CCEA GCE Physics (1210) · Unit A2 2: Fields, Capacitors and Particle Physics
Mini-Lesson
Fields, Capacitors & Particle Physics
This mini-lesson covers CCEA Unit A2 2: gravitational fields (Newton's law of gravitation, satellites, Kepler's third law), electric fields (Coulomb's law), capacitors (charge, discharge, time constant, energy stored), magnetic fields (F = BIl, F = Bqv, flux, Faraday and Lenz, the a.c. generator and the transformer), particle accelerators and fundamental particles.
The unifying idea: a field is a region where a body experiences a force at a distance. Gravitational fields act on mass, electric fields on charge, magnetic fields on moving charge. Two of them obey an inverse square law — and that similarity is worth exam marks.
Press Start when you are ready.
5.1–5.2 Gravitational fields
Newton's law of gravitation and satellites
Gravitational field strength g is the force per unit mass: g = F/m (N kg⁻¹). Field lines point towards the mass — gravity is always attractive.
F = GMm / r² · g = GM / r²G = 6.67 × 10⁻¹¹ N m² kg⁻². r is measured from the centre of the (spherical) body, not its surface.
Satellites. Gravity supplies the centripetal force, so GMm/r² = mv²/r. The satellite's mass cancels — every satellite at a given radius has the same speed. Setting v = 2πr/T and rearranging gives Kepler's third law:
T² = (4π² / GM) r³ so T² ∝ r³Which is exactly what Newton's law of gravitation predicts — a triumph for the theory.
Geostationary satellite: must have a period of exactly 24 hours, orbit directly above the equator, and travel west to east (the same direction as the Earth's rotation). Only then does it stay above the same point on the ground — which is why satellite dishes never need to move.
Calculate
Your turn — field strength
1Calculate the gravitational field strength at the Earth's surface. Take M = 6.0 × 10²⁴ kg, r = 6.4 × 10⁶ m, G = 6.67 × 10⁻¹¹ N m² kg⁻².
?Which set of conditions is required for a geostationary satellite?
5.3 Electric fields
Coulomb's law and electric field strength
Electric field strength E is the force per unit positive charge: E = F/q (N C⁻¹ or V m⁻¹).
F = q₁q₂ / 4πε₀r² = kq₁q₂ / r²k = 1/4πε₀ ≈ 8.99 × 10⁹ N m² C⁻²; ε₀ = 8.85 × 10⁻¹² F m⁻¹. Like charges repel, unlike charges attract.
E = kq / r² (point charge) · E = V / d (uniform field)Between parallel plates the field is uniform: the same strength everywhere, field lines straight, parallel and equally spaced.
Similarities and differences (5.3.7): both are inverse-square, both have field strength defined as force per unit "something", and both have radial field patterns around a point source. But: gravity acts on mass and is only attractive; the electric force acts on charge and can be attractive or repulsive. The electric force is also enormously stronger — for two protons, the electrostatic repulsion is about 10³⁶ times their gravitational attraction.
Calculate
Your turn — Coulomb's law
2Two point charges of 2.0 nC and 3.0 nC are 50 mm apart. Calculate the force between them, in µN. (k = 8.99 × 10⁹ N m² C⁻²)
Tap a particle, then tap the family it belongs to.
🔹 Lepton (or antilepton)
🔺 Baryon
🔸 Meson
5.4 Capacitors
Capacitance, energy and the time constant
A capacitor stores charge (and energy) by separating charge onto two plates. Its capacitance is the charge stored per volt:
C = Q / VThe farad (F) is one coulomb per volt — a huge unit, so real capacitors are µF, nF or pF.
energy stored = ½QV = ½CV² = ½Q²/C= the area under a Q–V graph. The ½ is there because the p.d. rises from zero as the charge builds up.
Combinations (note they are the "wrong way round" compared with resistors):
parallel: C = C₁ + C₂ · series: 1/C = 1/C₁ + 1/C₂
Discharge through a resistor is exponential:
Q = Q₀e−t/CR · V = V₀e−t/CR · I = I₀e−t/CRThe time constant τ = CR (in seconds) is the time to fall to 1/e ≈ 37% of the initial value.
Confirming the exponential (5.4.7): plot ln V against t. If the decay is exponential you get a straight line of gradient −1/CR — which also gives you the time constant. Applications: a camera flash gun stores energy slowly and releases it in milliseconds; a defibrillator delivers a controlled pulse of energy of a few hundred joules.
Calculate
Your turn — energy stored
3A 470 µF capacitor is charged to 12 V. Calculate the energy stored, in mJ.
mJ
Hint: E = ½CV² = 0.5 × 470 × 10⁻⁶ × 12² = 0.5 × 470 × 10⁻⁶ × 144 J. Multiply by 1000 for mJ.
