20/08/2026
# JUPEB Physics — Definitions, Laws & Formula Sheet
# # # (For Essay/Theory Exam Prep — PHY 001–004)
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# # PHY 001: MECHANICS AND PROPERTIES OF MATTER
# # # 1. Physical Quantities and Units
**Definitions**
- **Fundamental (basic) quantities**: physical quantities that cannot be expressed in terms of other quantities — length, mass, time, electric current, temperature, luminous intensity, amount of substance.
- **Derived quantities**: quantities obtained by combining fundamental quantities (e.g. area, velocity, force).
- **Dimensional analysis**: the study of the relationship between physical quantities using their dimensions (base units), used to check the homogeneity of equations and derive relationships.
- **Mass**: the quantity of matter in a body; it is constant everywhere.
- **Weight**: the force of gravity acting on a body (W = mg); it varies with location.
**Key Points for Essays**
- Dimensional analysis is important because it: (i) checks the correctness of physical equations, (ii) helps derive formulas, (iii) converts units between systems.
- Mass vs weight: mass is scalar and constant (kg); weight is a vector force (N) and varies with g.
**Formulas**
- Dimensions: [L], [M], [T]
- Density: ρ = m/V
---
# # # 2. Vectors
**Definitions**
- **Scalar quantity**: has magnitude only (e.g. mass, time, speed).
- **Vector quantity**: has both magnitude and direction (e.g. displacement, velocity, force).
- **Resolution of a vector**: splitting a vector into components along chosen axes (usually perpendicular).
**Formulas**
- Resultant of two vectors (parallelogram law): R = √(A² + B² + 2AB cos θ)
- Components: Aₓ = A cos θ, Aᵧ = A sin θ
- Dot product: **A**·**B** = AB cos θ (scalar result)
- Cross product: **A**×**B** = AB sin θ (vector result, direction by right-hand rule)
---
# # # 3. Kinematics
**Definitions**
- **Distance**: total length of path travelled (scalar).
- **Displacement**: shortest distance from initial to final position, in a specified direction (vector).
- **Speed**: rate of change of distance with time (scalar).
- **Velocity**: rate of change of displacement with time (vector).
- **Acceleration**: rate of change of velocity with time.
- **Uniform velocity**: equal displacements in equal time intervals.
- **Projectile motion**: motion of a body under gravity alone after being given an initial velocity, following a curved (parabolic) path.
**Laws/Equations of Motion** (constant acceleration)
- v = u + at
- s = ut + ½at²
- v² = u² + 2as
- s = ½(u + v)t
**Projectile Motion**
- Time of flight: T = 2u sin θ / g
- Maximum height: H = u² sin²θ / 2g
- Range: R = u² sin 2θ / g
---
# # # 4. Dynamics
**Newton's Laws of Motion**
- **First Law (Law of Inertia)**: A body remains at rest or in uniform motion in a straight line unless acted upon by a net external force.
- **Second Law**: The rate of change of momentum of a body is directly proportional to the applied force and takes place in the direction of the force. F = ma (or F = dp/dt).
- **Third Law**: To every action, there is an equal and opposite reaction.
**Definitions**
- **Force**: an agent that changes or tends to change the state of rest or motion of a body.
- **Friction**: a force that opposes relative motion between two surfaces in contact.
- **Equilibrium**: a state in which the net force and net torque on a body are zero.
- **Linear momentum**: product of mass and velocity (p = mv), a vector quantity.
- **Elastic collision**: collision in which both momentum and kinetic energy are conserved.
- **Inelastic collision**: collision in which momentum is conserved but kinetic energy is not.
**Law of Conservation of Linear Momentum**: In the absence of external forces, the total momentum of a system before collision equals the total momentum after collision.
**Formulas**
- F = ma
- Momentum: p = mv
- Conservation: m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂
- Frictional force: F = μN (μ = coefficient of friction, N = normal reaction)
- Moment of a force (torque): τ = F × d
---
# # # 5. The Gravitational Field
**Newton's Law of Universal Gravitation**: Every particle attracts every other particle with a force directly proportional to the product of their masses and inversely proportional to the square of the distance between them.
