OCR A-Level Physics: Capacitors and Fields

Capacitors and fields constitute the most calculation-dense module in OCR A-Level Physics A (H556). Modules 6.1, 6.2 and 6.3 together carry the highest density of formulae per spec page anywhere in the course — and they reward fluency disproportionately because every formula appears in some form across all three papers. Capacitors deliver the exponential decay arithmetic that recurs in radioactive decay (Module 6.4); Coulomb's law and electric potential mirror gravitational fields almost line-for-line; Faraday-Lenz and the transformer equation underpin every applied electromagnetism context in Paper 3 unified items.

H556 examiners weight this module heavily because the calculations are genuinely synoptic. The same exponential mathematics underwrites RC discharge, RC charging, radioactive decay and capacitor energy release into a defibrillator pulse; the same inverse-square geometry underwrites Coulomb's law for charges and Newton's law for masses; the same magnetic-flux argument underwrites the motor effect, the dynamo effect and the transformer. A candidate who masters the unified mathematical framework here has a toolkit for half of Paper 2 and a meaningful share of Paper 3; a candidate who treats the formulae as independent recall items spends three times the effort and gets two-thirds of the marks.

Course 10 of the H556 Physics learning path on LearningBro, Capacitors and Fields, sets out the electrostatics-and-magnetism scaffolding that underpins Module 6. It opens with capacitance, capacitor combinations and energy storage, moves through RC charging and discharging exponentials, develops electric field strength and Coulomb's law alongside electric potential, then layers in magnetic fields, the force on currents and charges, electromagnetic induction via Faraday-Lenz, and the transformer equation. It sits at the core of the LearningBro OCR A-Level Physics learning path and feeds directly into Nuclear, Particle and Medical Physics (where exponential decay reappears, and where magnetic-field deflection underwrites particle physics) and into Astrophysics and Cosmology (where inverse-square geometry underwrites stellar luminosity). Get the field-and-flux fluency here and Paper 2's calculation density becomes recognition rather than improvisation.

Guide Overview

The Capacitors and Fields course is built as a twelve-lesson sequence that moves from capacitance through electrostatics to magnetism and electromagnetic induction.

OCR H556 Specification Coverage

This course addresses OCR H556 Module 6.1 (capacitors), Module 6.2 (electric fields) and Module 6.3 (magnetic fields and electromagnetic induction) in full. Refer to the official OCR specification document for the exact statement wording; the table below summarises the lesson-to-spec mapping descriptively.

Sub-topic	Spec area	Primary lesson(s)
Capacitance Q = CV; capacitor combinations	OCR H556 Module 6.1.1	Capacitance; Capacitors in Series and Parallel
Energy stored W = ½CV² = ½QV = Q²/(2C)	OCR H556 Module 6.1.2	Energy Stored in Capacitors
RC discharging exponential Q = Q₀e^(-t/RC)	OCR H556 Module 6.1.3	Discharging Capacitors
RC charging exponential Q = Q₀(1 - e^(-t/RC))	OCR H556 Module 6.1.3	Charging Capacitors
Electric field strength E = F/Q = V/d; radial vs uniform	OCR H556 Module 6.2.1	Electric Field Strength
Coulomb's law F = Qq / (4πε₀r²)	OCR H556 Module 6.2.2	Coulomb's Law
Electric potential V = Q / (4πε₀r); equipotentials	OCR H556 Module 6.2.3	Electric Potential
Magnetic flux density B; F = BIL; F = BQv	OCR H556 Module 6.3.1	Magnetic Fields and Forces
Velocity selector and circular motion in B-field	OCR H556 Module 6.3.1	Force on Moving Charges and Velocity Selector
Magnetic flux Φ = BA; Faraday's and Lenz's laws	OCR H556 Module 6.3.2	Magnetic Flux and Electromagnetic Induction
Transformer equation V_s/V_p = N_s/N_p; power transmission	OCR H556 Module 6.3.3	Transformers

Module 6 is examined across all three H556 papers. Paper 1 (Modelling Physics) carries the routine RC and Coulomb calculations; Paper 2 (Exploring Physics) carries multi-mark electromagnetism items reliably; Paper 3 (Unified Physics) reuses the exponential and inverse-square frameworks against medical, particle and engineering contexts.

