IB Physics

Teach to this depth — Go beyond SI unit recall. Distinguish random from systematic error; define precision and accuracy as independent properties. Derive combined uncertainty for addition, subtraction, multiplication, division, and powers using absolute and fractional forms. Propagate uncertainty through multi-step calculations. Express results as (value +/- uncertainty) unit with correct significant figures. Read a vernier calliper and micrometer screw gauge.

Connects to — Every experiment and IA; uncertainty propagation recurs whenever a quantity is derived from measurements; significant figures discipline runs through all Paper 1 numerical answers.

IA & investigative angle — Foundation of all IA lab work. Tier 1 practice must demand full uncertainty calculation chains, not formula recall. Tier 2 questions should include multi-step propagation from a given data set.

Teach to this depth — Define vector and scalar with examples drawn from every later topic. Add and subtract vectors graphically (tip-to-tail) and analytically (components). Find resultant magnitude and direction. Resolve any vector into perpendicular components in a chosen coordinate system. Include scale-diagram construction as an alternative method.

Connects to — Forces in Phase B depend entirely on vector resolution; momentum and impulse are vectors; electric and gravitational fields are vectors; all wave-quantity directions in Phase D.

IA & investigative angle — Vector resolution is the most-applied mathematical skill in IB Physics. Tier 2 practice must require students to draw the diagram first — the error almost always lives in the diagram, not the algebra.

Teach to this depth — Plot data with correct scales, labelled axes with units, and error bars. Draw best-fit lines and worst-fit lines through error bars. Determine gradient and intercept with units and uncertainty from the spread of best/worst-fit gradients. Linearise non-linear relationships (e.g. plot T^2 vs L for a pendulum; ln A vs t for radioactive decay). Understand what the gradient and intercept represent physically. Identify outliers and comment on their effect.

Connects to — Every experimental topic in the course; the IA demands a linearised graph with a physically meaningful gradient; Paper 3 data-analysis questions are this topic assessed under timed conditions.

IA & investigative angle — Linearisation discriminates shallow from deep IAs. Teach: what variable transformation makes this relationship linear, and what will the gradient mean? Tier 2 must include graph interpretation, gradient extraction with uncertainty, and linearisation design.

Teach to this depth — Recognise and use SI prefixes from femto to giga. Check equations using dimensional analysis — identify if an equation is dimensionally consistent. Estimate quantities to the nearest order of magnitude using physical reasoning. Know approximate values of key physical constants. Use powers-of-ten notation fluently in multi-step calculations.

Connects to — Nuclear physics (femtometre scales); astrophysics (parsec conversions); every calculation where a student must judge whether an answer is plausible.

IA & investigative angle — Estimation questions appear in Paper 1 as order-of-magnitude MCQs. Dimensional analysis saves marks in extended-response derivations. Tier 1 should include both skills.

Teach to this depth — Apply ratios, percentages, and proportional reasoning. Use trigonometric functions, the sine rule, and the cosine rule in physical contexts. Apply logarithms and exponentials to physical models (half-life, exponential decay, Wien’s law). Interpret and use linear, logarithmic, and power-law graphs. Understand the concept of gradient as a rate of change.

Connects to — Every quantitative topic; logarithmic graphs are essential for radioactive decay and RC circuits; trigonometry underpins wave analysis, force resolution, and optics.

IA & investigative angle — Tier 1 practice should use physical contexts exclusively — not abstract maths problems. Students should always interpret the mathematical result in physical terms.

Teach to this depth — Define position, distance, displacement, speed (average and instantaneous), velocity, and acceleration precisely. Derive and apply the four kinematic (SUVAT) equations from first principles using a v-t graph. Interpret displacement-time, velocity-time, and acceleration-time graphs fluently: gradient = velocity (on s-t), gradient = acceleration (on v-t), area = displacement (on v-t). Apply to free-fall and vertical motion. Distinguish scalar from vector versions of each quantity.

Connects to — Projectile motion splits kinematics into two independent components; Newton’s laws explain why objects accelerate; energy and momentum use velocity as input; SHM position/velocity equations mirror kinematics form.

IA & investigative angle — Classic IA: measuring g by free fall or video analysis. Tier 2 must include graph-reading and derivation — not only numerical SUVAT substitution. Tier 3 mock must include a multi-part kinematics problem requiring both graph and equation methods.

Teach to this depth — Resolve initial velocity into horizontal and vertical components. Treat horizontal motion as uniform (constant velocity) and vertical as free fall (constant downward acceleration g) simultaneously and independently. Solve for time of flight, range, maximum height, and final velocity — including launches from a height, at angles, and below horizontal. Derive the parabolic trajectory form algebraically. Analyse the effect of fluid resistance qualitatively.