- F = Gm₁m₂/r² (G = 6.67 × 10⁻¹¹ Nm²kg⁻²)
**Definitions**
- **Gravitational field strength (g)**: force per unit mass at a point in a gravitational field. g = F/m = GM/r²
- **Gravitational potential**: work done in bringing a unit mass from infinity to a point in the field. V = −GM/r
- **Escape velocity**: minimum velocity needed for a body to escape a planet's gravitational field permanently.
**Kepler's Laws**
1. Planets move in elliptical orbits with the Sun at one focus.
2. A line joining a planet to the Sun sweeps out equal areas in equal times.
3. T² ∝ r³ (square of orbital period ∝ cube of orbital radius)
**Formulas**
- Escape velocity: v = √(2GM/r)
- Orbital velocity: v = √(GM/r)
---
# # # 6. Work, Energy and Power
**Definitions**
- **Work**: done when a force moves its point of application through a distance in the direction of the force. W = Fs cos θ
- **Energy**: the capacity to do work.
- **Power**: the rate of doing work. P = W/t
- **Kinetic energy**: energy possessed by a body due to its motion.
- **Potential energy**: energy possessed by a body due to its position or state.
**Law of Conservation of Energy**: Energy cannot be created or destroyed, only transformed from one form to another; total energy of an isolated system remains constant.
**Formulas**
- KE = ½mv²
- PE = mgh
- P = Fv
- 1 kWh = 3.6 × 10⁶ J
- 1 horsepower = 746 W
---
# # # 7. Circular and Oscillatory Motion
**Definitions**
- **Angular velocity (ω)**: rate of change of angular displacement.
- **Centripetal acceleration**: acceleration directed toward the centre of a circular path.
- **Centripetal force**: the resultant force directed toward the centre, causing circular motion.
- **Centrifugal force**: the fictitious (pseudo) outward force experienced in a rotating frame of reference (reaction to centripetal force).
- **Simple Harmonic Motion (SHM)**: periodic motion in which acceleration is directly proportional to displacement from a fixed point and is always directed toward that point.
**Formulas**
- ω = 2π/T = 2πf
- v = ωr
- Centripetal acceleration: a = v²/r = ω²r
- Centripetal force: F = mv²/r = mω²r
- SHM defining equation: a = −ω²x
- Displacement: x = A sin ωt (or A cos ωt)
- Velocity: v = ω√(A² − x²)
- Period of SHM: T = 2π√(m/k) (spring) or T = 2π√(l/g) (simple pendulum)
- Energy in SHM: E = ½mω²A²
- Angular momentum: L = Iω
- Rotational KE: KE = ½Iω²
---
# # # 8. Elasticity
**Definitions**
- **Hooke's Law**: within the elastic limit, extension is directly proportional to the applied force. F = ke
- **Elastic limit**: the maximum stress a material can withstand and still return to its original shape when the stress is removed.
- **Stress**: force applied per unit cross-sectional area. σ = F/A
- **Strain**: ratio of extension (or change in dimension) to original dimension. ε = e/L
- **Young's Modulus**: ratio of stress to strain for a material under tension/compression, within the elastic limit. E = stress/strain
- **Ductile substance**: one that can be drawn into wires without breaking (undergoes large plastic deformation before fracture).
- **Brittle substance**: one that breaks with little or no plastic deformation.
**Formulas**
- E (Young's modulus) = FL/(Ae)
- Energy stored in a stretched wire: U = ½Fe
- Energy per unit volume = ½ × stress × strain
---
# # # 9. Hydrostatics
**Definitions**
- **Pressure**: force per unit area. P = F/A
- **Archimedes' Principle**: when a body is wholly or partially immersed in a fluid, it experiences an upthrust equal to the weight of fluid displaced.
- **Principle of Floatation**: a floating body displaces its own weight of the fluid in which it floats.
- **Stokes' Law**: the viscous drag force on a small sphere moving through a fluid is F = 6πηrv.
- **Terminal velocity**: the maximum constant velocity attained by a body falling through a fluid when the net force on it becomes zero.
**Formulas**
- Pressure in a fluid: P = hρg
- Upthrust: U = ρVg (weight of fluid displaced)
- Stokes' Law: F = 6πηrv
---
# # # 10. Hydrodynamics
**Definitions**
- **Laminar flow**: smooth, orderly flow in parallel layers with no disruption between layers.
