JUPEB physics syllabus

JUPEB syllables and study plan: use this syllabus as your study guide, follow it step by step. The golden rule is, 70% of your efforts should be into reading your materials (texts) and 30% should be in invested in practising JUPEB past questions. FreshNote app has commusulated past questions and answers.

JUPEB Examination Prep

Physics Syllabus

Complete, topic-by-topic JUPEB Physics syllabus — all 4 courses, First & Second Semester

⚗️ Chemistry Syllabus 🧬 Biology Syllabus

About JUPEB Physics JUPEB Physics covers four courses phy 001-004. A pass qualifies you for Direct Entry into Medicine, Nursing, Engineering, Computer Science, and all Natural & Biological Science programmes at 200 Level in Nigerian universities. Exams are held annually in June.

Aims & Objectives

At the end of this programme, students should be able to:

1. Describe the properties of matter and waves, and various physical phenomena at the microscopic and macroscopic levels.
2. Analyze and apply physics laws and principles to solve real-life problems.
3. Design, implement, and draw meaningful inferences from the results of experiments.
4. Explain natural and physical phenomena using physics laws and concepts.
5. Demonstrate sound understanding of both classical and modern physics principles.
6. Apply mathematical tools to model and solve physical problems quantitatively.

Course Structure

📘 First Semester

PHY001

Mechanics & Properties of Matter

3 Credit Units

PHY002

Heat, Waves & Optics

3 Credit Units

📗 Second Semester

PHY003

Electricity & Magnetism

3 Credit Units

PHY004

Modern Physics

3 Credit Units

Complete Syllabus

PHY001 — Mechanics & Properties of Matter  |  First Semester

1

Units & Measurements

6 subtopics

▼

• Order of magnitude and scientific notation
• Definition and standards of fundamental units: Length, Mass, and Time (SI system)
• Unit conversion and dimensional analysis (L, M, T dimensions only)
• Methods of measuring Length (ruler, vernier caliper, micrometer screw gauge), Mass (balance), and Time (stopwatch, oscillation method)
• Basic (fundamental) and Derived units — examples and derivations
• Significant figures, errors (systematic and random), precision and accuracy in measurements

Key focus: Dimensional analysis — checking the homogeneity of equations and deriving unknown quantities.

2

Vectors

7 subtopics

▼

• Distinction between scalar (magnitude only) and vector (magnitude + direction) quantities with examples
• Vector representation: magnitude, direction, arrow notation, unit vectors
• Addition and Subtraction of vectors using geometrical methods (triangle rule, parallelogram rule)
• Resolution of vectors into horizontal and vertical components; component method of addition
• Vector multiplication: dot product (scalar product) A·B = AB cosθ, and cross product (vector product) |A×B| = AB sinθ
• Vectors in Cartesian coordinate system: i, j, k unit vectors; position vector
• Resultant of concurrent coplanar forces; equilibrant force

3

Particle Kinematics

9 subtopics

▼

• Types of motion: translational, random, oscillatory, and rotational — definitions and examples
• Linear motion equations: v = u + at, s = ut + ½at², v² = u² + 2as, s = ½(u+v)t
• Distance-time and velocity-time graphs — slope interpretation, area under v-t graph = displacement
• Instantaneous velocity (dx/dt) and instantaneous acceleration (dv/dt)
• Average velocity (Δx/Δt) and average acceleration (Δv/Δt) in two and three dimensions
• Relative velocity and relative motion in one and two dimensions
• Free fall: g = 9.8 m/s² downward; equations of free fall; time of flight and height
• Projectile motion: horizontal (uniform velocity) and vertical (free fall) components; time of flight T = 2u sinθ/g; maximum height H = u² sin²θ/2g; range R = u² sin2θ/g
• Applications of projectile motion: ballistics, sports, engineering

Projectile motion is heavily tested — master the independence of horizontal and vertical components.

4

Dynamics

10 subtopics

▼

• Newton's First Law (law of inertia), Second Law (F = ma), and Third Law (action-reaction pairs)
• Types of forces: gravitational, normal, tension, friction, applied; Newton's Universal Law of Gravitation: F = Gm₁m₂/r²
• Equilibrium of concurrent forces: translational equilibrium (ΣF = 0) and rotational equilibrium (Στ = 0)
• Centre of Mass (for systems of particles: x_cm = Σmᵢxᵢ/Σmᵢ) and Centre of Gravity; stability
• Moment of a force (torque τ = Fd); couples; principle of moments
• Linear momentum: p = mv; Impulse J = FΔt = Δp; impulse-momentum theorem
• Law of Conservation of linear momentum; proof and applications (rockets, recoil)
• Elastic collisions: both momentum and kinetic energy conserved; coefficient of restitution e = 1
• Inelastic collisions: momentum conserved, KE not conserved; perfectly inelastic (objects stick together)
• Collisions in two dimensions (oblique); motion on inclined planes; static friction (f ≤ μN) and kinetic friction (f = μₖN)

Understand the difference between elastic and inelastic collisions. Know the coefficient of restitution.