Connects to — Charged-particle trajectories in uniform electric fields (Phase E) are structurally identical to projectile motion; terminal speed in fluids extends the vertical-motion picture.

IA & investigative angle — Projectile investigation (varying launch angle or height) is a strong IA context. Tier 2 practice must include non-symmetric launches and the effect of changing launch angle on range.

Teach to this depth — State all three Newton’s laws precisely and distinguish clearly between them. Draw complete, correctly labelled free-body diagrams with one arrow per force, labelled with type and agent. Apply Newton’s second law F=ma in component form to multi-body systems. Identify Newton’s third-law pairs (same type, opposite direction, different bodies). Apply to connected bodies: Atwood machines, pulleys, and systems on inclines. Understand Newton’s first law as a statement about inertia and reference frames.

Connects to — Every mechanics topic depends on correct force identification; circular motion adds centripetal acceleration; gravitation extends Newton’s second law to orbital contexts.

IA & investigative angle — Extended-response questions often ask students to justify the shape of a v-t graph in terms of the net force. Tier 2 must include multi-body systems and situations where net force is zero.

Teach to this depth — Resolve forces on inclined planes by choosing axes parallel and perpendicular to the slope. Distinguish static and kinetic friction; apply the friction model (F_k = mu_k * N). Analyse equilibrium situations using sum(F) = 0 in all directions. Apply Hooke’s law F = -kx and understand the elastic limit. Understand buoyant force (upthrust) using Archimedes’ principle and Stokes’ law for viscous drag qualitatively.

Connects to — Fluid resistance and terminal speed follow from these force concepts; elastic potential energy requires Hooke’s law; the spring constant k feeds SHM (Phase D).

IA & investigative angle — A friction or spring-extension investigation is a well-controlled IA context. Tier 2 must emphasise the FBD stage — errors in the diagram propagate through the entire solution.

Teach to this depth — Explain qualitatively why objects accelerate, decelerate, and reach a terminal (constant) velocity in a fluid. Apply Stokes’ law F = 6*pi*eta*r*v for small spheres at low speed. Draw and interpret velocity-time and force diagrams at different stages of fall. Relate the terminal speed condition to the balance of weight, buoyancy, and drag forces.

Connects to — The concept of a limiting speed from force balance extends to charged particles in a velocity selector (Phase E); exponential approach to terminal speed is mathematically analogous to capacitor charging.

IA & investigative angle — Measuring terminal speed of a ball bearing in oil — a classic practical. Tier 2: sketch the v-t graph for a falling sphere and explain the shape in terms of forces at each stage.

Teach to this depth — Define work W = Fd cos(theta) with correct sign convention. Derive and apply the work-energy theorem. Define translational kinetic energy, gravitational PE, and elastic PE = (1/2)kx^2. Define power as rate of work done; apply P = Fv. Understand efficiency and represent energy transfers using Sankey diagrams. Calculate energy stored per unit volume from a stress-strain graph (area under curve).

Connects to — Momentum provides a complementary tool — use energy for before-after comparisons; thermodynamics generalises energy transfer to heat and internal energy; elastic PE feeds SHM energy analysis.

IA & investigative angle — Sankey diagram construction and efficiency calculation. Tier 2: calculate the power output of a motor, the efficiency of an engine, and the elastic PE stored in a spring — all in one connected scenario.

Teach to this depth — Apply conservation of energy to systems with multiple energy types: KE, gravitational PE, elastic PE, and internal energy (heat from friction). Identify when mechanical energy is and is not conserved. Solve multi-step problems combining energy conservation with kinematics or Newton’s laws. Apply to pendulums, roller-coasters, springs, and projectile problems.

Connects to — SHM energy analysis (Phase D) is a direct application; collisions in Phase B use energy conservation to distinguish elastic from inelastic; orbital energy in Phase E requires both KE and gravitational PE.

IA & investigative angle — Energy conservation investigation (ball rolling down a ramp; bungee-cord stretch). Tier 2 must require students to state clearly which energy types are present and which are conserved.

Teach to this depth — Define momentum p = mv as a vector. Define impulse J = F*delta_t = delta_p. State and apply conservation of linear momentum to 1D collisions and explosions. Distinguish elastic (KE conserved) from inelastic (KE not conserved) collisions. Interpret the area under a force-time graph as impulse. Apply Newton’s second law in the general form F = delta_p/delta_t. Analyse one-dimensional collision and explosion scenarios fully.

Connects to — Kinetic theory derives gas pressure from momentum transfer to walls (Phase C); nuclear reactions (Phase F) use momentum conservation alongside energy conservation.

IA & investigative angle — Collision investigations (air track, dynamics trolleys) allow precise momentum measurement. Tier 2 must include explosion scenarios and the elastic/inelastic distinction.