- **Turbulent flow**: irregular, chaotic flow with eddies and mixing.
- **Viscosity**: the internal friction (resistance to flow) of a fluid.
- **Surface tension**: the property by which the surface of a liquid behaves like a stretched elastic membrane, tending to minimize surface area.
- **Cohesion**: force of attraction between molecules of the same substance.
- **Adhesion**: force of attraction between molecules of different substances.
- **Capillarity**: the rise or fall of liquid in a narrow tube due to surface tension.
- **Bernoulli's Principle**: for a steady, non-viscous, incompressible fluid flow, the sum of pressure energy, kinetic energy and potential energy per unit volume is constant.
**Formulas**
- Equation of continuity: A₁v₁ = A₂v₂
- Bernoulli's equation: P + ½ρv² + ρgh = constant
- Reynold's number: Re = ρvd/η (determines laminar vs turbulent flow)
- Poiseuille's equation: Q = πPr⁴/(8ηL)
---
# # PHY 002: HEAT, WAVES AND OPTICS
# # # 1. Temperature and Thermometry
**Definitions**
- **Heat**: a form of energy that flows from a body at higher temperature to one at lower temperature.
- **Temperature**: the degree of hotness or coldness of a body; a measure of the average kinetic energy of molecules.
- **Thermal equilibrium**: state in which two bodies in contact have no net heat flow between them (same temperature).
**Formulas**
- Celsius to Kelvin: T(K) = T(°C) + 273
- Linear expansion: ΔL = LαΔθ
- Area expansion: ΔA = AβΔθ (β ≈ 2α)
- Volume expansion: ΔV = VγΔθ (γ ≈ 3α)
---
# # # 2. Heat and Energy
**Definitions**
- **Heat capacity**: quantity of heat required to raise the temperature of a body by 1 K (or 1°C).
- **Specific heat capacity (c)**: quantity of heat required to raise the temperature of 1 kg of a substance by 1 K.
- **Latent heat**: heat absorbed or released during a change of state without a change in temperature.
- **Specific latent heat**: heat required to change the state of 1 kg of a substance without change of temperature.
- **Blackbody**: an idealized object that absorbs all incident radiation and is also a perfect emitter of radiation.
**Laws**
- **Stefan-Boltzmann Law**: the total energy radiated per unit surface area of a blackbody per unit time is proportional to the fourth power of its absolute temperature. E = σT⁴
**Formulas**
- Q = mcΔθ
- Q = mL (L = specific latent heat)
---
# # # 3. Ideal Gases
**Gas Laws**
- **Boyle's Law**: at constant temperature, the pressure of a fixed mass of gas is inversely proportional to its volume. PV = constant
- **Charles' Law**: at constant pressure, the volume of a fixed mass of gas is directly proportional to its absolute temperature. V/T = constant
- **Pressure Law (Gay-Lussac's Law)**: at constant volume, the pressure of a fixed mass of gas is directly proportional to its absolute temperature. P/T = constant
- **Dalton's Law of Partial Pressures**: the total pressure of a mixture of non-reacting gases equals the sum of the partial pressures of each gas.
**Definitions**
- **Kinetic theory of gases**: gases consist of tiny particles in constant random motion, colliding elastically with each other and the container walls.
**Formulas**
- Equation of state: PV = nRT
- Kinetic theory: PV = ⅓Nm⟨c²⟩
- KE of a molecule: KE = ½m⟨c²⟩ = (3/2)kT
---
# # # 4. Thermodynamics
**Definitions**
- **Internal energy**: sum of the kinetic and potential energies of the molecules of a system.
- **Isothermal process**: occurs at constant temperature.
- **Adiabatic process**: occurs with no heat exchange with surroundings.
**Laws**
- **First Law of Thermodynamics**: the heat supplied to a system equals the increase in internal energy plus the work done by the system. Q = ΔU + W
- **Second Law of Thermodynamics**: heat cannot spontaneously flow from a colder body to a hotter body without external work being done (or: the entropy of an isolated system never decreases).
**Formulas**
- Work done by gas: W = PΔV
- Efficiency of heat engine: η = W/Qₕ = 1 − (Q_c/Qₕ)
---
# # # 5. Waves
**Definitions**
- **Wave**: a disturbance that transfers energy from one point to another without transferring matter.