5

The Gravitational Field

7 subtopics

▼

• Kepler's Three Laws: (1) Elliptical orbits with Sun at one focus, (2) Equal areas in equal times, (3) T² ∝ r³
• Newton's Law of Universal Gravitation: F = Gm₁m₂/r²; G = 6.674×10⁻¹¹ N m² kg⁻²
• Gravitational field strength: g = GM/r²; variation with altitude (g decreases with height) and latitude
• Measurement of G: Cavendish torsion balance experiment
• Gravitational potential: V = –GM/r (negative, zero at infinity); gravitational potential energy U = –GMm/r
• Satellite motion: orbital speed v = √(GM/r); orbital period T = 2π√(r³/GM); geostationary satellites (period = 24 hrs, altitude ≈ 36,000 km)
• Escape velocity: v_e = √(2GM/R) ≈ 11.2 km/s for Earth; derivation using energy conservation

6

Work, Energy & Power

8 subtopics

▼

• Work done by a constant force: W = Fd cosθ; zero work (perpendicular force); negative work (opposing force)
• Work done by a variable force: W = ∫F·dx (area under F-x graph)
• Kinetic Energy: KE = ½mv²; Gravitational PE: U = mgh; elastic PE: U = ½kx²
• Sources of energy: renewable (solar, wind, hydro, geothermal, tidal) and non-renewable (fossil fuels, nuclear)
• Types of energy and their interconversions; energy transformation chains
• Work-Energy theorem: W_net = ΔKE = ½mv² – ½mu²
• Conservation of mechanical energy: KE + PE = constant in absence of friction; with friction: energy lost = work done by friction
• Power: P = W/t = Fv; units (Watts, kW, horsepower); Kilowatt-hour (1 kWh = 3.6×10⁶ J); efficiency η = useful output/total input

7

Circular & Oscillatory Motion

12 subtopics

▼

• Angular displacement (θ in radians), angular velocity ω = dθ/dt = 2πf, period T = 2π/ω
• Relationship between linear and angular quantities: v = rω, a_t = rα (tangential), a_c = rω² = v²/r (centripetal)
• Torque: τ = Iα; moment of inertia I = Σmr² for various geometries (rod, disk, ring, sphere)
• Rotational kinetic energy: KE_rot = ½Iω²; total KE = ½mv² + ½Iω² (rolling bodies)
• Angular momentum: L = Iω; Newton's 2nd law for rotation: τ = dL/dt
• Conservation of angular momentum: when τ_ext = 0, L = constant (ice skater, diver, planetary motion)
• Centripetal acceleration: a_c = v²/r = rω² (directed toward centre)
• Centripetal force: F_c = mv²/r = mrω²; examples — banked roads, conical pendulum, satellite orbits
• Simple Harmonic Motion (SHM): F = –kx; x = A cos(ωt + φ); v = –Aω sin(ωt); a = –Aω² cos(ωt)
• Energy in SHM: KE = ½mω²(A²–x²), PE = ½mω²x², total E = ½mω²A²; pendulum and spring-mass systems
• Damped oscillations: light damping (decaying amplitude), critical damping (fastest return), heavy/overdamping (slow return); forced oscillations (driving frequency)
• Resonance: when driving frequency = natural frequency → maximum amplitude; examples: Tacoma Narrows Bridge, MRI, musical instruments, radio tuning

SHM equations are extensively tested. Know displacement, velocity, and acceleration at any position, and the energy expressions.