Calculate
Your turn — capacitor discharge
4A 100 µF capacitor charged to 9.0 V discharges through a 47 kΩ resistor. Calculate the p.d. across it after 10 s.
?Two capacitors of 2.0 µF and 3.0 µF are connected in parallel. What is the total capacitance?
5.5 Magnetic fields
Forces, flux, Faraday and Lenz
A current-carrying conductor in a magnetic field feels a force. Use Fleming's left-hand rule (thuMb = Motion/force, First finger = Field, seCond finger = Current):
F = BIl · F = BqvB is the magnetic flux density, in tesla (T): the force per unit current per unit length on a conductor at right angles to the field. Both formulae assume the field is perpendicular.
Φ = BA · flux linkage = NΦ = NBAFlux Φ is in webers (Wb).
Faraday's law: the induced e.m.f. is equal to the rate of change of flux linkage. Lenz's law: the induced current flows in the direction that opposes the change producing it (a direct consequence of conservation of energy — otherwise you would get energy for nothing).
e.m.f. = − N ΔΦ / ΔtThe a.c. generator: a coil rotating in a field gives E = BANω sin ωt.
Transformer: an alternating current in the primary produces a changing flux in the iron core, inducing an e.m.f. in the secondary: Vs/Vp = Ns/Np. Power losses come from the resistance of the coils (I²R), eddy currents (reduced by laminating the core) and hysteresis. High-voltage transmission means a smaller current for the same power, and since the heat lost in the cables is I²R, dramatically smaller losses.
Calculate
Your turn — force on a wire
5A wire of length 0.12 m carrying a current of 3.0 A lies at right angles to a magnetic field of flux density 0.25 T. Calculate the force on it, in mN.
mN
Hint: F = BIl = 0.25 × 3.0 × 0.12 = 0.090 N. Convert to mN (× 1000).
Calculate
Your turn — Faraday's law
6A coil of 200 turns and area 4.0 × 10⁻³ m² sits at right angles to a magnetic field. The flux density falls uniformly from 0.30 T to zero in 0.20 s. Calculate the magnitude of the induced e.m.f.
?A magnet is pushed north pole first into a coil connected to a sensitive ammeter. Which statement is correct?
5.6–5.8 Particles
Accelerators, antimatter and the quark model
A charge in a uniform electric field feels F = qE (in the field direction for a positive charge). A charge moving across a magnetic field feels F = Bqv, always perpendicular to its velocity — so it moves in a circle. That is the basis of the synchrotron: electric fields accelerate the particles, while magnetic fields (strengthened in step with the rising momentum) bend them round a fixed ring.
As particles approach the speed of light, their relativistic mass increases, so ever more energy is needed for ever less speed. When particles collide at high energy, matter–antimatter pairs can be created. In annihilation, a particle and its antiparticle vanish and their entire mass–energy appears as photons, conserving charge, energy and momentum.
The particle zoo, sorted:
Leptons — fundamental, not made of quarks (electron, muon, neutrinos).
Hadrons — made of quarks. Baryons = three quarks (proton uud, neutron udd). Mesons = a quark–antiquark pair (pions, kaons).
Gauge bosons — the exchange particles: photon (electromagnetic), W and Z (weak), gluon (strong), graviton (gravity, hypothetical).
β⁻ decay: n → p + e⁻ + ν̄eIn the quark model, a down quark changes into an up quark: d → u + e⁻ + ν̄e. Charge, lepton number and baryon number are each conserved.
Conservation checks: charge (0 → +1 −1 + 0 ✓); baryon number (1 → 1 + 0 + 0 ✓); lepton number (0 → 0 + 1 + (−1) ✓). If any one of these fails, the reaction cannot happen.
Quick check
Build a proton
?A proton has charge +1e. Which quark combination gives it? (u = +⅔e, d = −⅓e)
Quick check
Check the conservation laws
?In beta-minus decay, a neutron decays to a proton and an electron. Why must an electron antineutrino also be emitted?
Match it
Match each equation to its field
Tap an item on the left, then its partner on the right.
Equation
What it describes
Recap
Unit A2 2 — the big ideas
Gravity: F = GMm/r²; g = GM/r²; T² ∝ r³; geostationary = 24 h, equatorial, west→east
Electric: F = kq₁q₂/r²; E = kq/r²; E = V/d; attractive OR repulsive (gravity is only attractive)
Capacitors: C = Q/V; E = ½QV = ½CV²; τ = CR; V = V₀e^(−t/CR); parallel adds
Magnetic: F = BIl; F = Bqv; Φ = BA; Faraday (rate of change of flux linkage); Lenz (opposes the change)