Teach to this depth — Define angular speed omega and relate to linear speed v = r*omega and period T. Define centripetal acceleration a = v^2/r = omega^2*r directed toward the centre. Identify the centripetal force as the net inward force provided by existing forces — not a new force. Analyse circular motion at the top and bottom of a vertical circle, on a banked road, and in a conical pendulum. Explain why ‘centrifugal force’ does not exist in an inertial frame.

Connects to — Gravitation (next topic) is circular motion with gravity as centripetal force; charged particles in magnetic fields (Phase E) move in circles; SHM phasor model uses circular motion.

IA & investigative angle — Conical pendulum or banked-road investigation. Tier 2 must include the top and bottom of a vertical circle (where normal force varies) — a frequent exam target.

Teach to this depth — State and apply Newton’s law of universal gravitation F = GMm/r^2. Define gravitational field strength g = F/m = GM/r^2. Apply Kepler’s third law T^2 proportional to r^3, derived from Newton’s law and circular motion. Analyse orbital speed and the relationship between orbital radius and period. Understand that atmospheric drag causes orbital speed to increase paradoxically (lower orbit = faster speed). Define and apply the concept of gravitational potential qualitatively.

Connects to — Electric fields (Phase E) are structurally identical to gravitational fields — Coulomb’s law parallels Newton’s law; stellar physics (Phase F) uses gravitational collapse and orbital mechanics.

IA & investigative angle — Measuring g experimentally and comparing to GM/R^2. Tier 2 must include Kepler’s third law calculation and the paradox of drag reducing orbital energy while increasing speed.

Teach to this depth — Distinguish elastic from plastic (permanent) deformation. Draw and interpret force-extension and stress-strain graphs: identify the limit of proportionality, elastic limit, yield point, and fracture point. Calculate Young’s modulus E = stress/strain. Calculate elastic potential energy from the area under a force-extension graph. Compare the behaviour of metals, rubber, and brittle materials from their stress-strain curves.

Connects to — Hooke’s law (Topic 9) is the linear region of the force-extension graph; elastic PE in SHM uses the same (1/2)kx^2 relationship; material selection connects to engineering applications.

IA & investigative angle — Measuring Young’s modulus of a wire — a classic IA with excellent scope for uncertainty analysis. Tier 2 must include graph interpretation and classification of material behaviour from a given curve.

Teach to this depth — Describe the properties of solids, liquids, and gases in terms of particle arrangement, separation, motion, and forces. Define mass density rho = m/V. Understand temperature as a measure of mean molecular KE. Define internal energy as the sum of all molecular KE and PE. Describe thermal equilibrium and Zeroth Law of thermodynamics. Understand phase changes (melting, boiling, freezing, condensation) and the microscopic explanation for why temperature stays constant during a phase change.

Connects to — Gas laws (next topics) extend this to quantitative relationships; thermal transfer (Topic 19) builds on internal energy; specific heat and latent heat (Topic 18) use phase change directly.

IA & investigative angle — Tier 2 practice: explain, in terms of particles, why a liquid evaporates more quickly at higher temperature and lower pressure. Connect the explanation explicitly to the particle model.

Teach to this depth — Distinguish temperature, heat, and internal energy precisely. Define specific heat capacity c and apply Q = mc*delta_T. Define specific latent heat L and apply Q = mL, distinguishing latent heat of fusion from vaporisation. Perform calorimetry calculations including multi-stage heating plus phase change. Read and interpret temperature-time graphs for heating and cooling experiments.

Connects to — Internal energy is defined in Topic 17 and quantified here; thermal energy transfer (Topic 19) uses these as inputs; radiation topics require energy-balance calculations using specific heat.

IA & investigative angle — Measuring specific heat capacity of a material — a well-defined IA with clear uncertainty analysis and comparison to an accepted value. Tier 2 must include reading a temperature-time graph and identifying each phase.

Teach to this depth — Describe conduction at the mechanism level (phonon/electron transfer through a material, driven by a temperature gradient). Describe convection as bulk fluid motion driven by density differences. Describe radiation as electromagnetic emission from all objects above absolute zero. Apply Newton’s law of cooling qualitatively. Compare the relative importance of each mechanism in a given physical context.

Connects to — Radiation at the mechanism level previews Stefan-Boltzmann law (Topic 24); conduction and convection are relevant to the greenhouse effect; thermal insulation design combines all three.

IA & investigative angle — Tier 2: for a given scenario (e.g. a house losing heat, a flask keeping liquid hot), identify the dominant mechanism of heat transfer and explain how it could be reduced.

