they cross.
3. Note where the equipotentials are closest together.
Look for Field lines cross equipotentials at right angles, and closely spaced equipotentials mark a strong field.
Open on 3JCN Physics
3JCN Physics Simulation by Thomas Nguyen · CC BY 4.0
3JCN PhysicsCore9702 18.5 · 9702 18.2 · IB D.2
Equipotential Surfaces Capacitor
Equipotential surfaces between capacitor plates
Try this
1. Look at the spacing of the equipotential surfaces between the plates.
2. Compare the equipotentials near the plate edges with those in the middle.
Look for Between the plates the equipotentials are evenly spaced planes, showing a uniform field.
Open on 3JCN Physics
3JCN Physics Simulation by Thomas Nguyen · CC BY 4.0
3JCN PhysicsCore9702 18.5 · IB D.2
Equipotential Surfaces Point & Plate
Equipotentials between a point charge and a plate
Try this
1. Look at the equipotentials near the point charge and near the plate.
2. Follow the field direction between them.
Look for Equipotentials are spherical near the point and flat near the plate, with the field always perpendicular to them.
Open on 3JCN Physics
3JCN Physics Simulation by Thomas Nguyen · CC BY 4.0
3JCN PhysicsCore9702 18.5 · IB D.2
Equipotential Surfaces Point & Shell
Equipotentials between a point charge and a conducting shell
Try this
1. Look at the equipotentials between the point charge and the shell.
2. Compare the potential across the conducting shell itself.
Look for A conductor is an equipotential, so no potential difference exists across the shell.
Open on 3JCN Physics
3JCN Physics Simulation by Thomas Nguyen · CC BY 4.0

Key formulas

Tap any symbol to reveal exactly what it means and its units.

KEY RELATION

$V = \frac{W}{Q}$

Tap a symbol — great for exam definitions

KEY RELATION

$V = \frac{1}{4\pi\epsilon_0} \frac{Q}{r}$

Tap a symbol — great for exam definitions

KEY RELATION

$U = \frac{Q_1Q_2}{4\pi\epsilon_0 r}$

Tap a symbol — great for exam definitions

KEY RELATION

$W = Q\Delta V$

Tap a symbol — great for exam definitions

KEY RELATION

$E = \frac{\Delta V}{d}$

Tap a symbol — great for exam definitions

Full topic notes

Formal explanation with the rigour you need for the exam.

What is Electric Potential?

$V = \frac{W}{Q}$

18.5 Electric potential.
Electric potential is defined as the work done per unit positive charge in bringing a small test charge from infinity to a defined point.
Electric potential is a scalar quantity.
Although electric potential (V) is a scalar quantity it can have a negative or positive sign.
The electric potential in the field due to a point charge is defined as: 𝑉 = 𝑄 4𝜋𝜀 0 𝑟.
Here Q is the point charge producing the charge (C).

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Electric Potential from a Point Charge

$V = \frac{1}{4\pi\epsilon_0} \frac{Q}{r}$

$Q$ is the source charge creating the potential.
$\\epsilon_0$ is the permittivity of free space.
The sign of $V$ is the same as the sign of $Q$ .
Potential is highest (most positive or least negative) near the charge.
Potential decreases with distance, approaching zero at infinity.

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Electric Potential Energy

$U = \frac{Q_1Q_2}{4\pi\epsilon_0 r}$

Represents the work done to assemble a system of charges.
Positive $U$ means work was done on the system (charges repel).
Negative $U$ means the field did work (charges attract).
Units are Joules (J).

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Work Done by a Charge Moving Through Potential Difference

$W = Q\Delta V$

$W$ is work done, $Q$ is the charge, $\Delta V$ is potential difference.
If $W$ is positive, work is done on the charge (its energy increases).
If $W$ is negative, work is done by the field (its energy decreases).
Positive charges naturally move from higher to lower potential.

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Equipotential Lines and Electric Fields

Lines connecting points of equal electric potential.
Electric field lines are always perpendicular to equipotential lines.
No work is done by the electric field when a charge moves along them.
Closer spacing indicates a stronger electric field (steeper potential gradient).
The electric field strength ( $E$ ) is the negative gradient of the potential: $E = -\frac{\Delta V}{\Delta r}$ .

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Uniform Electric Fields

$E = \frac{\Delta V}{d}$

Applies to uniform fields, e.g., between parallel plates.
$d$ is the distance between the plates or points.
Units of E can be V/m, equivalent to N/C.

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Worked examples

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EXAMPLE 1

1
Identify knowns: $Q = +5.0 \times 10^{-9} \text{ C}$ (remember nano = $10^{-9}$ ), $r = 0.20 \text{ m}$ , $k = 8.99 \times 10^9 \text{ N m}^2 \text{ C}^{-2}$ .

