Physics 9702 · Paper 4

Charges in Uniform Fields

Between parallel plates the field is the same everywhere — the electrical version of free fall, and the most frequently examined corner of the topic.

E = V/d and the forces it makes

E = \dfrac{\Delta V}{\Delta d}

Symbols

$E$ = uniform field strength between the plates (V m⁻¹)
$\Delta V$ = potential difference across the plates (V)
$\Delta d$ = plate separation (m)

You met this at AS; A2 chains it: $F = QE$ gives the force, then $a = F/m$ the acceleration. An electron between plates 0.041 m apart at 58 kV feels $E = 1.4\times10^{6}$ V m−¹ and accelerates at $2.5\times10^{17}$ m s−² (9702/42/M/J/25 Q6(b)) — enormous, because the electron's mass is tiny.
Sketching $V$ against position between the plates: a straight line from $(0, V)$ at the positive plate down to zero at the earthed plate — constant gradient is exactly what “uniform field” means (9702/42/F/M/25 Q2(c)).

Worked example

A floating oil droplet (2023 paper)

A charged oil droplet hangs stationary between horizontal plates 5.2 cm apart with 1200 V across them (top plate positive). Its charge is $3.2\times10^{-19}$ C. Find its mass (9702/42/O/N/23 Q5(c)).

Stationary means the electric force balances the weight: $mg = EQ$ — so the droplet's charge must be negative (pulled up towards the positive plate).
$E = V/d = 1200/0.052$ , so $m = \dfrac{1200 \times 3.2\times10^{-19}}{9.81 \times 0.052} = 7.5\times10^{-16}\ \text{kg}$ .

Answer

m \approx 7.5\times10^{-16}\ \text{kg}

The charge here is $2e$ — this is Millikan's historic experiment, which first showed charge comes in steps of $e$ .

Moving charges: the parabola

Deflection marks are itemised: a smooth curve only while between the plates, straight lines before and after, and the bend is toward the positive plate. The force never changes direction, so the path is a parabola — not a circle.

A charge moving across a uniform field is a projectile: constant velocity along the plates, constant force across them. The path is a parabola inside the plates and a straight line outside — both features are drawing marks, plus the bend towards the correct plate (electrons bend towards the positive plate) (9702/41/M/J/24 Q5(b)(iii)).
Why not a circle? The banked answer: the force is not always perpendicular to the velocity — it keeps one fixed direction (9702/42/F/M/23 Q4(c)(iii)). (A magnetic force is always perpendicular; that contrast is the next chapter's opening.)

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