Topic-by-Topic Walkthrough

Capacitance and Capacitor Combinations

The capacitance lesson defines C = Q/V with units farads (F = C V⁻¹), notes that real capacitors are typically in the μF to pF range, and develops the parallel-plate geometry C = ε₀ε_r A/d as a structural insight (larger plate area or smaller separation means more charge stored per volt). The capacitors in series and parallel lesson develops the combination rules: parallel C_total = C₁ + C₂ + ... (charges sum at the same voltage), series 1/C_total = 1/C₁ + 1/C₂ + ... (voltages sum at the same charge). The series rule is the structural opposite of the resistor series rule, and the parallel rule is the structural opposite of the resistor parallel rule — examiners reward candidates who can articulate why (capacitors in parallel see the same V but stack their charges; in series they see the same Q but stack their voltages).

Energy Stored in Capacitors

The energy stored lesson develops W = ½QV = ½CV² = Q²/(2C). The factor of ½ is the geometric average that arises because voltage builds up from zero to V as charge accumulates; the W = QV expression (without the ½) would apply only if the charge were delivered against the full final voltage from the start, which it isn't. A worked example: a 470 μF capacitor charged to 12 V stores W = ½ × 470 × 10⁻⁶ × 12² = 0.034 J. This energy can be released as a brief pulse — the defibrillator capacitor at a few hundred μF charged to ≈ 5 kV stores ≈ 400 J, delivered in milliseconds, which is why the discharge looks so dramatic. The energy density per unit volume in the dielectric is u = ½ε₀ε_r E², a foundational result that reappears in undergraduate electromagnetism.

RC Discharging and Charging Exponentials

The discharging capacitors lesson develops Q = Q₀ e^(-t/RC) where RC is the time constant τ with units of seconds. After one time constant the charge has fallen to Q₀ / e ≈ 0.37 Q₀; after five time constants the charge has fallen to ≈ 0.0067 Q₀, conventionally treated as "fully discharged". The exponential form mirrors radioactive decay's N = N₀ e^(-λt) — the same exponential mathematics, different physical context — and this synoptic link is examined explicitly. The charging capacitors lesson develops Q = Q₀ (1 - e^(-t/RC)) for charging through a resistor from a constant voltage source: charge rises asymptotically to Q₀ = CV with the same time constant τ = RC. A worked calculation: a 100 μF capacitor charging through a 10 kΩ resistor has τ = 100 × 10⁻⁶ × 10⁴ = 1.0 s; after 3 s the capacitor is at Q = Q₀(1 - e⁻³) = 0.95 Q₀.

Electric Field Strength, Coulomb's Law and Electric Potential

The electric field strength lesson defines E = F/Q (force per unit charge on a test charge) with units V m⁻¹ or N C⁻¹, then develops two canonical geometries: uniform field between parallel plates E = V/d (which is why capacitor plates produce a constant E across the gap), and radial field from a point charge E = Q / (4πε₀r²) (inverse-square in r). The Coulomb's law lesson develops F = Qq / (4πε₀r²) with ε₀ ≈ 8.85 × 10⁻¹² F m⁻¹ — the inverse-square law for the force between two point charges. The structural identity with Newton's law of gravitation F = GMm/r² is examined explicitly. The electric potential lesson develops V = Q / (4πε₀r) — the work done per unit positive test charge in bringing it from infinity to a distance r from a source charge Q. The sign conventions are crucial: positive Q gives positive V (work done against the field if the test charge is also positive); negative Q gives negative V (the test charge is attracted in). Equipotential surfaces are perpendicular to field lines, and no work is done moving a charge along an equipotential.

Magnetic Fields, Forces and Velocity Selectors

The magnetic fields and forces lesson develops the magnetic flux density B in tesla (T = kg s⁻² A⁻¹), the force on a current-carrying wire F = BIL sin θ, and Fleming's left-hand rule for the direction of the force (first finger field, second finger current, thumb thrust). The lesson stresses the perpendicular-only nature of magnetic force on charges: the force is always perpendicular to velocity, so magnetic forces do no work and the speed of a charged particle in a magnetic field is conserved. The force on moving charges lesson develops F = BQv sin θ and the radius of circular motion in a uniform B field: r = mv/(BQ), the canonical formula for mass spectrometers, cyclotrons and the LHC. The velocity selector — crossed E and B fields perpendicular to the beam — picks out particles for which the electric force QE balances the magnetic force BQv, so v = E/B; this is the standard input filter for mass spectrometers and a Paper 2 fixture.

