A-Level Physics — 14) Electric Fields (IP-Friendly Guide)

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14 Jul 2025, 00:00 Z

TL;DR
Electric field questions are the hinge between mechanics and circuits. Nail the three k-values (force, field, potential), the V/d shortcut for plates and the \(\frac12\)-factor for capacitor energy, and you will harvest marks across Papers 1-3 and the practical.

1 Coulomb 's law: the force glue

The syllabus demands you recall and use

\[ F = \frac{1}{4 \pi \varepsilon_0} \space \frac{Q_1Q_2}{r^2}. \]

1.1 Quick-fire cues

SI unit for charge is \(\pu{C}\).
Sign mistakes: repulsive if charges share sign, attractive otherwise.

1.2 Mini-drill

Two \(\pu{+2.0 \space nC}\) charges sit \(\pu{5.0 \space cm}\) apart in air. Calculate \(F\). Answer: \(\pu{1.4 \space mN}\).

2 Radial electric fields & potentials

Because \(E = F/q\), the field around a point charge is

\[ E = \frac{1}{4 \pi \varepsilon_0} \space \frac{Q}{r^2}. \]

Integrating this field gives the scalar potential

\[ V = \frac{1}{4 \pi \varepsilon_0} \space \frac{Q}{r}. \]

2.1 Zero reference

Infinity is the zero-potential reference unless the question states otherwise.

2.2 Potential energy pair

Two point charges form a system with

\[ U_E = \frac{1}{4 \pi \varepsilon_0} \space \frac{Q_1Q_2}{r}. \]

3 Potential gradients & equipotentials

Field lines show direction of \(\vec{E}\).
Equipotential surfaces are always perpendicular to field lines.
Mathematically, \(E = -\dfrac{\mathrm{d}V}{\mathrm{d}r}\).

Exam cue: check sign conventions when taking gradients.

4 Uniform electric fields

Between parallel plates:

\[ E = \frac{V}{d}. \]

4.1 Force & motion

A charge \(q\) experiences \(F = qE\).
With constant \(a = F/m\), kinematics mirrors vertical projectile motion.

4.2 Mini-drill

An electron enters a \(\pu{600 \space V}\) plate pair \(\pu{8.0 \space mm}\) apart, velocity horizontal. Find vertical displacement after \(\pu{1.0 \space cm}\) of travel.

5 Capacitance fundamentals

Definition: \(C = Q/V\). Unit: farad \((\pu{F} = \pu{C.V-1})\).

5.1 Energy store

Area under \(V\)-\(Q\) graph (triangle) gives

\[ U = \frac12 QV = \frac12 C V^2 = \frac12 \frac{Q^2}{C}. \]

5.2 Exam-class graph sketch

Label axes, mark triangle area, read \(\frac12\) factor directly.

6 Three timing hacks for WA & prelims

Copy units first — minimizes careless mistakes.
Vector-check every force sum.
Leave capacitor energy algebra until numbers are parked.

7 IP-specific pitfalls

Pitfall	Fix
Treating \(\varepsilon_0\) as 0	Memorise \(8.85 \times 10-12 \pu{F.m-1}\).
Confusing \(F=qE\) and \(E=V/d\)	Write a “fields toolkit” flashcard.
Forgetting \(\frac12\) in energy	Draw the \(Q\)-\(V\) triangle before calculating.

8 Further reading

9 Call-to-action

Parents: book a 60-min Electric Fields clinic before the next weighted assessment.
Students: screenshot the “fields toolkit” and test it on three past-year MCQs tonight.

Last updated 14 Jul 2025. Next review when SEAB issues the 2027 draft syllabus.