- **Progressive wave**: a wave that transfers energy continuously away from the source.
- **Stationary (standing) wave**: formed by the superposition of two progressive waves of equal frequency and amplitude travelling in opposite directions; no net transfer of energy.
- **Principle of Superposition**: when two or more waves meet at a point, the resultant displacement is the vector sum of the individual displacements.
- **Interference**: the superposition of two coherent waves resulting in regions of reinforcement (constructive) and cancellation (destructive).
**Formulas**
- v = fλ
- T = 1/f
---
# # # 6. Electromagnetic Waves
**Definitions**
- **Electromagnetic spectrum**: the continuous range of electromagnetic waves arranged in order of frequency/wavelength — radio, microwave, infrared, visible light, ultraviolet, X-rays, gamma rays.
**Key point**: All EM waves travel at the speed of light (c = 3 × 10⁸ m/s) in a vacuum.
---
# # # 7. Sound Waves
**Definitions**
- **Pitch**: subjective sensation related to frequency of a sound.
- **Loudness**: subjective sensation related to the intensity/amplitude of a sound.
- **Quality (timbre)**: characteristic that distinguishes sounds of the same pitch and loudness from different sources, due to overtones.
- **Beats**: periodic variation in loudness produced by the superposition of two sound waves of slightly different frequencies.
- **Doppler Effect**: the apparent change in frequency of a wave due to relative motion between the source and observer.
**Formulas**
- Beat frequency: f_beat = |f₁ − f₂|
- Doppler effect (source moving toward stationary observer): f' = fv/(v − vₛ)
- Intensity level (decibel): β = 10 log(I/I₀)
---
# # # 8. Geometrical Optics
**Laws**
- **Laws of Reflection**: (i) the incident ray, reflected ray and normal all lie in the same plane; (ii) the angle of incidence equals the angle of reflection.
- **Laws of Refraction (Snell's Law)**: (i) the incident ray, refracted ray and normal lie in the same plane; (ii) the ratio of sine of angle of incidence to sine of angle of refraction is constant for a given pair of media. n = sin i/sin r
**Definitions**
- **Total internal reflection**: occurs when light travelling from a denser to a less dense medium strikes the boundary at an angle greater than the critical angle, and is entirely reflected back.
- **Critical angle**: the angle of incidence in the denser medium for which the angle of refraction is 90°.
- **Dispersion**: the splitting of white light into its constituent colours by a prism due to differing refractive indices for different wavelengths.
**Formulas**
- Mirror formula: 1/f = 1/u + 1/v
- Refractive index: n = c/v (speed of light in vacuum/medium)
- Critical angle: sin C = 1/n
---
# # # 9. Lenses and Optical Instruments
**Formulas**
- Lens formula: 1/f = 1/v − 1/u
- Magnification: m = v/u = hᵢ/hₒ
- Lens power: P = 1/f (in dioptres, f in metres)
- Power of combined lenses in contact: P = P₁ + P₂
**Definitions**
- **Defects of vision**: short-sightedness (myopia, corrected with diverging lens), long-sightedness (hypermetropia, corrected with converging lens), astigmatism.
---
# # # 10. Wave Theory of Light
**Definitions**
- **Huygens' Principle**: every point on a wavefront acts as a source of secondary wavelets, and the new wavefront is the envelope of these wavelets.
- **Diffraction**: the bending/spreading of waves around obstacles or through apertures.
- **Coherent sources**: sources with a constant phase difference and the same frequency.
- **Resolving power**: the ability of an optical instrument to distinguish between two closely spaced objects.
- **Polarization**: the restriction of the vibration of a transverse wave to a single plane; only transverse waves can be polarized.
**Formulas**
- Young's double-slit: λ = ax/D (a = slit separation, x = fringe spacing, D = slit-to-screen distance)
- Diffraction grating: d sin θ = nλ
---
# # PHY 003: ELECTRICITY AND MAGNETISM
# # # 1. Electrostatics
**Laws**
- **Coulomb's Law**: the force between two point charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. F = kq₁q₂/r² = q₁q₂/(4πε₀r²)
- **Gauss's Law**: the total electric flux through a closed surface is equal to 1/ε₀ times the total charge enclosed. Φ = Q/ε₀
**Definitions**
- **Electric field**: the region around a charge where another charge experiences a force. E = F/q
- **Electric potential**: work done in bringing a unit positive charge from infinity to a point in the field.