Magnetic Flux, Faraday-Lenz and Transformers

The magnetic flux and electromagnetic induction lesson defines magnetic flux Φ = BA cos θ (units weber Wb = T m²), flux linkage NΦ for a coil of N turns, and Faraday's law: induced EMF ε = -d(NΦ)/dt. The minus sign is Lenz's law: the induced current opposes the change in flux that produced it (so a magnet pushed into a coil induces a current that creates a field repelling the magnet — energy conservation in action). The lesson works the standard examples: a magnet falling through a coil, a coil rotating in a uniform field (the AC generator), a conducting rod sliding along rails in a B field. The transformers lesson develops V_s/V_p = N_s/N_p for an ideal transformer with negligible losses, and I_s/I_p = N_p/N_s for power conservation (V_p I_p = V_s I_s). Transformers only work on AC because their operation depends on a continuously changing flux; this is why national-grid power transmission uses AC and steps voltage up to hundreds of kV to reduce I²R transmission losses.

A Typical H556 Paper 2 Question

A standard Paper 2 prompt gives candidates a defibrillator-like circuit: a capacitor of stated capacitance charged to a stated voltage and discharged through a stated resistance representing the patient. The route is fixed: compute the stored energy W = ½CV²; compute the time constant τ = RC; compute the charge remaining after a specified time using Q = Q₀ e^(-t/τ); compute the residual energy using the new V or Q and the energy formula; explain why the pulse duration must be short enough to deliver most of the energy in the desired biological window. The AO split is typically AO1 1-2 marks (recall the energy and exponential formulae), AO2 4-5 marks (substitute the given numbers), AO3 2-3 marks (justify the design choices — why a high voltage, why a short pulse, why this RC value). The Top-band discriminator is the explicit medical-physics rationale: the heart's refractory period determines the optimal pulse duration, and the capacitor's RC time constant must be tuned to that.

Synoptic Links

Capacitors and fields are the synoptic spine of Module 6. The exponential decay Q = Q₀ e^(-t/RC) developed for capacitors is mathematically identical to the radioactive decay N = N₀ e^(-λt) developed in Nuclear, Particle and Medical Physics; the time constant τ = RC for capacitors mirrors the mean lifetime τ = 1/λ for radioactive nuclei. Coulomb's law for charges is structurally identical to Newton's law of gravitation in Circular Motion, SHM and Gravity: both inverse-square laws, with one signed (charge can repel) and one unsigned (mass only attracts). Electric potential V = Q/(4πε₀r) mirrors gravitational potential V = -GM/r, with the same inverse dependence on r. The circular motion of a charged particle in a B-field r = mv/(BQ) underwrites particle physics, where the Standard Model particles in Nuclear, Particle and Medical Physics are characterised by their tracks in detectors. Magnetic flux changes drive the AC generation that powers transformers, which in turn step voltages up and down for the national grid — the engineering context that closes the Module 6 sequence.

Paper 3 'Unified Physics' items typically deploy this module against unfamiliar contexts. A medical-physics scenario might give a defibrillator's capacitor and ask candidates to compute the stored energy, the discharge time constant, and the residual energy after the pulse. A particle-physics scenario might give a beam of unknown ions entering a velocity selector then a mass spectrometer, asking for the velocity selected and the mass-to-charge ratio measured. A grid-engineering scenario might give the transformer ratios and transmission-line resistance for a section of the national grid and ask candidates to compute the percentage power loss at low versus high transmission voltage. In every case the underlying skill is the unified-field-and-flux fluency built in Module 6.

What Examiners Reward

Top-band marks on this module cluster around unit discipline, explicit time-constant reasoning, and Lenz's-law direction-argument fluency. For RC calculations, examiners want τ = RC stated explicitly with units (s) and the exponential evaluated step-by-step, not skipped. For Coulomb's law and electric potential, they want sign conventions explicit: positive for like charges or work against the field, negative for unlike charges or work with the field. For Faraday-Lenz items, they want the minus sign in ε = -dΦ/dt acknowledged and the direction-of-induced-current explicitly stated, with the energy-conservation rationale ("the induced current opposes the change in flux that produced it because creating a current consumes energy"). For magnetic-force-on-charge items, they want the perpendicularity acknowledged ("magnetic forces do no work because they are always perpendicular to velocity") and Fleming's left-hand rule applied with the correct finger conventions.

