What is the electric force between two point charges?

The electric force between two point charges is the force of attraction or repulsion between them due to their electric charges. According to Coulomb's Law, this force is directly proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between them. The formula is F = k * (|q1 * q2| / r^2), where F is the force, q1 and q2 are the charges, r is the distance between the charges, and k is Coulomb's constant.

How does the distance between point charges affect the electric force?

The distance between point charges significantly affects the electric force. According to Coulomb's Law, the electric force is inversely proportional to the square of the distance between the charges. This means that as the distance increases, the force decreases rapidly. For example, if the distance is doubled, the force becomes one-fourth of its original value.

What role does Coulomb's constant play in calculating electric force?

Coulomb's constant (k) is a proportionality factor in Coulomb's Law that helps calculate the electric force between two point charges. Its value is approximately 8.99 x 10^9 N m²/C² in a vacuum. This constant ensures that the units of charge and distance are consistent with the units of force, allowing for accurate calculations of the electric force in Physics, especially at the Cambridge International A Levels.

How do the signs of point charges affect the direction of the electric force?

The signs of point charges determine whether the electric force is attractive or repulsive. If both charges have the same sign (both positive or both negative), the force is repulsive, meaning the charges push away from each other. If the charges have opposite signs (one positive and one negative), the force is attractive, meaning the charges pull towards each other. This concept is crucial in understanding electric fields in Physics.

Can electric force between point charges be zero? If so, under what conditions?

Yes, the electric force between point charges can be zero if the net force acting on a charge is balanced by other forces. This can occur when multiple charges are present, and the vector sum of the forces from other charges cancels out. For example, in a system of three charges, the force on one charge can be zero if the forces from the other two charges are equal in magnitude and opposite in direction. This concept is often explored in Cambridge International A Levels Physics problems involving electric fields.

Why is "Signs in Coulomb's law" a common mistake in Electric force between point charges?

Why it happens: Confusion. How to avoid it: Same-sign charges → POSITIVE F (repulsion). Opposite signs → NEGATIVE F (attraction). Cambridge usually asks for magnitude. Source: 9702 Examiner Reports 2022-2024

Cambridge International A Levels Physics (9702)

Electric force between point charges

0% Complete

3 tasks remaining

Short Notes - Electric force between point charges

Detailed Study Notes

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

Coulomb's Law Study Notes — Cambridge International A Level Physics 9702 (2025-2027 syllabus)

Force between point charges. Inverse square.

At a glance

$F = Q_1 Q_2 / (4\pi\epsilon_0 r^2)$ .
Same sign: repulsion.
Opposite signs: attraction.
$\epsilon_0 = 8.85 \times 10^{-12}$ .

What you’ll learn

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

18.3.1 — Apply Coulomb's law.

Coulomb's law

Inverse-square force.

Formula. $F = \frac{Q_1 Q_2}{4\pi\epsilon_0 r^2}$ .

Like gravity but stronger; and can be attractive OR repulsive.

Repulsion for same-sign charges; attraction for opposite.

$r$ measured between point charges.

Cambridge tip. Charges quoted in nC or μC — convert to C.

Figure 1 — Coulomb's law: force between two point charges

Coulomb force acts along the line between the charges with magnitude proportional to 1/r²; like signs repel, opposite signs attract. Note that r is measured centre to centre.

Figure 2 — The inverse-square fall of the Coulomb force

The inverse-square law is much harsher than it looks: three times the distance means one ninth of the force. The curve approaches the axis but never touches it.

Figure 3 — Converting charges to coulombs before substituting

Charges in exam questions are almost always quoted in nC or μC. Both charges appear as a product, so an unconverted prefix is squared into the error.

Figure 4 — Coulomb's law compared with Newton's law of gravitation

The two laws have identical mathematical form. The physical difference is that charge comes in two signs, so the Coulomb force can act either way.

How the force responds to a change.

Change made	Effect on $F$
Double $Q_1$	$F$ doubles
Double both $Q_1$ and $Q_2$	$F$ becomes $4\times$
Double the separation $r$	$F$ falls to $\frac{1}{4}$
Halve the separation $r$	$F$ becomes $4\times$
Reverse the sign of one charge	Same size, direction reverses

Inverse square.
Repulsion or attraction.
$\epsilon_0 = 8.85 \times 10^{-12}$ .

See the full worked example for electric force between point charges →

Quick recap

$F = Q_1Q_2/(4\pi\epsilon_0 r^2)$ .
Inverse square.

Memorise this

Verbatim phrases and definitions Cambridge mark schemes credit.

Coulomb's law.
$\epsilon_0$ value.

How it’s examined

Coulomb's law on 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.

Take this whole topic with you

Step-by-step worked examples — Electric force between point charges

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

1Force between charges (5 marks)
Extended• Adapted from 9702/42 May/Jun 2024• Coulomb
Question
Two $+3.0 \times 10^{-6}$ C charges are 0.20 m apart. Find force. $\epsilon_0 = 8.85 \times 10^{-12}$ . (5 marks)
Step-by-step solution
1. Step 1
  $F = Q_1 Q_2 / (4\pi\epsilon_0 r^2)$ .
  $F = \dfrac{(3 \times 10^{-6})^2}{4\pi(8.85 \times 10^{-12})(0.04)} \approx 2.02 \text{ N}$
Answer
$F \approx 2.02$ N (repulsive).

Key Formulae — Electric force between point charges

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

Coulomb's law
$F = \dfrac{Q_1 Q_2}{4\pi\epsilon_0 r^2}$
$\epsilon_0$
permittivity of free space, $8.85 \times 10^{-12}$
When to use
Force between point charges in vacuum. Repulsive if same sign, attractive if opposite.

Key Definitions and Keywords — Electric force between point charges

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

Coulomb's law
Examiner keyword
Force between two point charges is proportional to product of charges and inversely proportional to square of distance.
Permittivity of free space $\epsilon_0$
Examiner keyword
$8.85 \times 10^{-12}$ F/m. Universal constant.

Common Mistakes and Misconceptions — Electric force between point charges

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

✕Signs in Coulomb's law
9702 Examiner Reports 2022-2024
Why it happens
Confusion.
How to avoid it
Same-sign charges → POSITIVE $F$ (repulsion). Opposite signs → NEGATIVE $F$ (attraction). Cambridge usually asks for magnitude.