- **Equipotential surface**: a surface on which every point has the same electric potential.
**Formulas**
- E = kQ/r²
- V = kQ/r
- E = V/d (uniform field)
---
# # # 2. Capacitors
**Definitions**
- **Capacitance**: the ability of a conductor to store electric charge. C = Q/V
- **Dielectric**: an insulating material placed between capacitor plates to increase capacitance.
- **Time constant**: the time taken for the charge/voltage in a C-R circuit to fall to 1/e (or rise to 1−1/e) of its initial/final value.
**Formulas**
- C = Q/V
- Parallel plate capacitor: C = ε₀εᵣA/d
- Capacitors in series: 1/C = 1/C₁ + 1/C₂ + ...
- Capacitors in parallel: C = C₁ + C₂ + ...
- Energy stored: U = ½QV = ½CV² = Q²/2C
- Time constant: τ = RC
- Charging: Q = Q₀(1 − e^(−t/RC))
- Discharging: Q = Q₀e^(−t/RC)
---
# # # 3. Current Electricity
**Laws**
- **Ohm's Law**: the current through a conductor is directly proportional to the potential difference across it, provided temperature remains constant. V = IR
- **Kirchhoff's Current Law**: the sum of currents entering a junction equals the sum of currents leaving it (conservation of charge).
- **Kirchhoff's Voltage Law**: the sum of EMFs in a closed loop equals the sum of potential drops (conservation of energy).
**Definitions**
- **Electric current**: the rate of flow of electric charge. I = Q/t
- **Resistance**: opposition offered by a conductor to current flow. R = V/I
- **Resistivity**: resistance per unit length per unit cross-sectional area of a material, a property of the material itself.
- **Ohmic conductor**: obeys Ohm's law (V-I graph is a straight line through the origin).
- **Non-ohmic conductor**: does not obey Ohm's law (e.g. diode, filament lamp).
- **EMF (electromotive force)**: the total energy supplied per unit charge by a source, including energy lost to internal resistance.
**Formulas**
- I = Q/t
- V = IR
- R = ρL/A
- Resistors in series: R = R₁ + R₂ + ...
- Resistors in parallel: 1/R = 1/R₁ + 1/R₂ + ...
- Power: P = IV = I²R = V²/R
- EMF and internal resistance: ε = I(R + r)
- Temperature coefficient of resistance: Rθ = R₀(1 + αθ)
---
# # # 4. Magnetic Field
**Definitions**
- **Magnetic field**: the region around a magnet or current-carrying conductor where a magnetic force can be detected.
- **Magnetic flux**: the total number of magnetic field lines passing through an area. Φ = BA
- **Magnetic flux density (B)**: magnetic flux per unit area.
---
# # # 5. Force on Conductor and Moving Charge
**Rules**
- **Fleming's Left-Hand Rule**: used to determine the direction of force on a current-carrying conductor in a magnetic field (Thumb = Thrust/Force, First finger = Field, seCond finger = Current).
**Laws**
- **Ampere's Law**: relates the integrated magnetic field around a closed loop to the electric current passing through the loop.
- **Biot-Savart's Law**: gives the magnetic field produced by a current-carrying conductor at a point, proportional to the current and inversely proportional to the square of the distance.
**Formulas**
- Force on current-carrying conductor: F = BIL sin θ
- Force on moving charge: F = qvB sin θ
- Force between two parallel conductors: F/L = μ₀I₁I₂/(2πd)
- Torque on a coil: τ = NBIA sin θ
---
# # # 6. Electromagnetic Induction
**Laws**
- **Faraday's Law**: the induced EMF in a circuit is directly proportional to the rate of change of magnetic flux linkage.
- **Lenz's Law**: the direction of an induced current is such that it opposes the change producing it (conservation of energy).
- **Fleming's Right-Hand Rule**: used to determine the direction of induced current (Thumb = Motion, First finger = Field, seCond finger = Current).
**Definitions**
- **Self-inductance**: the property of a coil by which it opposes any change in current flowing through it.
