Physics Specification

Properties of Magnets

• North/South poles: Field lines emerge north, enter south
• Soft vs. hard magnetic materials: Soft easily magnetised; hard retain magnetisation

Magnetic Field of a Current

• Right-hand rule: Thumb = current direction; curled fingers = magnetic field around wire
• Solenoid: Field inside ≈ uniform; direction given by right-hand grip rule

Motor Effect

• Force on current-carrying conductor: F = BIL (N)
• Left-hand rule (Fleming): Thumb = force, first finger = field, second finger = current

Electromagnetic Induction

• Faraday's law: Induced emf ε = −N(ΔΦ/Δt) (V)
• Factors: Rate of change of magnetic flux, number of turns, field strength

Transformers

• Voltage ratio: V_p/V_s = N_p/N_s
• Power conservation (ideal): P_p = P_s → V_p × I_p = V_s × I_s

Kinematics

• Displacement: s (m) – distance in a given direction
• Velocity: v = s/t (m s⁻¹) – displacement per unit time
• Acceleration: a = v/t (m s⁻²) – change in velocity per unit time
• Equation of motion (constant a): v = u + at; s = ut + ½at²; v² = u² + 2as

Forces & Newton's Laws

• First law: Object at rest stays at rest; object in motion stays in motion (inertia)
• Second law: F = ma – net force = mass × acceleration
• Third law: Action–reaction pairs – equal and opposite forces

Force-Extension (Hooke's Law)

• Elastic region: F = kx (N) – force proportional to extension
• Elastic potential energy: E_p = ½kx² (J)

Momentum & Energy

• Momentum: p = mv (kg m s⁻¹)
• Conservation: Total momentum before = total momentum after (closed system)
• Work: W = Fs (J) – force × distance
• Kinetic energy: E_k = ½mv² (J)
• Gravitational potential energy: E_g = mgh (J)

Conduction & Convection

• Conduction: Heat flow through solid material; rate depends on thermal conductivity and temperature gradient
• Convection: Heat transfer driven by density differences due to temperature gradients in fluids

Radiation

• Stefan-Boltzmann law: P = εσAT⁴ – power radiated proportional to absolute temperature to fourth power

Heat Capacity

• Heat absorbed/released: Q = mcΔT (J) – where c is specific heat capacity

States of Matter

• Solid: Fixed shape, definite volume
• Liquid: Definite volume, takes shape of container
• Gas: No shape or volume; particles far apart

Ideal Gas Law

• PV = nRT or pV = NkT – relates pressure, volume, temperature for ideal gases

Phase Changes

• Latent heat of fusion (L_f): Q = mL_f (J) – energy to melt solid → liquid
• Latent heat of vaporisation (L_v): Q = mL_v (J) – energy to boil liquid → gas

Density & Pressure

• Density: ρ = m/V (kg m⁻³)
• Pressure: P = F/A (Pa)
• Hydrostatic pressure: P = ρgh – pressure increases with depth in fluids

Wave Properties

• Speed: v = fλ (m s⁻¹) – frequency × wavelength
• Frequency: f = 1/T (Hz) – cycles per unit time; T is period

Wave Behaviour – Reflection & Refraction

• Reflection: Angle of incidence = angle of reflection (θᵢ = θᵣ)
• Refraction: Change in direction due to speed change in different media

Wave Phenomena – Reflection, Refraction & Doppler

Reflection of Waves

• Definition: Wave encounters barrier and returns into original medium; θᵢ = θᵣ
• Wave parameters after reflection: Speed unchanged, frequency unchanged, wavelength unchanged, direction reverses

Refraction of Waves

• Definition: Change in wave direction as it passes between media with different propagation speeds
• Snell's law (planar boundary): n₁ sin θ₁ = n₂ sin θ₂
• Consequences:
  • Speed decreases if entering higher refractive index medium (bends toward normal)
  • Wavelength changes: λ = v/f (frequency stays constant)
  • Direction: toward normal if n increases; away from normal if n decreases
  • Critical angle for total internal reflection when sin θ_c = n₂/n₁

Doppler Effect

• Definition: Apparent change in frequency (and pitch) when source and observer move relative to each other
• Moving source: f' = f × v/(v ± v_s)
• Moving observer: f' = f × (v ± v_o)/v
• Sign chosen for approach (+) or recession (−); v = wave speed, v_s = source speed, v_o = observer speed