8

Elasticity

12 subtopics

▼

• Hooke's Law: F = ke; spring constant k (N/m); force-extension graph; springs in series (1/k_eff = Σ1/kᵢ) and parallel (k_eff = Σkᵢ)
• Elastic limit and proportionality limit; yield point; ultimate tensile strength; breaking point
• Elastic deformation (material returns to original shape) vs Plastic deformation (permanent change)
• Ductile materials (copper, steel — large plastic region) and Brittle materials (glass, cast iron — fracture at elastic limit)
• Tensile/compressive stress: σ = F/A (Pa or N/m²)
• Tensile/compressive strain: ε = ΔL/L (dimensionless ratio)
• Complete stress-strain curve: proportional limit, elastic limit, yield point, plastic region, necking, fracture
• Young's Modulus: E = σ/ε = FL/(AΔL); typical values for metals, rubber, bone
• Elastic potential energy stored: E = ½Fe = ½ke²; area under F-e graph
• Elastic energy density (energy per unit volume) = ½ × stress × strain = σ²/(2E)
• Shear modulus G = shear stress / shear strain; rigidity of materials
• Bulk modulus: K = –P / (ΔV/V); compressibility = 1/K; applies to liquids and gases under pressure

9

Hydrostatics

10 subtopics

▼

• States of matter and their properties: definite shape/volume (solid), definite volume (liquid), neither definite (gas)
• Density: ρ = m/V; relative density (specific gravity) = ρ_substance/ρ_water; measurement using density bottle, Archimedes' method
• Fluid pressure: P = ρgh; atmospheric pressure; pressure varies with depth not shape of container; Pascal's Principle
• Change of phases: melting, freezing, boiling, condensation, sublimation; latent heat of fusion L_f and vaporisation L_v
• Archimedes' Principle: buoyant force = weight of fluid displaced; F_b = ρ_fluid × V_displaced × g; applications (hydrometers, submarines)
• Principle of Floatation: object floats when weight = buoyant force; floating objects displace their own weight of fluid
• Stoke's Law: viscous drag F = 6πηrv on a sphere of radius r moving at speed v in fluid of viscosity η
• Terminal velocity: when F_drag + F_upthrust = Weight; v_terminal = 2r²(ρ_sphere – ρ_fluid)g / 9η
• Bernoulli's Principle: P + ½ρv² + ρgh = constant along a streamline; applications (aerofoil lift, Venturi meter, carburettor, atomiser)
• Pitot-static tube: measures fluid speed from difference between stagnation and static pressure; v = √(2ΔP/ρ)

10

Hydrodynamics

12 subtopics

▼

• Molecular properties of fluids: intermolecular forces, free movement of molecules in liquids and gases
• Viscosity (η): resistance to flow; Newton's law of viscosity (F/A = η dv/dy); dynamic and kinematic viscosity; viscosity decreases with temperature for liquids
• Surface tension (T): force per unit length; surface energy per unit area; measurement by capillary rise method
• Adhesion (liquid-solid): wetting; contact angle < 90° (wets) or > 90° (doesn't wet)
• Cohesion (liquid-liquid): holds liquid together; surface tension is a cohesive property
• Capillarity: rise h = 2T cosθ / (ρgr); rise in water (θ < 90°) and depression in mercury (θ > 90°)
• Pressure inside a liquid drop: ΔP = 2T/r; inside a soap bubble: ΔP = 4T/r (two surfaces)
• Bernoulli's Equation: P + ½ρv² + ρgh = constant; derivation from work-energy theorem; applications
• Pascal's Principle: pressure applied to enclosed fluid is transmitted equally in all directions; hydraulic press, brakes, jack
• Reynolds' Number: Re = ρvD/η; Re < 2000 (laminar), Re > 4000 (turbulent), 2000–4000 (transition)
• Laminar flow: smooth, parallel layers; Turbulent flow: chaotic, swirling; engineering significance
• Poiseuille's Equation: Q = πr⁴ΔP / (8ηL); flow rate in a cylindrical pipe; resistance to flow; application to blood flow in arteries

PHY002 — Heat, Waves & Optics  |  First Semester

11

Ideal Gases

7 subtopics

▼

• Boyle's Law: PV = constant (constant T); Charles' Law: V/T = constant (constant P); Pressure Law: P/T = constant (constant V)
• Combined gas law: P₁V₁/T₁ = P₂V₂/T₂; Ideal Gas Equation: PV = nRT (R = 8.314 J mol⁻¹ K⁻¹)
• Avogadro's number N_A = 6.022×10²³; Boltzmann constant k_B = R/N_A = 1.38×10⁻²³ J/K; PV = Nk_BT
• Kinetic Theory assumptions: large number of identical molecules, random motion, elastic collisions, negligible volume and intermolecular forces
• Pressure from kinetic theory: P = ⅓ρ<c²> = ⅓Nm<c²>/V
• Mean kinetic energy per molecule: ½m<c²> = (3/2)k_BT; internal energy of ideal gas U = (3/2)nRT
• RMS speed: c_rms = √(3RT/M); most probable speed: c_p = √(2RT/M); mean speed: c_mean = √(8RT/πM); Maxwell-Boltzmann speed distribution