- **Mutual inductance**: the property by which a changing current in one coil induces an EMF in a neighbouring coil.
- **Eddy currents**: circulating currents induced in a conductor by a changing magnetic field.
**Formulas**
- ε = −N(dΦ/dt)
- ε = −L(dI/dt)
- Energy stored in an inductor: U = ½LI²
- Transformer equation: Vₚ/Vₛ = Nₚ/Nₛ
---
# # # 7. Alternating Current (A.C.) Circuits
**Definitions**
- **Period**: time taken for one complete cycle.
- **Frequency**: number of cycles per second.
- **Peak value**: maximum instantaneous value of current/voltage.
- **RMS value**: the value of steady (DC) current/voltage that would produce the same heating effect as the AC — RMS = peak/√2.
- **Resonance**: occurs in an L-C-R circuit when inductive reactance equals capacitive reactance, giving maximum current.
**Formulas**
- Iᵣₘₛ = I₀/√2, Vᵣₘₛ = V₀/√2
- Inductive reactance: Xₗ = ωL = 2πfL
- Capacitive reactance: X_c = 1/(ωC) = 1/(2πfC)
- Impedance (L-C-R series): Z = √(R² + (Xₗ − X_c)²)
- Resonant frequency: f₀ = 1/(2π√(LC))
- Power in AC circuit: P = Vᵣₘₛ Iᵣₘₛ cos φ (cos φ = power factor)
---
# # PHY 004: MODERN PHYSICS
# # # 1. Atomic Structure
**Definitions**
- **Isotopes**: atoms of the same element with the same number of protons but different numbers of neutrons.
- **Specific charge**: the ratio of charge to mass (e/m) of a particle.
**Key Experiments**
- **Millikan's Oil Drop Experiment**: determined the charge of an electron by balancing gravitational and electric forces on charged oil droplets.
- **Cathode Ray Oscilloscope**: used to determine e/m of the electron and display waveforms.
---
# # # 2. Elements of Modern Physics
**Definitions**
- **Blackbody radiation**: electromagnetic radiation emitted by a blackbody, whose spectrum depends only on temperature.
- **Ultraviolet catastrophe**: the failure of classical (wave) theory to predict blackbody radiation correctly at short wavelengths — resolved by Planck's quantum theory.
- **Photoelectric emission**: the emission of electrons from a metal surface when light of sufficiently high frequency falls on it.
- **Thermionic emission**: the emission of electrons from a heated metal surface.
- **Bohr's Theory**: electrons orbit the nucleus in fixed energy levels (stationary states) without radiating energy; radiation is emitted/absorbed only when an electron transitions between levels.
**Formulas**
- Photoelectric equation (Einstein): hf = W₀ + KE_max (W₀ = work function)
- Bohr model energy levels: Eₙ = −13.6/n² eV (for hydrogen)
- Photon energy: E = hf = hc/λ
---
# # # 3. X-Rays
**Laws**
- **Bragg's Law**: nλ = 2d sin θ (used for X-ray diffraction by crystals)
- **Moseley's Law**: relates the frequency of characteristic X-rays to the atomic number of the emitting element. √f ∝ (Z − b)
**Definitions**
- **X-rays**: high-frequency, short-wavelength electromagnetic radiation produced when fast-moving electrons are decelerated suddenly (bremsstrahlung) or by electron transitions in inner shells.
---
# # # 4. Wave-Particle Duality
**Definitions**
- **De Broglie hypothesis**: matter (particles) can exhibit wave-like properties; every moving particle has an associated wavelength.
- **Compton Effect**: the increase in wavelength of X-rays when scattered by electrons, demonstrating the particle nature of light.
- **Heisenberg's Uncertainty Principle**: it is impossible to simultaneously know both the exact position and exact momentum of a particle; the more precisely one is known, the less precisely the other can be known.
**Formulas**
- De Broglie wavelength: λ = h/p = h/(mv)
- Uncertainty principle: Δx·Δp ≥ h/4π
---
# # # 5. Radioactivity and Nuclear Energy
**Definitions**
- **Radioactivity**: the spontaneous disintegration of unstable atomic nuclei with emission of radiation (α, β, γ).
- **Mass defect**: the difference between the mass of a nucleus and the sum of the masses of its individual nucleons.