EXAMPLE 2

1
Strategy: First, calculate the electric potential at points A and B due to the source charge $Q$ . Then, find the potential difference $\Delta V$ . Finally, use the relationship between work and potential energy to find the work done by the field.

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MAIN IDEAElectric potential

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Glossary

Key terms for this topic — skim now; the Check step will test them.

electric potential energy: While electric potential is energy per unit charge, electric potential energy ( $U$ ) is the total work done to bring a specific charge from infinity to a point in an electric field.
Absolute electric potential (V): The work done per unit positive test charge to move it from infinity to a specific point in an electric field without acceleration.
Electric potential energy (U): The work done to bring a positive charge from infinity to a specific point within an electric field.
Equipotential lines: Imaginary lines (or surfaces) connecting points in an electric field that all have the same electric potential.
Electron-volt (eV): A unit of energy equal to the work done on an electron when it moves through a potential difference of one volt. It is the kinetic energy gained by an electron accelerated through 1V. $1 \text{ eV} = 1.60 \times 10^{-19} \text{ J}$ .
electric potential: The electric potential inside a charged hollow conducting sphere is constant everywhere within the sphere and is equal to the potential on its surface.

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1 / 14 · ← → space

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18.5 Electric potential.
Electric potential is defined as the work done per unit positive charge in bringing a small test charge from infinity to a defined point.
Electric potential is a scalar quantity.
Although electric potential (V) is a scalar quantity it can have a negative or positive sign.
The electric potential in the field due to a point charge is defined as: 𝑉 = 𝑄 4𝜋𝜀 0 𝑟.
Here Q is the point charge producing the charge (C).

Practice — then mark it

The whole point: a real Cambridge question, marked mark-by-mark.

Question 1 of 29702/42 · Q5(c)

PhysicsMay/June 2024

(c)

Do it on paper → mark itMARKED MARK-BY-MARK · B1 / M1 / A1 · OFFICIAL SCHEME

9702/42/M/J/24

Question 2 of 29702/42 · Q5(a)

PhysicsMay/June 2024

(a)

Define electric potential at a point.

Do it on paper → mark itMARKED MARK-BY-MARK · B1 / M1 / A1 · OFFICIAL SCHEME

9702/42/M/J/24

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Frequently asked

What is the difference between electric potential and electric potential energy?

Why is electric potential at infinity considered zero?

How can electric potential be negative?

What's the difference between work done 'by the field' and work done 'on the charge'?

Checkpoint

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Revise Electric potential for Cambridge 9702 (18.5)

In simple terms

What this topic covers

Explore the concept

Simulations

Electrostatics Landscapes

Electric Two-Shell Analysis

Equipotential Surfaces 2 Points

Equipotentials & Electric Field of Two Charges

Potential Energy and Electric Potential

Electric Field & Potential

Electric Field & Equipotential Mapping

Equipotential Surfaces Capacitor

Equipotential Surfaces Point & Plate

Equipotential Surfaces Point & Shell

Key formulas

Full topic notes

What is Electric Potential?

Electric Potential from a Point Charge

Electric Potential Energy

Work Done by a Charge Moving Through Potential Difference

Equipotential Lines and Electric Fields

Uniform Electric Fields

Worked examples

How it all connects

Glossary

Quick check

Teach it back

Revision flashcards

Key takeaways

Practice — then mark it

Extra simulations & links

Frequently asked

Checkpoint

Reading it isn’t knowing it — prove it.

Discuss Electric potential

Revise Electric potential for Cambridge 9702 (18.5)

In simple terms

What this topic covers

Explore the concept

Simulations

Electrostatics Landscapes

Electric Two-Shell Analysis

Equipotential Surfaces 2 Points

Equipotentials & Electric Field of Two Charges

Potential Energy and Electric Potential

Electric Field & Potential

Electric Field & Equipotential Mapping

Equipotential Surfaces Capacitor

Equipotential Surfaces Point & Plate

Equipotential Surfaces Point & Shell

Key formulas

Full topic notes

What is Electric Potential?

Electric Potential from a Point Charge

Electric Potential Energy

Work Done by a Charge Moving Through Potential Difference

Equipotential Lines and Electric Fields

Uniform Electric Fields

Worked examples

How it all connects

Glossary

Quick check

Teach it back

Revision flashcards

Key takeaways

Practice — then mark it

Extra simulations & links

Frequently asked

Checkpoint

Reading it isn’t knowing it — prove it.

Discuss Electric potential