What is electric potential in the context of electric fields?

Electric potential, often denoted by V, is a measure of the potential energy per unit charge at a point in an electric field. It represents the work done in bringing a positive test charge from infinity to that point without any acceleration. In the Cambridge International A Levels Physics curriculum, understanding electric potential is crucial as it helps in analyzing how electric fields influence charges.

How is electric potential different from electric potential energy?

Electric potential is a scalar quantity that represents the potential energy per unit charge at a point in an electric field, measured in volts (V). In contrast, electric potential energy is the total energy a charge possesses due to its position in an electric field, measured in joules (J). For a charge q at a point with electric potential V, the electric potential energy is given by U = qV.

How do you calculate the electric potential due to a point charge?

The electric potential V due to a point charge Q at a distance r from the charge is calculated using the formula V = kQ/r, where k is Coulomb's constant (approximately 8.99 × 10^9 N m²/C²). This formula is essential for Cambridge International A Levels students to understand how potential varies with distance in electric fields.

What is the relationship between electric field and electric potential?

The electric field E is related to the electric potential V by the negative gradient of the potential. Mathematically, E = -dV/dr, where dV/dr is the rate of change of potential with respect to distance. This relationship indicates that the electric field points in the direction of decreasing potential and is a key concept in the study of electric fields in the Cambridge International A Levels Physics syllabus.

Why is electric potential considered a scalar quantity?

Electric potential is considered a scalar quantity because it only has magnitude and no direction. Unlike vector quantities such as electric field, which have both magnitude and direction, electric potential simply represents the amount of potential energy per unit charge at a point. This scalar nature simplifies calculations and is an important aspect for students studying electric fields in the Cambridge International A Levels Physics curriculum.

Why is "Treating electric potential as always negative (like gravity)" a common mistake in Electric potential?

Why it happens: Comparison with gravity. How to avoid it: V is POSITIVE near + charge; NEGATIVE near − charge. Unlike gravity (always attractive), electric force can be either. Source: 9702 Examiner Reports 2022-2024

Cambridge International A Levels Physics (9702)

Electric potential

0% Complete

3 tasks remaining

Short Notes - Electric potential

Detailed Study Notes

Detailed notes on Electric Fields for Cambridge International A Levels Physics, covering key concepts, explanations, examples, and exam-focused revision points.

Electric Potential Study Notes — Cambridge International A Level Physics 9702 (2025-2027 syllabus)

$V = Q/(4\pi\epsilon_0 r)$ . Work per unit charge.

At a glance

$V = Q/(4\pi\epsilon_0 r)$ .
$U = qV$ .
Positive near + charge.
Negative near − charge.
Zero at infinity.

What you’ll learn

Mapped to the Cambridge International A Level 9702 syllabus (2025-2027).

18.5.1 — Define electric potential.
18.5.2 — Compute potential and PE.

Electric potential

Work per unit + charge.

Definition. Work done per unit POSITIVE charge to bring test charge from infinity to point.

Formula. $V = Q/(4\pi\epsilon_0 r)$ for point charge.

Sign. Positive near + charge; negative near − charge. Unlike gravity (always negative).

PE of charge $q$ at potential $V$ . $U = qV$ .

Total PE of two point charges. $U = Q_1 Q_2 / (4\pi\epsilon_0 r)$ .

Cambridge tip. $V \to 0$ at infinity.

Figure 1 — Electric potential against distance from a point charge

Electric potential varies as 1/r, not 1/r². Its sign follows the sign of the source charge, which is the key difference from gravitational potential.

Figure 2 — Electric potential is defined from infinity

Potential is always measured relative to infinity. Because a positive charge must be pushed against the repulsion of +Q, positive work is done and the potential near a positive charge comes out positive.

Figure 3 — Electric potential compared with gravitational potential

The two potentials have the same 1/r shape, but electric potential is positive near a positive charge and negative near a negative one, while gravitational potential is negative everywhere.

Figure 4 — From potential to potential energy

Potential is a property of a point in the field; potential energy is what a particular charge has when placed there. The two are linked by U = qV.

Potential and potential energy at a glance.