Optics – Plane Mirrors & Refraction

Ray Diagrams for Reflection

• Plane mirror: Draw incident ray, normal at point of incidence, reflected ray such that θᵢ = θᵣ
• Image formation: Virtual, upright, laterally inverted, same size as object

Ray Diagrams for Refraction

• Planar boundary: Show incident ray, normal, refracted ray; use Snell's law to set angles
• Critical angle: For total internal reflection when sin θ_c = n₂/n₁

Production & Medium

• Produced by: Vibrating source that periodically compresses and rarefies surrounding air (or medium)
• Type: Longitudinal wave; particle displacement parallel to wave propagation

Loudness & Pitch

• Loudness ∝ amplitude: Pressure variation of sound wave
• Pitch ∝ frequency: Hz; human audible range 20 Hz – 20 kHz

Echoes & Ultrasound

• Echo: Reflection of sound from surface returning to listener
• Ultrasound: Frequencies > 20 kHz; applications include:
  • Sonar (underwater navigation)
  • Medical imaging (echocardiograms, fetal scans)

Region	Wavelength	Frequency	Key Property	Common Uses	Hazards
Radio	> 0.1 m	< 3 MHz	Long-range propagation	Broadcasting, radar	Low ionising potential
Microwave	0.001 – 0.1 m	300 MHz – 3 GHz	Heats polar molecules	Cooking, satellite comms	Tissue heating
Infrared (IR)	10⁻⁶ – 10⁻³ m	3 × 10¹¹ – 3 × 10¹⁴ Hz	Thermal radiation	Remote controls, thermal imaging	Minimal
Visible	4 × 10⁻⁷ – 7 × 10⁻⁷ m	4 × 10¹⁴ – 7 × 10¹⁴ Hz	Human eye sensitivity	Lighting, displays	None
Ultraviolet (UV)	10⁻⁸ – 4 × 10⁻⁷ m	> 7 × 10¹⁴ Hz	Electronic excitation	Sterilisation, fluorescence	Skin burns, DNA damage
X-ray	10⁻¹² – 10⁻⁸ m	> 10¹⁸ Hz	Penetrates soft tissue	Medical imaging, security scanning	Ionising; tissue damage
Gamma	< 10⁻¹² m	> 10²⁰ Hz	Highest energy photons	Cancer radiotherapy, sterilisation	Strong ionising; severe health risk

All EM waves are transverse waves travelling at c ≈ 3 × 10⁸ m s⁻¹ in vacuum.

Atomic Structure (Nuclear Model)

• Composition: Protons (+1 e), neutrons (0 e), electrons (−1 e); masses ≈ 1 u for protons/neutrons, ≈ 0 u for electrons
• Atomic number (Z): Number of protons
• Mass number (A): Protons + neutrons
• Isotope: Same Z, different A
• Nuclide notation: ᴬ_Z X (e.g., ¹⁴_6 C)
• Ionisation: Gain/loss of electrons → formation of ions

Radioactive Decay Types

Decay	Emitted Particle	Change in A	Change in Z	Penetrating Power
α	Helium nucleus (⁴₂He)	−4	−2	Low
β⁻	Electron	0	+1	Medium
β⁺	Positron	0	−1	Medium
γ	Photon (no mass/charge)	0	0	High

• Nuclear equations: Conserve A and Z on each side

Ionising Radiation

• Penetration order (low → high): α < β < γ
• Ionising ability order (high → low): α > β > γ (α particles densely ionise but stop quickly)
• Deflection:
  • α and β are charged → deflected by electric/magnetic fields
  • α deflects opposite direction to β (opposite charge)
  • γ (neutral) is not deflected
• Background radiation: Natural sources (cosmic rays, terrestrial radionuclides)

Half-Life

• Definition: t₁/₂ = time required for half of radioactive sample to decay
• Exponential decay law: N(t) = N₀ × (1/2)^(t/t₁/₂) where λ = ln(2)/t₁/₂
• Calculations: After n half-lives, remaining fraction = (1/2)ⁿ
• Example: If t₁/₂ = 5 years, amount left after 10 years is ¼ of original
• Graphical representation: Exponential decay curve; decay product shown as second curve (if also radioactive)
• Applications & hazards: Medical imaging (PET), cancer radiotherapy, carbon dating; protection needed for ionising damage