What is the electric field of a point charge?

The electric field of a point charge is a region around the charge where other charges experience a force. It is represented by the vector field E, which points away from a positive charge and towards a negative charge. The magnitude of the electric field is given by the formula E = k * |q| / r^2, where k is Coulomb's constant, q is the charge, and r is the distance from the charge.

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

To calculate the electric field strength due to a point charge, use the formula E = k * |q| / r^2. Here, E is the electric field strength, k is Coulomb's constant (approximately 8.99 x 10^9 N m²/C²), q is the magnitude of the charge, and r is the distance from the charge to the point where the field is being measured. This formula is crucial for understanding electric fields in the Cambridge International A Levels Physics curriculum.

What is the direction of the electric field around a point charge?

The direction of the electric field around a point charge depends on the sign of the charge. For a positive point charge, the electric field radiates outward, away from the charge. Conversely, for a negative point charge, the electric field points inward, towards the charge. This directional property is fundamental in understanding electric fields in Physics, especially at the Cambridge International A Levels.

How does the distance from a point charge affect the electric field strength?

The electric field strength decreases with the square of the distance from a point charge. According to the formula E = k * |q| / r^2, as the distance r increases, the electric field strength E decreases proportionally to 1/r². This inverse square law is a key concept in the study of electric fields in the Cambridge International A Levels Physics syllabus.

Why is understanding the electric field of a point charge important in Physics?

Understanding the electric field of a point charge is crucial because it forms the basis for analyzing more complex electric field configurations. It helps in predicting how charges interact in various scenarios, which is essential for solving problems in electrostatics. This knowledge is particularly important for students studying Physics at the Cambridge International A Levels, as it lays the groundwork for more advanced topics in electricity and magnetism.

Why is "Using test charge in $E$ formula" a common mistake in Electric field of a point charge?

Why it happens: Confusion with F formula. How to avoid it: E = Q/(4\epsilon_0 r^2) depends only on SOURCE Q (not test charge). Source: 9702 Examiner Reports 2022-2024

Cambridge International A Levels Physics (9702)

Electric field of a point charge

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Short Notes - Electric field of a point charge

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 Field of Point Charge Study Notes — Cambridge International A Level Physics 9702 (2025-2027 syllabus)

$E = Q/(4\pi\epsilon_0 r^2)$ . Radial.

At a glance

$E = Q/(4\pi\epsilon_0 r^2)$ .
Radial outward from + charge.
Inverse square.

What you’ll learn

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

18.4.1 — Compute $E$ from point charge.

Field of point charge

$Q/(4\pi\epsilon_0 r^2)$ .

Formula. $E = Q/(4\pi\epsilon_0 r^2)$ .

Direction. Radial. Outward from + charge; toward − charge.

Comparison with gravity. $g = GM/r^2$ ; same form but $\epsilon_0$ instead of $G$ and charges instead of masses.

Cambridge tip. $E$ depends only on source — independent of test charge.

Figure 1 — Radial electric field of a positive point charge

The electric field of a positive point charge points radially outward; magnitude falls as 1/r².

Figure 2 — Field strength against distance from a point charge

The field of a point charge falls away as the inverse square of the distance. The same shape appears for the gravitational field of a point mass.

Figure 3 — Field strength does not depend on the test charge

The forces differ because F = qE, but E itself is set entirely by the source charge and the distance. That is why a field exists at a point even when nothing is placed there.

Figure 4 — The field vector: radial direction, inverse-square length

Field lines show direction well but not strength. Drawing the field as vectors makes both visible at once: the arrows on the outer circle are a quarter the length of those on the inner one.

The electric field of a point charge, beside the gravitational field of a point mass.

	Electric field	Gravitational field
Formula	$E = \dfrac{Q}{4\pi\epsilon_0 r^2}$	$g = \dfrac{GM}{r^2}$
Source of the field	Charge $Q$	Mass $M$
Constant involved	$\epsilon_0$ (in the denominator)	$G$ (in the numerator)
Direction	Away from $+Q$ , towards $-Q$	Always towards $M$
Depends on the test object?	No	No

Both are inverse-square and both are properties of the source alone.

$E = Q/(4\pi\epsilon_0 r^2)$ .
Radial.
Independent of test charge.

See the full worked example for electric field of a point charge →

Quick recap

$E = Q/(4\pi\epsilon_0 r^2)$ .
Radial from point charge.

Memorise this

Verbatim phrases and definitions Cambridge mark schemes credit.

$E$ from point charge.

How it’s examined

Paper 4 typically 5 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.

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Step-by-step worked examples — Electric field of a point charge

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

1 $E$ from point charge (5 marks)
Extended• Adapted from 9702/42 May/Jun 2024• point charge
Question
Find $E$ at 0.50 m from a $+5.0 \times 10^{-9}$ C charge. (5 marks)
Step-by-step solution
1. Step 1
  $E = Q/(4\pi\epsilon_0 r^2)$ .
  $E = \dfrac{5.0 \times 10^{-9}}{4\pi(8.85 \times 10^{-12})(0.25)} \approx 180 \text{ V/m}$
Answer
$E \approx 180$ V/m.

Key Formulae — Electric field of a point charge

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

Field of point charge
$E = \dfrac{Q}{4\pi\epsilon_0 r^2}$
When to use
Field at distance $r$ from point charge $Q$ . Radial.

Key Definitions and Keywords — Electric field of a point charge

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

Radial electric field
Examiner keyword
Field of a point charge — directed along line from charge, magnitude depends on $r$ .

Common Mistakes and Misconceptions — Electric field of a point charge

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

✕Using test charge in $E$ formula
9702 Examiner Reports 2022-2024
Why it happens
Confusion with $F$ formula.
How to avoid it
$E = Q/(4\pi\epsilon_0 r^2)$ depends only on SOURCE $Q$ (not test charge).