- **Binding energy**: the energy required to separate a nucleus into its individual nucleons; equivalent to the energy released when the nucleus is formed.
- **Half-life**: the time taken for half the radioactive nuclei in a sample to decay.
- **Nuclear fission**: the splitting of a heavy nucleus into two lighter nuclei with release of energy.
- **Nuclear fusion**: the combination of two light nuclei to form a heavier nucleus with release of energy.
**Formulas**
- Einstein's mass-energy relation: E = mc²
- Radioactive decay law: N = N₀e^(−λt)
- Half-life: t½ = ln2/λ = 0.693/λ
- Activity: A = λN
---
# # # 6. Introduction to Semiconductors
**Definitions**
- **Semiconductor**: a material with electrical conductivity between that of a conductor and an insulator (e.g. silicon, germanium).
- **Intrinsic semiconductor**: a pure semiconductor with no added impurities.
- **Extrinsic semiconductor**: a semiconductor doped with impurities to increase conductivity (n-type or p-type).
- **Doping**: the process of adding impurity atoms to a pure semiconductor to alter its electrical properties.
- **p-n junction diode**: a device formed by joining p-type and n-type semiconductors, allowing current to flow in one direction only.
**Key Points**
- Rectification: process of converting AC to DC. A bridge rectifier uses four diodes for full-wave rectification.
- A transistor can act as an amplifier (small signal → large output) or a switch (on/off states).
---
# # # 7. Applied Physics
**Definitions**
- **Ultrasound**: sound waves with frequency above the range of human hearing (>20 kHz), used in medical imaging.
- **CT scan (Computed Tomography)**: uses X-rays taken from multiple angles, processed by computer, to produce cross-sectional images of the body.
- **Nuclear Magnetic Resonance (NMR/MRI)**: uses strong magnetic fields and radio waves to produce detailed images of soft tissue, based on the resonance behaviour of hydrogen nuclei.
**Power Generation**
- **Solar**: converts sunlight directly to electricity via photovoltaic cells.
- **Geothermal**: uses heat from within the Earth to generate steam and drive turbines.
- **Tidal**: uses the kinetic energy of tidal movements to generate electricity.
---
# # EXAM STRATEGY NOTES
**For essay/theory questions, examiners typically want:**
1. A clear, precise **definition** of the term or law (memorize word-for-word where possible).
2. The **statement of any relevant law** (e.g., "state Newton's law of gravitation...").
3. A **diagram** where relevant (circuits, ray diagrams, force diagrams) — always label clearly.
4. **Derivations** for formula-based questions — show each step, don't skip algebra.
5. **Units** stated correctly for every quantity in a formula.
6. **Worked examples/applications** — link theory to real-life or lab examples (JUPEB often asks "state a suggested experiment" or asks you to describe an experimental setup).
**Constants worth memorizing:**
- g = 9.8 m/s² (or 10 m/s² as approximation)
- G = 6.67 × 10⁻¹¹ Nm²kg⁻²
- c = 3.0 × 10⁸ m/s
- h (Planck's constant) = 6.63 × 10⁻³⁴ Js
- e (electron charge) = 1.6 × 10⁻¹⁹ C
- k (Coulomb's constant) = 9.0 × 10⁹ Nm²C⁻²
- ε₀ = 8.85 × 10⁻¹² Fm⁻¹
- NA (Avogadro's number) = 6.02 × 10²³ mol⁻¹
- R (gas constant) = 8.31 J mol⁻¹K⁻¹
- 1 eV = 1.6 × 10⁻¹⁹ J
**Topics that frequently appear as essay questions (based on syllabus emphasis):**
- Newton's Laws + applications
- Simple pendulum experiment (SHM, determining g)
- Gas laws + kinetic theory derivation
- First/Second Law of Thermodynamics
- Coulomb's Law vs Gauss's Law
- Kirchhoff's Laws + circuit problems
- Faraday's/Lenz's Law + applications (transformer, generator)
- Photoelectric effect vs thermionic emission
- Radioactive decay + half-life calculations
- Semiconductor p-n junction and rectification
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*Compiled from the JUPEB Physics syllabus (PHY 001–004). Use alongside past questions and your practical write-ups for full exam coverage.*