Teach to this depth — State and apply Boyle’s law (pV = constant at constant T), Charles’s law (V/T = constant at constant p), and Gay-Lussac’s law (p/T = constant at constant V). Unify as the ideal gas law pV = nRT = NkT. Define the mole and Avogadro’s constant. Apply the ideal gas law to problems with changing state variables. Understand when the ideal gas model is a good approximation and when it fails (high pressure, low temperature).

Connects to — Kinetic theory (Topic 21) provides the microscopic explanation for the gas laws; the gas laws are used in thermodynamic cycle calculations; the ideal gas equation connects to internal energy.

IA & investigative angle — Gas law investigation — verify Boyle’s law experimentally using a syringe and pressure gauge. Tier 2 must include problems where students must select the correct gas law and justify the choice.

Teach to this depth — State the assumptions of the kinetic theory of an ideal gas. Derive the kinetic theory expression p = (1/3)*rho*c^2 from Newton’s laws and statistical reasoning. Define root-mean-square speed c_rms. Derive and apply the result that mean translational KE = (3/2)kT. Use the kinetic model to explain why pressure increases with temperature at constant volume, and why a gas exerts pressure on its container walls.

Connects to — The ideal gas law (Topic 20) is the macroscopic summary of kinetic theory; the Boltzmann constant k links microscopic energy to macroscopic temperature; distribution of speeds qualitatively connects to nuclear reaction thresholds.

IA & investigative angle — Tier 2: explain, using the kinetic theory, why a gas in a sealed container at constant volume exerts greater pressure when heated. The answer must reference momentum transfer, collision rate, and the temperature-KE relationship.

Teach to this depth — Read and draw circuit diagrams using standard IB symbols. Define current I = delta_Q/delta_t and relate to charge carriers. Define potential difference as work done per unit charge. Define resistance R = V/I and resistivity rho = RA/L. Apply Ohm’s law and identify ohmic vs non-ohmic behaviour from I-V graphs. Calculate power P = IV = I^2*R = V^2/R. Understand the physical origin of resistance in terms of electron collisions with the lattice.

Connects to — DC circuits (Topic 23) build directly on these definitions; resistivity measurements are a common IA method; power calculations underpin all energy-balance problems in circuits.

IA & investigative angle — Measuring the I-V characteristic of a component (bulb, diode) — a clean, controlled IA. Tier 2 must include graph interpretation and the distinction between ohmic and non-ohmic behaviour.

Teach to this depth — Apply Kirchhoff’s current and voltage laws to multi-loop circuits. Derive and apply series and parallel resistance formulas. Model a battery with internal resistance r: terminal voltage V = EMF – Ir. Analyse the variation of terminal voltage with current (gradient = -r, y-intercept = EMF). Use potential dividers. Analyse circuits with combinations of series and parallel elements. Understand why voltmeters need very high resistance and ammeters very low resistance. Understand variable resistors and light-dependent resistors in sensor circuits.

Connects to — Potential dividers are the basis of temperature, light, and pressure sensor circuits; the V-I graph analysis connects to graphical skills from Phase A; power calculations connect to electrical energy topics.

IA & investigative angle — Determining internal resistance and EMF of a battery from a V-I graph — a classic, well-structured IA. Tier 2 must include multi-loop circuits, potential dividers, and internal resistance problems.

Teach to this depth — Apply the Stefan-Boltzmann law L = sigma*A*T^4. Apply Wien’s displacement law lambda_max*T = 2.9×10^-3 m*K. Define albedo and emissivity. Derive the effective temperature of Earth from the solar constant and albedo. Understand the greenhouse effect at the mechanism level — absorption and re-emission of IR by greenhouse gas molecules. Discuss climate feedback mechanisms and the significance of small changes in albedo or emissivity.

Connects to — The same Stefan-Boltzmann and Wien’s law equations are used in Topic 25 for stellar physics — the connection must be made explicit; the energy balance calculation connects to electrical power from Topic 22.

IA & investigative angle — Tier 2: calculate the effective temperature of a planet given its albedo and distance from the Sun; estimate the change in surface temperature from a given change in albedo. Both calculations must show full working.

Teach to this depth — Apply luminosity L = sigma*A*T^4 to stars. Use the inverse-square law b = L/(4*pi*d^2) to relate apparent brightness to luminosity and distance. Use Wien’s law to determine stellar surface temperature from the peak wavelength of the spectrum. Calculate stellar radius from luminosity and temperature. Understand that stellar spectra are approximately blackbody spectra with absorption lines superimposed. Use stellar parallax to measure distances to nearby stars.

Connects to — Radiation, climate, and energy balance (Topic 24) introduced these same laws; stellar evolution and the HR diagram (Phase F) builds on luminosity, temperature, and radius relationships.

IA & investigative angle — Tier 2: given the luminosity and surface temperature of a star, calculate its radius. Given two stars’ apparent brightness and distances, find their luminosity ratio. Both require clear multi-step working.