Common pitfalls cluster around six recurring mistakes. First, dropping the ½ factor in W = ½CV², which gives an answer twice the correct value. Second, confusing the parallel and series rules for capacitors with those for resistors (capacitors in series behave like resistors in parallel and vice versa, because capacitors store charge while resistors dissipate power). Third, applying Faraday's law without the N for flux linkage in a multi-turn coil, giving an answer N times too small. Fourth, treating the time constant τ as the time for complete discharge rather than the time for the charge to fall to Q₀/e ≈ 0.37 Q₀. Fifth, applying the right-hand rule (the convention for vector cross-products) when Fleming's left-hand rule (the convention for the force on a positive current in a B field) is needed, reversing the force direction. Sixth, forgetting that transformers only work on AC; a DC supply produces no flux change and therefore no induced EMF in the secondary coil.

Practical Activity Groups (PAGs)

This course anchors PAG 8 (Capacitors) through the RC discharge and charging experiments. The standard apparatus is a charged capacitor connected through a resistor and stopwatch, with voltage logged against time; plotting ln(V) against t gives a straight line of gradient -1/RC, from which the time constant is extracted experimentally and compared against the calculated τ = RC. The lesson on discharging capacitors explicitly develops this graph-linearisation technique, which is a Paper 2 staple. PAG 9 (Magnetic fields) is anchored by the force-on-a-current-carrying-wire experiment: a wire suspended above a magnet on a top-pan balance experiences a downward reaction force when current flows, measured directly from the balance reading. The slope of force versus current gives BL, from which B is extracted given L. The Faraday-Lenz qualitative demonstrations — magnet through a coil into an oscilloscope, magnet falling through a copper tube — are also standard tabletop work that anchors the lesson on magnetic flux and electromagnetic induction.

Going Further

Undergraduate analogues of this material extend in three directions. First, electromagnetism generalises Coulomb's law and Faraday's law into Maxwell's four equations — the unified theory of electric and magnetic fields, whose wave-equation solutions are light itself. Second, AC circuit theory generalises the RC time constant into the complex-impedance formalism Z = R + 1/(jωC) used throughout electronic engineering. Third, condensed-matter physics generalises capacitor dielectrics into the rich physics of polarisation, ferroelectricity and the high-κ dielectrics used in modern semiconductor devices. Suggested reading at this level includes Griffiths' Introduction to Electrodynamics, Purcell and Morin's Electricity and Magnetism, and Feynman Volume II for the conceptual treatment. Oxbridge-style interview prompts include: "Why is energy stored in a capacitor only ½QV rather than QV?" "If you double the separation of the plates of a charged isolated capacitor, what happens to the stored energy and where does it come from?" "Why is electricity transmitted at high voltage on the national grid even though it would be safer at low voltage?"

The Core Equations, Set Out Cleanly

Module 6 is the most formula-dense stretch of H556, but the formulae fall into three tight families. Learn each family as a unit and the cross-links do half your revision for you.

Capacitors. Definition, energy stored (three equivalent forms), and the RC exponentials:

$C = \dfrac{Q}{V} \qquad W = \tfrac{1}{2}QV = \tfrac{1}{2}CV^2 = \dfrac{Q^2}{2C}$

$Q = Q_0\,e^{-t/RC} \quad \text{(discharge)} \qquad Q = Q_0\left(1 - e^{-t/RC}\right) \quad \text{(charge)}$

The combination rules are the structural opposite of the resistor rules: capacitors in parallel add ( $C_\text{total} = C_1 + C_2 + \cdots$ ), while in series their reciprocals add ( $\tfrac{1}{C_\text{total}} = \tfrac{1}{C_1} + \tfrac{1}{C_2} + \cdots$ ).

Electric fields. Field strength (two geometries), Coulomb's law, and electric potential:

$E = \dfrac{F}{Q} = \dfrac{V}{d} \qquad E = \dfrac{Q}{4\pi\varepsilon_0 r^2}$

$F = \dfrac{Qq}{4\pi\varepsilon_0 r^2} \qquad V = \dfrac{Q}{4\pi\varepsilon_0 r}$

Magnetic fields and induction. Forces on currents and charges, radius of circular motion, flux and Faraday-Lenz, and the transformer relation:

$F = BIL\sin\theta \qquad F = BQv\sin\theta \qquad r = \dfrac{mv}{BQ}$

$\Phi = BA\cos\theta \qquad \varepsilon = -\dfrac{\mathrm{d}(N\Phi)}{\mathrm{d}t} \qquad \dfrac{V_s}{V_p} = \dfrac{N_s}{N_p} = \dfrac{I_p}{I_s}$

The data-sheet constant is the permittivity of free space $\varepsilon_0 \approx 8.85 \times 10^{-12}\ \text{F m}^{-1}$ ; note that $1/(4\pi\varepsilon_0) \approx 8.99 \times 10^{9}\ \text{N m}^2\,\text{C}^{-2}$ , the Coulomb constant, which some questions quote directly. The time constant $\tau = RC$ has units of seconds — check this dimensionally if you ever doubt a rearrangement.

