Physics 9702 · Paper 4

Coulomb's Law

Newton's gravitation law has an electrical twin, stated in four sessions out of nine with the same two-mark scheme.

The statement (two marks)

: the force between two point charges is proportional to the product of the charges and inversely proportional to the square of their separation. One mark per half — and “square” must be said (9702/42/F/M/23 Q4(a)) (9702/42/O/N/23 Q5(a)) (9702/41/M/J/25 Q2(a)).

F = \dfrac{Q_1 Q_2}{4\pi\varepsilon_0 r^2}

Symbols

$F$ = force on each charge (equal and opposite) (N)
$Q_1, Q_2$ = the two point charges (C)
$\varepsilon_0$ = permittivity of free space, 8.85 × 10⁻¹² (F m⁻¹)
$r$ = separation of the charges (centre to centre) (m)

The constant $\dfrac{1}{4\pi\varepsilon_0} = 8.99 \times 10^{9}\ \text{N m}^2\text{C}^{-2}$ is enormous compared with $G$ — electricity is the strong sibling. Like charges give a positive (repulsive) force; unlike charges attract.
Uniformly charged spheres count as point charges at their centres, so $r$ is always the centre-to-centre distance — a sphere question that quotes a surface gap wants you to add the radii first.

Worked example

The hanging sphere (2023 paper, full chain)

Sphere X (+96 nC) is fixed. Sphere Y (+64 nC) hangs beside it on a 1.2 m thread, pushed aside so their centres are 0.080 m apart horizontally. Find the mass of Y (9702/42/F/M/23 Q4(b)).

Coulomb force: $F = \dfrac{96\times10^{-9} \times 64\times10^{-9}}{4\pi\varepsilon_0 \times 0.080^2} = 8.6 \times 10^{-3}\ \text{N}$ .
Thread angle from vertical: $\sin^{-1}(0.080/1.2) = 3.8^\circ$ .
The three forces on Y (weight, tension, electric) balance: $W = F/\tan 3.8^\circ = 0.13\ \text{N}$ , so $m = 0.13/9.81 = 0.013\ \text{kg}$ .

Answer

m \approx 0.013\ \text{kg}

AS equilibrium plus one new force law — most Coulomb marks are old mechanics wearing new units.

Coulomb's law as the engine of an atom

A 2025 question modelled helium: the nucleus (+2e) pulls each orbiting electron with

F = 1.6\times10^{-8}

N, and that attraction is the centripetal force — set

F = mv^2/r

and the electron's speed (

1.7\times10^{6}

m s−¹) and period (

6.2\times10^{-16}

s) follow (9702/41/M/J/25 Q2). Circular motion from Chapter 12, force law from this one.

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