Teach to this depth — Define SHM by the condition a = -(omega^2)*x. Derive and apply x = A*sin(omega*t + phi), v = A*omega*cos(omega*t + phi). Derive the period of a mass-spring system T = 2*pi*sqrt(m/k) and a simple pendulum T = 2*pi*sqrt(L/g). Track continuous KE-PE exchange: E_total = (1/2)*m*omega^2*A^2 = constant. Sketch x-t, v-t, and a-t graphs and relate them to each other. Draw KE and PE vs displacement and vs time.

Connects to — Every particle in a transverse wave undergoes SHM; resonance (Topic 32) uses the SHM natural frequency; the spring constant k from Topic 9 feeds directly into T = 2*pi*sqrt(m/k).

IA & investigative angle — Pendulum or mass-spring investigation — varying length, mass, or amplitude. Measure omega experimentally and compare to the theoretical prediction. Tier 2 must include the energy equation and graph interpretation at different positions in the oscillation.

Teach to this depth — Define and distinguish transverse and longitudinal waves. Define amplitude, wavelength, period, frequency, wave speed, and phase. Apply v = f*lambda. Define wavefronts and rays. Understand the physical differences between mechanical and electromagnetic waves — what oscillates, medium requirement, propagation speed. Know the EM spectrum with approximate wavelengths and frequencies for each region. Describe characteristics of sound waves.

Connects to — All of Phase D builds on this foundation; the Doppler effect manipulates f and lambda; all wave interactions (interference, diffraction) require a clear picture of what a wave is.

IA & investigative angle — Tier 1 practice: given a wave diagram, identify all six wave properties with correct units. Tier 2 must distinguish transverse from longitudinal in a given physical context and justify the classification.

Teach to this depth — State the principle of superposition. Distinguish constructive and destructive interference and relate to path difference: constructive when path difference = n*lambda; destructive when = (n + 1/2)*lambda. Apply Young’s double-slit formula d*sin(theta) = n*lambda and the small-angle approximation fringe spacing = lambda*L/d. Analyse single-slit diffraction: condition for first minimum a*sin(theta) = lambda. Understand why diffraction is maximised when slit width ~= wavelength.

Connects to — Standing waves are a special case of superposition (Topic 29); electron diffraction (Phase F) confirms de Broglie’s hypothesis; the Young’s experiment formula feeds directly into diffraction grating analysis (Topic 31).

IA & investigative angle — Laser diffraction investigation — measuring slit width or wavelength from fringe patterns. Tier 2 must include path-difference derivations from geometry, not just formula substitution.

Teach to this depth — Derive standing waves as the superposition of two identical waves travelling in opposite directions. Define nodes and antinodes and their spacing (lambda/4 between adjacent node and antinode). Establish boundary conditions: fixed ends = nodes, open ends = antinodes. Derive the harmonic series for strings (all harmonics) and open/closed pipes. Connect resonance frequency to the standing wave condition. Understand that resonance occurs when a driving frequency matches the natural frequency.

Connects to — SHM gave the resonance concept (Topic 26); standing waves give it geometric form; damping and forced oscillations (Topic 32) complete the resonance picture.

IA & investigative angle — Melde’s experiment (standing waves on a string) or Kundt’s tube. Measuring wave speed in a string as a function of tension — a clean, controllable IA. Tier 2: derive the harmonic series for a closed pipe and explain why even harmonics are absent.

Teach to this depth — Explain qualitatively why observed frequency changes when source or observer moves. Apply the Doppler equations for sound (source moving, observer moving). Apply the formula for light and electromagnetic waves. Connect galactic redshift z = delta_lambda/lambda to recession velocity using v ~ z*c for small z. Distinguish redshift from blueshift. Apply to real contexts: medical ultrasound, radar speed cameras, stellar velocity measurement.

Connects to — Stellar physics and Hubble’s law (Phase F) use Doppler redshift to measure galactic recession; stellar spectra use Doppler shift to measure radial velocity of stars.

IA & investigative angle — Tier 2: identify which form of the Doppler formula applies; calculate the observed frequency; comment on whether the shift is a redshift or blueshift and state what this implies physically.

Teach to this depth — Apply the Young’s double-slit formula d*sin(theta) = n*lambda and the small-angle fringe spacing formula. Apply the diffraction grating equation d*sin(theta) = n*lambda for maxima. Understand how a grating resolves wavelengths more sharply than a double slit (more slits = narrower, brighter maxima). Compare double-slit and grating patterns. Use the grating to measure wavelength of a monochromatic source experimentally.

Connects to — Superposition and interference (Topic 28) provided the conceptual foundation; stellar spectroscopy (Phase F) uses diffraction gratings to resolve absorption and emission lines in stellar spectra.