Extended Worked Examples

Worked example 1 — energy released by a discharging capacitor

A $2200\ \mu\text{F}$ capacitor is charged to $9.0\ \text{V}$ and then discharged through a $47\ \text{k}\Omega$ resistor. Find (a) the initial stored energy, (b) the time constant, (c) the charge remaining after $150\ \text{s}$ , and (d) the energy remaining at that instant.

(a) Initial energy:

$W = \tfrac{1}{2}CV^2 = \tfrac{1}{2} \times 2200 \times 10^{-6} \times (9.0)^2 = 0.089\ \text{J}$

(b) Time constant:

$\tau = RC = 47 \times 10^{3} \times 2200 \times 10^{-6} = 103\ \text{s}$

(c) Charge after 150 s. First the initial charge $Q_0 = CV = 2200 \times 10^{-6} \times 9.0 = 1.98 \times 10^{-2}\ \text{C}$ . Then

$Q = Q_0\,e^{-t/\tau} = 1.98 \times 10^{-2} \times e^{-150/103} = 1.98 \times 10^{-2} \times 0.233 = 4.6 \times 10^{-3}\ \text{C}$

(d) Energy at that instant. The voltage has fallen to $V = Q/C = 4.6 \times 10^{-3} / 2200 \times 10^{-6} = 2.10\ \text{V}$ , so

$W = \tfrac{1}{2}CV^2 = \tfrac{1}{2} \times 2200 \times 10^{-6} \times (2.10)^2 = 4.9 \times 10^{-3}\ \text{J}$

The teaching point buried in part (d): energy falls off twice as fast as charge, because $W \propto V^2 \propto Q^2$ . After one time constant $Q$ drops to $37\%$ of its start value but $W$ drops to $37\%^2 \approx 14\%$ . Examiners love to probe this asymmetry.

Worked example 2 — Coulomb's law and superposition

Two point charges, $+3.0\ \text{nC}$ and $-5.0\ \text{nC}$ , are $4.0\ \text{cm}$ apart in a vacuum. Find the magnitude of the electrostatic force between them.

$F = \dfrac{Qq}{4\pi\varepsilon_0 r^2} = \dfrac{(3.0 \times 10^{-9})(5.0 \times 10^{-9})}{4\pi \times 8.85 \times 10^{-12} \times (0.040)^2}$

$F = \dfrac{1.5 \times 10^{-17}}{4\pi \times 8.85 \times 10^{-12} \times 1.6 \times 10^{-3}} \approx 8.4 \times 10^{-5}\ \text{N}$

Because the charges are opposite, the force is attractive. Note the two silent traps: the distance must be in metres ( $4.0\ \text{cm} = 0.040\ \text{m}$ , squared to $1.6 \times 10^{-3}\ \text{m}^2$ ), and the nanocoulombs must become $10^{-9}\ \text{C}$ . Miss either and the answer is out by a clean power of ten.

Worked example 3 — charged particle in a magnetic field

A proton ( $m = 1.67 \times 10^{-27}\ \text{kg}$ , $Q = 1.60 \times 10^{-19}\ \text{C}$ ) moves at $2.0 \times 10^{6}\ \text{m s}^{-1}$ perpendicular to a uniform magnetic field of flux density $0.35\ \text{T}$ . Find the radius of its circular path.

$r = \dfrac{mv}{BQ} = \dfrac{1.67 \times 10^{-27} \times 2.0 \times 10^{6}}{0.35 \times 1.60 \times 10^{-19}} \approx 6.0 \times 10^{-2}\ \text{m}$

The path is circular because the magnetic force $F = BQv$ is always perpendicular to the velocity — it changes the direction of motion but never the speed, so it does no work. That "magnetic forces do no work" statement is a recurring one-mark gift on the extended items, and it is the conceptual foundation of mass spectrometers, cyclotrons and the LHC.