12

Temperature & Thermometry

8 subtopics

▼

• Heat Capacity: C = Q/ΔT (J/K); depends on substance, mass, and state
• Specific Heat Capacity: c = Q/mΔT (J kg⁻¹ K⁻¹); measurement by method of mixtures and electrical method
• Latent heat of fusion L_f (melting/solidification) and vaporisation L_v (boiling/condensation); heating and cooling curves; Q = mL
• Internal energy: sum of KE and PE of all molecules; increases with temperature for ideal gas
• Thermal Conductivity k: Fourier's Law: dQ/dt = kA(ΔT/L); good conductors (metals) vs poor conductors (insulators); composite walls
• Modes of heat transfer: conduction (contact, solids), convection (fluids, bulk motion), radiation (no medium required, EM waves)
• Blackbody radiation: Stefan-Boltzmann Law P = σεAT⁴ (σ = 5.67×10⁻⁸ W m⁻² K⁻⁴); Wien's Displacement Law λ_max T = 2.898×10⁻³ m·K
• Temperature scales: Celsius (°C), Kelvin (K = °C + 273.15), Fahrenheit; fixed points (ice point, steam point); types of thermometers (liquid-in-glass, thermocouple, resistance, infrared)

13

Thermodynamics

6 subtopics

▼

• Work done by a gas: W = PΔV at constant pressure; W = area under P-V graph for any process
• Internal energy of a gas: U = (3/2)nRT (monoatomic ideal gas); changes with temperature only for ideal gases
• First Law of Thermodynamics: ΔU = Q – W; energy conservation in thermodynamic systems; sign conventions
• Second Law of Thermodynamics: Kelvin-Planck statement (no engine converts all heat to work); Clausius statement (heat flows spontaneously from hot to cold); entropy S always increases in isolated system
• Isothermal process: ΔT = 0 → ΔU = 0 → Q = W; Adiabatic process: Q = 0 → ΔU = –W → PVᵞ = constant (γ = C_p/C_v)
• Carnot cycle (isothermal expansion → adiabatic expansion → isothermal compression → adiabatic compression); Carnot efficiency η = 1 – T_cold/T_hot; maximum possible efficiency of any heat engine

14

Electromagnetic Waves

5 subtopics

▼

• Nature of EM waves: oscillating electric and magnetic fields perpendicular to each other and to direction of propagation; transverse waves; speed c = 3×10⁸ m/s in vacuum; c = fλ
• EM spectrum in order of increasing frequency (decreasing wavelength): Radio (10³–10⁹ Hz) → Microwave → Infrared → Visible (400–700 nm) → Ultraviolet → X-ray → Gamma ray (10¹⁸–10²³ Hz)
• Properties common to all EM waves: travel at speed c in vacuum, no medium needed, transverse, can be reflected, refracted, diffracted, interfered, and polarised
• Applications: radio/TV (communication), microwave (radar, cooking, satellite communication), IR (remote control, thermal imaging, night vision), UV (sterilisation, fluorescence, vitamin D), X-ray (medical imaging, security scanning, crystallography), gamma (cancer radiotherapy, sterilisation of equipment, PET scans)
• Production of EM waves: accelerating charges; detection methods for each type of radiation

15

Geometrical Optics

9 subtopics

▼

• Rectilinear propagation of light: evidence from shadows (umbra and penumbra), solar/lunar eclipses, pinhole camera (inverted image)
• Laws of Reflection: angle of incidence = angle of reflection; incident ray, reflected ray, and normal are coplanar
• Snell's Law of Refraction: n₁ sinθ₁ = n₂ sinθ₂; refractive index n = c/v = sin i/sin r
• Plane mirrors: virtual, upright, laterally inverted, same size, image distance = object distance; curved mirrors: concave (converging) and convex (diverging); mirror formula 1/f = 1/v + 1/u; magnification m = –v/u
• Refraction at plane surfaces: apparent depth = real depth / n; real depth and apparent depth relationship
• Total Internal Reflection (TIR): occurs when light travels from denser to less dense medium and angle of incidence exceeds critical angle
• Critical angle: sin C = n₂/n₁ = 1/n (for air-glass interface); relationship with refractive index
• Applications of TIR: optical fibres (telecommunications, endoscopes), diamond brilliance, periscopes with prisms, mirages
• Dispersion by a prism: different wavelengths refracted by different amounts (red least, violet most); angle of deviation; minimum deviation condition; formation of visible spectrum