Quantity	Formula	Scalar or vector?	Falls off as
Field strength $E$	$\dfrac{Q}{4\pi\epsilon_0 r^2}$	Vector	$1/r^2$
Potential $V$	$\dfrac{Q}{4\pi\epsilon_0 r}$	Scalar	$1/r$
Energy of a charge $q$ at potential $V$	$U = qV$	Scalar	$1/r$
Energy of a pair of charges	$\dfrac{Q_1 Q_2}{4\pi\epsilon_0 r}$	Scalar	$1/r$

$V$ and $U$ are both zero at infinity, and both carry the sign of the charges involved.

$V$ is scalar.
Work per + test charge.
Sign matches source charge.

See the full worked example for electric potential →

Quick recap

$V = Q/(4\pi\epsilon_0 r)$ .
$U = qV$ .
Sign matters.

Memorise this

Verbatim phrases and definitions Cambridge mark schemes credit.

$V = Q/(4\pi\epsilon_0 r)$ .
$U = qV$ .

How it’s examined

Electric potential on Paper 4. Most-tested: $V$ at distance (5 marks), PE between charges (7 marks).

Sources: Cambridge International A Level Physics 9702 syllabus (2025-2027); 9702 Examiner Reports 2022-2024; 9702/42 May/Jun 2024 question paper and mark scheme. Last reviewed 2026-05-11.

Take this whole topic with you

Step-by-step worked examples — Electric potential

Step-by-step solutions to past-paper-style questions on electric potential, written exactly the way a tutor would explain them at the board.

1Potential at distance (5 marks)
Extended• Adapted from 9702/42 May/Jun 2024• potential
Question
Find potential at 0.10 m from $+5.0 \times 10^{-9}$ C charge. (5 marks)
Step-by-step solution
1. Step 1
  $V = Q/(4\pi\epsilon_0 r)$ .
  $V = \dfrac{5.0 \times 10^{-9}}{4\pi(8.85 \times 10^{-12})(0.10)} \approx 450 \text{ V}$
Answer
$V \approx 450$ V.

Key Formulae — Electric potential

The formulae you need to memorise for electric potential on the Cambridge International A Level 9702 paper, with every variable defined in plain English and a note on when to use it.

Electric potential of point charge
$V = \dfrac{Q}{4\pi\epsilon_0 r}$
When to use
PE per unit positive charge at distance $r$ . Zero at infinity. Positive for + charge.
Electrical PE
$U = qV = \dfrac{Qq}{4\pi\epsilon_0 r}$
When to use
Energy of charge $q$ at potential $V$ .

Key Definitions and Keywords — Electric potential

Definitions to memorise and the exact keywords mark schemes credit for electric potential answers — sharpened from recent examiner reports for the 2026 Cambridge International A Level 9702 sitting.

Electric potential
Examiner keyword
Work done per unit POSITIVE charge to bring charge from infinity to point. Units: V = J/C.

Common Mistakes and Misconceptions — Electric potential

The traps other students keep falling into on electric potential questions — taken from recent Cambridge International A Level 9702 examiner reports and mark schemes — and how to avoid them.

✕Treating electric potential as always negative (like gravity)
9702 Examiner Reports 2022-2024
Why it happens
Comparison with gravity.
How to avoid it
$V$ is POSITIVE near + charge; NEGATIVE near − charge. Unlike gravity (always attractive), electric force can be either.

Electric potential — frequently asked questions

The things students keep getting wrong in this sub-topic, answered.

Quantity

Formula

Scalar or vector?

Falls off as

Field strength

E

\dfrac{Q}{4\pi\epsilon_0 r^2}

Vector

1/r^2

Potential

V

\dfrac{Q}{4\pi\epsilon_0 r}

Scalar

1/r

Energy of a charge

q

at potential

V

U = qV

Scalar

1/r

Energy of a pair of charges

\dfrac{Q_1 Q_2}{4\pi\epsilon_0 r}

Scalar

1/r

Electric potential

Short Notes - Electric potential

Detailed Study Notes

At a glance

What you’ll learn

Electric potential

Quick recap

Memorise this

How it’s examined

Take this whole topic with you

1Potential at distance (5 marks)

Electric potential of point charge

Electrical PE

Electric potential

✕Treating electric potential as always negative (like gravity)

Electric potential — frequently asked questions

Electric potential

Short Notes - Electric potential

Detailed Study Notes

At a glance

What you’ll learn

Electric potential

Quick recap

Memorise this

How it’s examined

Take this whole topic with you

1Potential at distance (5 marks)

Electric potential of point charge

Electrical PE

Electric potential

✕Treating electric potential as always negative (like gravity)

Electric potential — frequently asked questions