IA & investigative angle — Diffraction grating investigation — measuring wavelength of laser light from the grating equation and comparing to the manufacturer’s value. Tier 2 must distinguish between double-slit and grating patterns.

Teach to this depth — Define damping and distinguish light, heavy (overdamped), and critical damping. Draw x-t graphs for each type and identify the physical situation where each is useful (e.g. car suspension = critical damping). Define natural frequency. Describe forced oscillations and resonance: amplitude peaks when the driving frequency equals the natural frequency. Show how increasing damping lowers and broadens the resonance peak. Discuss practical consequences of resonance (bridges, musical instruments, MRI).

Connects to — SHM (Topic 26) established the natural frequency; resonance is the driven version of the standing-wave resonance from Topic 29; damped oscillations are analogous to RC discharge curves.

IA & investigative angle — Tier 2: sketch the resonance curve for two oscillators with different damping; explain why the resonance peak is lower and broader for the more heavily damped system. Connect to a real engineering application.

Teach to this depth — Apply the law of reflection (angle of incidence = angle of reflection). Define refractive index n = c/v and apply Snell’s law n_1*sin(theta_1) = n_2*sin(theta_2). Derive the critical angle condition sin(theta_c) = n_2/n_1 and explain total internal reflection. Apply TIR to optical fibres and prisms. Understand dispersion — different wavelengths refract at different angles, producing a spectrum. Apply to real situations: mirages, rainbows, optical fibres.

Connects to — Wave superposition (Topic 28) established wave behaviour at boundaries; diffraction grating (Topic 31) uses refraction and geometry; refraction connects to the wave speed changing at a boundary.

IA & investigative angle — Tier 2: calculate the critical angle for a glass-air interface; determine whether TIR occurs for a given angle of incidence. Explain why an optical fibre can transmit a light signal around a curve.

Teach to this depth — State the properties of electric charge (quantised, conserved). Describe electrostatic charging by friction, contact, and induction. State and apply Coulomb’s law F = kq_1*q_2/r^2. Define electric field strength E = F/q. Draw electric field lines for point charges, uniform fields, and combined charge distributions. Understand that the field inside a conductor is zero in electrostatic equilibrium. Describe Millikan’s oil-drop experiment and what it demonstrates (quantisation of charge).

Connects to — Electric potential (qualitative) follows from field; magnetic force on charges (Topic 35) requires the charge concept; the parallel structure with gravitation must be made explicit — Coulomb’s law parallels Newton’s law.

IA & investigative angle — Tier 2: calculate the net electric field at a point midway between two charges of given sign and magnitude; draw the field lines for the arrangement; identify where the field is zero.

Teach to this depth — Describe magnetic field patterns around a long straight wire, inside a solenoid, and around a bar magnet. Apply F = BIL*sin(theta) to a current-carrying conductor using the left-hand rule (or F = IL x B). Apply F = qvB*sin(theta) to moving charges. Understand that magnetic force is always perpendicular to the velocity — it does no work and cannot change the speed of a charged particle. Describe the force between two parallel current-carrying conductors.

Connects to — Charged particles in fields (Topic 36) combine electric and magnetic forces; the force between parallel wires is the basis of the original definition of the ampere; this topic is structurally parallel to the electric force on a charge in a field.

IA & investigative angle — Tier 2: determine the direction of force on a current-carrying wire in a given magnetic field; find the direction of force on a moving positive charge in a 3D field configuration.

Teach to this depth — Analyse the circular motion of a charged particle in a uniform magnetic field: r = mv/qB. Analyse the velocity selector: when qE = qvB, only particles with v = E/B pass undeflected. Describe the mass spectrometer as an application of combined fields. Analyse the Hall effect — steady state when electric and magnetic forces balance. Analyse the trajectory of charged particles in uniform electric fields (identical in form to projectile motion).

Connects to — Projectile motion (Topic 7) is structurally identical to a charged particle in a uniform electric field — the connection must be made explicit; the velocity selector and mass spectrometer are direct applications of force balance.

IA & investigative angle — Analysing the path of a charged particle in a magnetic field from a bubble-chamber photograph — a classic IB data-analysis exercise. Tier 2 must include combined E and B field problems.

Teach to this depth — Describe and analyse Millikan’s oil-drop experiment in detail: balance gravitational force against electric force (qE = mg) to find the charge on a drop. Show that all measured charges are integer multiples of e, demonstrating charge quantisation. Apply field concepts to practical situations: lightning conductors (sharp points concentrate field), Van de Graaff generators, and electrostatic precipitators. Understand shielding — the field inside a hollow conductor is zero.

