Q: What does A-Level Physics: 14) Electric Fields Guide cover? A: From Coulomb's law to capacitor energy graphs, this post unpacks Section V Topic 14 of the 2026 H2 Physics syllabus for IP students and parents.
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 21-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=4πε01r2Q1Q2.
1.1 Quick-fire cues
SI unit for charge is C.
Sign mistakes: repulsive if charges share sign, attractive otherwise.
1.2 Mini-drill
Two +2.0nC charges sit 5.0cm apart in air. Calculate F. Answer: 1.4mN.
2 Radial electric fields & potentials
Because E=qF, the field around a point charge is
E=4πε01r2Q.
Integrating this field gives the scalar potential
V=4πε01rQ.
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
UE=4πε01rQ1Q2.
3 Potential gradients & equipotentials
Field lines show direction of E.
Equipotential surfaces are always perpendicular to field lines.
Mathematically, E=−drdV.
Exam cue: check sign conventions when taking gradients.
4 Uniform electric fields
Between parallel plates:
E=dV.
4.1 Force & motion
A charge q experiences F=qE. With constant a=mF, kinematics mirrors vertical projectile motion.
4.2 Mini-drill
An electron enters a 600V plate pair 8.0mm apart, velocity horizontal. Find vertical displacement after 1.0cm of travel.
5 Capacitance fundamentals
Definition:C=VQ. Unit: farad (F=C⋅V−1).
5.1 Energy store
Area under V-Q graph (triangle) gives
U=21QV=21CV2=21CQ2.
5.2 Exam-class graph sketch
Label axes, mark triangle area, read 21 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.
Start with Coulomb's inverse-square law. Divide by charge to get field strength; integrate to find potential. Between plates you can treat the field as uniform E=dV. Once you know E, the force on a charge is qE and motion follows mechanics. Capacitors store charge/energy; their energy formulas mirror triangular areas on Q-V graphs.
Key relations
Quantity
Expression / note
Coulomb's law
\( F = \dfrac{1}{4 \pi \varepsilon_0} \dfrac{Q_1 Q_2}{r^2} \)
Electric field (point charge)
\( E = \dfrac{F}{q} = \dfrac{1}{4 \pi \varepsilon_0} \dfrac{Q}{r^2} \)
Electric potential
\( V = \dfrac{1}{4 \pi \varepsilon_0} \dfrac{Q}{r} \)
Potential gradient relation
\( E = - \dfrac{\mathrm{d}V}{\mathrm{d}r} \)
Uniform field
\( E = \dfrac{V}{d} \)
Work/energy of charge
\( W = qV \)
Capacitance definition
\( C = \dfrac{Q}{V} \)
Capacitor energy
\( U = \dfrac{1}{2} C V^2 = \dfrac{1}{2} Q V = \dfrac{1}{2} \dfrac{Q^2}{C} \)
Field-potential link: integrate Coulomb's law to obtain potential; differentiate back to recover field.
Parallel plate field: derive E=dV by combining force and work definitions.
Energy stored in capacitor: integrate V with respect to Q to show factor 1/2.
Charged particle deflection: combine F=qE with SUVAT relations to predict trajectories in oscilloscopes or mass-spectrometer velocity selectors.
Worked example 1 - potential due to multiple charges
Two charges +4.0nC and −2.0nC are 12cm apart. Find the potential and field at a point midway between them.
Approach: potential adds algebraically, field adds vectorially; choose direction from positive to negative charge, compute magnitude using inverse-square.
Worked example 2 - capacitor discharge
A C=220×10−6F capacitor charged to V=12V discharges through R=4.7×103Ω. Calculate the initial energy stored and the initial discharge current. Discuss how energy is dissipated.
Solution: U=21CV2, I0=RV. Mention exponential decay of current and conversion to thermal energy.
Practical & data tasks
Map equipotentials using conductive paper and voltmeter; sketch electric field lines from data.
Use apparatus to show Millikan-style oil drop balancing (qualitative) linking gravitational and electric forces.
Build RC circuit and record V(t) to verify exponential decay; extract time constant.
Common misconceptions & exam traps
Treating potential as vector quantity; it is scalar.
Forgetting that equipotentials are perpendicular to field lines.
Mixing units (mm vs m) when using V/d.
Neglecting the 21 factor in capacitor energy or forgetting charge changes when voltage changes.
Quick self-check quiz
What is the electric field midway between two equal positive charges? - Zero by symmetry (fields cancel).
A proton accelerated through 500V gains how much kinetic energy? - 500eV≈8.0×10−17 J.
Doubling plate separation while keeping voltage constant does what to field strength? - Halves it.
State two ways to increase capacitance of a parallel-plate capacitor. - Increase plate area; decrease separation; insert dielectric with higher εr.
How does equivalent capacitance change when capacitors are in parallel? - Add directly Ceq=C1+C2+…
Revision workflow
Re-derive Coulomb-potential-field relationships weekly to cement mathematical links.
Solve combined problems involving charged particle motion in uniform fields and capacitor energy.
Prepare a flashcard sheet of dielectric constants and typical capacitor applications.
Work through past-paper RC discharge questions to stay fluent with exponential decay graphs.