Worked example 4 — transformer and power transmission

An ideal transformer steps $230\ \text{V}$ up to $11\,500\ \text{V}$ for local distribution. The primary coil has 400 turns. (a) How many turns on the secondary? (b) If the primary current is $50\ \text{A}$ , what is the secondary current?

(a) From $V_s/V_p = N_s/N_p$ :

$N_s = N_p \times \dfrac{V_s}{V_p} = 400 \times \dfrac{11\,500}{230} = 20\,000\ \text{turns}$

(b) For an ideal (100%-efficient) transformer, power in equals power out, so $V_p I_p = V_s I_s$ :

$I_s = I_p \times \dfrac{V_p}{V_s} = 50 \times \dfrac{230}{11\,500} = 1.0\ \text{A}$

This is the whole rationale of the national grid in miniature: step the voltage up and the current comes down in the same ratio, and since transmission losses are $P_\text{loss} = I^2 R$ , cutting the current by a factor of 50 cuts the line losses by a factor of $50^2 = 2500$ .

Exam Technique: Turning Knowledge into Marks

On RC exponential items, always state $\tau = RC$ explicitly with its unit before you use it, and keep charge, current and voltage exponentials straight: they all share the same $e^{-t/RC}$ factor on discharge, because $Q$ , $V$ and $I$ are all proportional to one another through $Q = CV$ and $I = V/R$ . When a question asks for "the time to fall to a given fraction", take natural logs: from $Q = Q_0 e^{-t/RC}$ , $t = -RC\ln(Q/Q_0)$ . Showing that rearrangement earns the method mark even if the arithmetic slips.

On the PAG-linked graph item, you will often be asked to linearise. Taking logs of the discharge equation gives $\ln V = \ln V_0 - t/RC$ , a straight line of gradient $-1/RC$ against $t$ . State the gradient-to-time-constant link explicitly; it is the single most examined data-analysis skill on this module.

On field items, sign conventions decide the AO marks. A positive source charge gives a positive potential; a negative source charge gives a negative potential. Equipotential surfaces are always perpendicular to field lines, and no work is done moving a charge along an equipotential — a favourite "explain" mark.

On Faraday-Lenz items, never drop the minus sign, and never forget the $N$ for a multi-turn coil: the EMF depends on the rate of change of flux linkage $N\Phi$ , not flux alone. When asked for the direction of an induced current, argue from Lenz's law and energy conservation: "the induced current opposes the change in flux that created it, because otherwise energy would be created from nothing."

Mark-scheme literacy

On the classic defibrillator item worth around 9 marks, the AO split is roughly: AO1 (recall the energy and exponential formulae) 1–2 marks; AO2 (substitute the given capacitance, voltage, resistance and time) 4–5 marks; AO3 (justify the design — why a high charging voltage, why a short pulse tuned to the RC time constant and the heart's refractory period) 2–3 marks. The AO3 design-justification marks are where the band gap opens: strong candidates explain why the numbers are chosen, not just what they are.

Common Mistakes and How to Avoid Them

Mistake 1 — dropping the factor of $\tfrac{1}{2}$ in $W = \tfrac{1}{2}CV^2$ . The energy is half $QV$ , not $QV$ , because the voltage rises from zero to $V$ as the capacitor charges — the charge is delivered against an average voltage of $V/2$ . Omitting the half doubles your answer.

Mistake 2 — swapping the series and parallel rules. Capacitors in series combine like resistors in parallel (reciprocals add), and vice versa. The physical reason: capacitors in series all carry the same charge but share the voltage, so adding one reduces the overall capacitance.

Mistake 3 — forgetting $N$ in flux linkage. For a coil of $N$ turns, the induced EMF is $\varepsilon = -\,\mathrm{d}(N\Phi)/\mathrm{d}t$ , which is $N$ times larger than for a single loop. Leaving out $N$ gives an answer a factor of $N$ too small.

Mistake 4 — treating $\tau$ as the time to fully discharge. After one time constant the charge has only fallen to $37\%$ of its initial value. "Fully discharged" is conventionally taken as five time constants ( $\approx 0.7\%$ remaining), not one.

Mistake 5 — using the right-hand rule for the motor effect. The force on a positive conventional current in a magnetic field follows Fleming's left-hand rule (thuMb = Motion, First finger = Field, seCond finger = Current). Reaching for the right hand reverses the predicted force direction.