Connects to — Coulomb’s law and field strength (Topic 34) provided the foundation; the force balance technique is the same as used in velocity selectors (Topic 36); the concept of charge quantisation connects to atomic structure (Phase F).

IA & investigative angle — Tier 2: given data from a Millikan-type experiment (drop radii, voltages, and measured charges), determine the elementary charge and evaluate how well the data support charge quantisation.

Teach to this depth — State and apply all three of Kepler’s laws of planetary motion. Derive Kepler’s third law T^2 proportional to r^3 from Newton’s law and circular orbital motion. Define gravitational field strength g = GM/r^2 and distinguish it from the gravitational force on a specific mass. Compare the gravitational field equation with Coulomb’s law — note the structural parallel. Understand satellite orbits: geostationary, polar, and the relationship between orbital radius, speed, and period.

Connects to — Circular motion (Topic 14) provided the centripetal force framework; the field concept was introduced in Topic 34 for electric fields — the parallel to gravitational fields is the key insight; stellar and planetary data in Phase F use Kepler’s laws.

IA & investigative angle — Tier 2: given the orbital period and radius of one satellite, predict the orbital period of a second satellite at a different radius using Kepler’s third law. Explain why a geostationary satellite must be above the equator.

Teach to this depth — Describe Rutherford’s gold-foil scattering experiment and what it reveals — the nuclear atom with a tiny, dense, positively charged nucleus. Distinguish continuous, emission (bright-line), and absorption (dark-line) spectra. Understand that discrete spectral lines require quantised energy levels. Calculate photon energy from frequency E = hf and wavelength E = hc/lambda. Write nuclear notation: mass number A, proton number Z, neutron number N = A – Z.

Connects to — The photoelectric effect (Topic 40) is the next quantum piece; Bohr energy levels connect to nuclear energy levels in Topic 42; stellar spectroscopy (Topic 45) uses these same spectral lines to determine stellar composition.

IA & investigative angle — Tier 2: identify the transition responsible for a given spectral line wavelength; calculate the energy of a photon emitted in that transition. Explain why the Rutherford scattering experiment disproved the Thomson ‘plum-pudding’ model.

Teach to this depth — Describe the photoelectric effect and list its experimental observations: threshold frequency exists; maximum KE depends on frequency, not intensity; emission is instantaneous. Explain clearly why the classical wave model fails to account for each observation. Apply Einstein’s photoelectric equation KE_max = hf – phi. Define the work function phi. Describe how a stopping-voltage experiment can determine Planck’s constant h from a graph of stopping voltage vs frequency.

Connects to — Atomic structure and quantised energy levels (Topic 39) set the stage; the photon model established here connects to de Broglie’s hypothesis (radiation has particle properties; matter has wave properties); nuclear emissions (Topic 41) use photon (gamma) energy.

IA & investigative angle — Stopping-voltage experiment — plotting V_stop vs f and extracting h from the gradient. Tier 2 must include explaining why each photoelectric observation is inconsistent with the classical wave model.

Teach to this depth — Describe alpha, beta-minus, beta-plus, and gamma decay — nature, penetration, and ionising power. Write and balance nuclear decay equations using conservation of nucleon number and proton number. Define activity A, decay constant lambda, and half-life t_half = ln(2)/lambda. Derive and apply the radioactive decay law N = N_0 * exp(-lambda*t). Determine half-life from experimental activity data (plot ln A vs t; gradient = -lambda). Correct activity measurements for background radiation. Describe uses of radioactive isotopes in medicine, industry, and archaeology.

Connects to — The exponential decay law is mathematically identical to the discharge of a capacitor (if studied at SL option level); nuclear structure (Topic 42) explains why some nuclei are unstable; radiocarbon dating is a direct application of the decay law.

IA & investigative angle — Half-life determination from a decay curve — plotting ln(A) vs t and extracting lambda from the gradient. Dice simulation as a Tier 1 activity. Tier 2 must include background correction and half-life determination from a data table.

Teach to this depth — Define binding energy as the energy required to completely separate all nucleons of a nucleus. Calculate mass defect delta_m = Z*m_p + (A-Z)*m_n – m_nucleus. Apply E = delta_m * c^2 to find binding energy. Plot and interpret the binding energy per nucleon (BE/A) vs mass number curve — the peak near iron (A ~ 56) explains why fission of heavy nuclei and fusion of light nuclei both release energy. Understand the roles of the strong nuclear force and electrostatic repulsion.

Connects to — Radioactivity (Topic 41) raised the question of why some nuclei are unstable — the BE/A curve provides the energetic answer; nuclear fission and fusion (Topic 43-44) use the same mass-energy equivalence to calculate Q-values.

IA & investigative angle — Tier 2: calculate the binding energy per nucleon for a given isotope from its atomic mass; use the BE/A curve to explain why iron-56 is the most stable nucleus; predict whether fission of a given heavy nucleus is energetically favourable.

Teach to this depth — Distinguish spontaneous from induced fission. Calculate the energy released in a fission reaction using Q = delta_m * c^2 from nuclear mass tables. Describe the chain reaction — critical mass, moderator (slows neutrons), control rods (absorb neutrons), coolant (removes heat), and shielding. Explain how a nuclear reactor maintains a controlled chain reaction. Discuss the management of radioactive waste: short-lived vs long-lived isotopes, geological storage.

Connects to — Mass-energy equivalence from Topic 42 is applied here; radioactive decay laws (Topic 41) are relevant to waste management timescales; the energy output per reaction connects to power output via activity.

IA & investigative angle — Tier 2: calculate the energy released in a specific fission reaction; explain the purpose of the moderator and the control rods; discuss why different fission products require different waste management strategies.

Teach to this depth — Describe fusion reactions in stars — the proton-proton chain. Calculate energy released in fusion reactions using Q = delta_m * c^2. Understand why fusion requires extremely high temperature (~10^7 K) — enough thermal KE to overcome electrostatic repulsion. Describe the formation of stars from nebulae (gravitational collapse). Trace the life cycle of a main-sequence star: protostar, main sequence, red giant, and then white dwarf, neutron star, or black hole depending on mass. Understand that heavy elements beyond iron are formed in supernova explosions.

Connects to — Binding energy (Topic 42) explains why fusion of light nuclei releases energy; the HR diagram (Topic 45) maps the life cycle stages of stars on a luminosity-temperature plot; stellar radiation (Topic 25) gave the tools to measure stellar properties.

IA & investigative angle — Tier 2: calculate the energy released in the pp-chain fusion reaction from mass data; explain the conditions required for sustained fusion and why these are difficult to achieve in a controlled laboratory setting.

Teach to this depth — Construct and interpret the Hertzsprung-Russell diagram: axes (luminosity vs surface temperature, or absolute magnitude vs spectral class). Identify the main sequence, red giant branch, supergiant region, and white dwarf region. Understand that stars spend most of their lives on the main sequence. Trace the evolutionary track of a low-mass star (like the Sun) and a high-mass star on the HR diagram. Apply the Stefan-Boltzmann law to explain why red giants are luminous despite low surface temperature (they are very large). Determine spectral class from the colour and absorption spectrum of a star.

Connects to — Emission spectra (Topic 39) determine spectral class; Stefan-Boltzmann law (Topic 25) determines stellar radius from L and T; nuclear fusion (Topic 44) provides the energy source that defines main-sequence lifetime; the HR diagram synthesises all of these.

IA & investigative angle — Tier 2: a star moves from the main sequence to the red giant region — describe the changes in its surface temperature, radius, and luminosity, and use the HR diagram to illustrate the evolutionary track.

Teach to this depth — Apply the cosmic distance ladder: stellar parallax (for nearby stars), spectroscopic parallax (using HR diagram and known luminosity class), and Cepheid variables (period-luminosity relation). Define parsec and light-year and convert between them and metres. Apply Hubble’s law v = H_0*d and understand its significance as evidence for the expanding universe. Calculate the age of the universe t ~ 1/H_0. Describe the evidence for the Big Bang: CMB radiation, galactic recession, and cosmic abundances of light elements.

Connects to — The Doppler effect (Topic 30) is the physical mechanism behind Hubble redshift; stellar luminosity and spectral class from the HR diagram (Topic 45) feed into spectroscopic parallax; the Big Bang evidence ties to CMB radiation — EM radiation from the early universe.

IA & investigative angle — Tier 2: a galaxy shows a redshift of z = 0.03. Calculate its recession velocity and distance using Hubble’s law. Explain why Type Ia supernovae are useful as standard candles for measuring very large distances.

Teach to this depth — Integrate the scientific inquiry cycle with physics practice: formulating a focused, testable research question from a broad topic; designing an experiment with clearly identified independent, dependent, and controlled variables; collecting reliable, reproducible data with appropriate precision; processing data using correct mathematical tools (means, uncertainties, graphs); interpreting patterns and relationships in data; drawing evidence-based conclusions that directly answer the research question; evaluating the investigation honestly — limitations, sources of error, and realistic improvements.

Connects to — Every phase of the course feeds the IA: uncertainty from Phase A; experimental design from Phases B-E; graphical analysis from Phase A; model critique from Phases C and D. This topic consolidates all inquiry skills into a coherent framework.

IA & investigative angle — This topic is best taught through iterative practice — small focused practicals throughout the course — rather than as a single block. Each phase mock should include one question that asks students to evaluate a given experimental design or identify sources of error in a presented method.