Mistake 6 — expecting a transformer to work on DC. Transformers depend on a continuously changing flux to induce a secondary EMF. A steady DC supply produces constant flux, zero rate of change, and therefore zero output. This is precisely why the grid uses AC.

Mini-FAQ

Why is the energy stored only $\tfrac{1}{2}QV$ and not $QV$ ? Because the voltage across the plates climbs from $0$ to $V$ as charge accumulates. Each increment of charge is moved against the voltage present at that moment, and integrating gives the average, $V/2$ . The "missing" half of $QV$ is dissipated in the charging resistor as heat — a lovely result worth quoting in an "explain" answer.

How is Coulomb's law related to gravitation? They are structural twins: both are inverse-square laws in $r$ . The differences are that gravity acts on mass (always attractive) while the Coulomb force acts on charge (attractive or repulsive), and the constants differ ( $G$ versus $1/4\pi\varepsilon_0$ ). Recognising this symmetry lets you carry field and potential intuition across both topics.

Why do magnetic forces do no work? Because $F = BQv$ is always perpendicular to the velocity. Work is force times displacement in the direction of the force, and here that component is always zero. The force therefore changes direction of motion (giving circular paths) but never speed or kinetic energy.

What sets the direction of an induced current? Lenz's law: the induced current always opposes the change in flux that produced it. Push a north pole into a coil and the near face becomes a north pole to repel it; pull it out and the near face becomes a south pole to attract it back. This is energy conservation made visible — you must do work against the induced field.

Why does the national grid transmit at high voltage? To minimise $I^2R$ losses in the cables. Transformers step the voltage up so the same power is carried at much lower current; because losses scale with the square of the current, even a modest voltage increase yields a large reduction in wasted energy. The high voltage is stepped back down for safe domestic use at the far end.

Authorship and Sign-off

This guide was authored independently by John Haigh, paraphrasing OCR H556 Modules 6.1, 6.2 and 6.3 as descriptive use. No verbatim spec text, mark-scheme phrasing, examiner-report quotation, or past-paper question reference appears. The worked examples and numerical values are original or drawn from canonical textbook physics (ε₀ ≈ 8.85 × 10⁻¹² F m⁻¹, typical defibrillator energy ≈ 400 J, RC ≈ 1.0 s for the 100 μF / 10 kΩ canonical example).

Start at the Capacitors and Fields course and work through every lesson in sequence. Once Q = CV, the RC exponentials, Coulomb's law, electric potential, F = BIL, F = BQv and Faraday-Lenz are automatic, every Paper 2 electromagnetism item and every Paper 3 synoptic question becomes a story about how charges and currents create fields, fields exert forces, and changing fluxes drive the EMFs that power the modern world — and the marks resolve into pattern recognition rather than panic.

OCR A-Level Physics: Capacitors and Fields

Guide Overview

The Capacitors and Fields course is built as a twelve-lesson sequence that moves from capacitance through electrostatics to magnetism and electromagnetic induction.

OCR H556 Specification Coverage

Sub-topic	Spec area	Primary lesson(s)
Capacitance Q = CV; capacitor combinations	OCR H556 Module 6.1.1	Capacitance; Capacitors in Series and Parallel
Energy stored W = ½CV² = ½QV = Q²/(2C)	OCR H556 Module 6.1.2	Energy Stored in Capacitors
RC discharging exponential Q = Q₀e^(-t/RC)	OCR H556 Module 6.1.3	Discharging Capacitors
RC charging exponential Q = Q₀(1 - e^(-t/RC))	OCR H556 Module 6.1.3	Charging Capacitors
Electric field strength E = F/Q = V/d; radial vs uniform	OCR H556 Module 6.2.1	Electric Field Strength
Coulomb's law F = Qq / (4πε₀r²)	OCR H556 Module 6.2.2	Coulomb's Law
Electric potential V = Q / (4πε₀r); equipotentials	OCR H556 Module 6.2.3	Electric Potential
Magnetic flux density B; F = BIL; F = BQv	OCR H556 Module 6.3.1	Magnetic Fields and Forces
Velocity selector and circular motion in B-field	OCR H556 Module 6.3.1	Force on Moving Charges and Velocity Selector
Magnetic flux Φ = BA; Faraday's and Lenz's laws	OCR H556 Module 6.3.2	Magnetic Flux and Electromagnetic Induction
Transformer equation V_s/V_p = N_s/N_p; power transmission	OCR H556 Module 6.3.3	Transformers