16

Lenses & Optical Instruments

8 subtopics

▼

• Types of lenses: converging/convex (thicker at centre) and diverging/concave (thinner at centre); principal axis, optical centre, principal focus F, focal length f
• Image formation by lenses using ray diagrams (3 principal rays); lens formula: 1/f = 1/v – 1/u; linear magnification m = v/u = image height/object height
• Power of a lens: P = 1/f (f in metres, P in dioptres); combination of thin lenses: P_total = P₁ + P₂; sign conventions (real is positive)
• Defects of vision: short-sightedness/myopia (far objects blurred, corrected by concave lens); long-sightedness/hypermetropia (near objects blurred, corrected by convex lens); astigmatism (cylindrical lens); presbyopia (age-related)
• The human eye: cornea, aqueous humour, lens, vitreous humour, retina (rods and cones), optic nerve; accommodation by ciliary muscles; near point (25 cm) and far point (infinity)
• Camera: f-number = focal length/aperture diameter; depth of field; shutter speed; film/sensor; refractor telescope (objective + eyepiece, both converging); angular magnification M = f_o/f_e; reflector telescope (concave mirror + eyepiece)
• Simple microscope (magnifying glass): object inside F; angular magnification M = D/f (for image at infinity, D = 25 cm) or M = 1 + D/f (for image at near point)
• Compound microscope: objective forms real magnified intermediate image; eyepiece acts as magnifying glass; total magnification M = m_obj × M_eye; tube length L; ophthalmoscope (illuminated view of retina using concave mirror and lens)

17

Oscillation of Waves

10 subtopics

▼

• Classification: mechanical waves (need medium — sound, water waves) vs EM waves (no medium); transverse (displacement ⊥ propagation) vs longitudinal (displacement ∥ propagation)
• Wave parameters: amplitude A (m), wavelength λ (m), frequency f (Hz), period T = 1/f (s), wave speed v = fλ (m/s), phase
• Displacement-distance graph (snapshot at one time) and displacement-time graph (at one point)
• Wave equation: y = A sin(ωt – kx) where ω = 2πf (angular frequency), k = 2π/λ (wave number)
• Progressive (travelling) waves: carry energy; wavefronts move; Stationary (standing) waves: nodes (zero amplitude) and antinodes (max amplitude) — formed by superposition of two identical waves travelling in opposite directions
• Reflection: angle of incidence = angle of reflection for waves; phase change of π (½λ) at fixed boundary (e.g., string tied at wall)
• Refraction of waves: speed and wavelength change when wave enters medium of different density; direction changes; frequency stays constant; Snell's law applies
• Diffraction: spreading of waves past edges of obstacles or through gaps; significant when gap width ≈ wavelength; examples: sound around corners, radio waves around hills
• Principle of Superposition: when two waves overlap, resultant displacement = algebraic sum of individual displacements at every point and time
• Interference: constructive (crest meets crest, path difference = nλ) and destructive (crest meets trough, path difference = (n+½)λ); conditions for observable interference: coherent, monochromatic, similar amplitudes

18

Wave Theory of Light

8 subtopics

▼

• Wave-Particle duality: light behaves as a wave (interference, diffraction, polarisation) and as particles/photons (photoelectric effect, Compton scattering)
• Huygens' Principle: every point on a wavefront acts as a source of secondary spherical wavelets; the new wavefront is the envelope of all secondary wavelets; explains reflection and refraction
• Interference of light: requires coherent (constant phase difference) and monochromatic sources; optical path difference determines constructive or destructive interference
• Coherent sources: lasers are ideal; Young's double slit produces coherent sources from a single source by division of wavefront
• Young's Double Slit Experiment: fringe spacing Δy = λD/d (D = slit-to-screen distance, d = slit separation); determination of wavelength; bright fringes at path difference = nλ, dark fringes at (n+½)λ
• Single slit diffraction: central maximum of width 2λD/a (a = slit width); secondary maxima; condition for minima: a sinθ = nλ
• Resolving Power: Rayleigh criterion θ_min = 1.22λ/D (D = aperture); minimum angular separation of two point sources; application to telescopes, microscopes, and human eye
• Diffraction grating: d sinθ = nλ (d = grating spacing, n = order); higher resolution than double slit; spectroscopy applications; Polarisation: transverse waves can be polarised; methods (polaroid filter, reflection at Brewster's angle, scattering); Malus's Law I = I₀cos²θ; applications (sunglasses, LCD screens, stress analysis, photography)

19

Sound Waves

8 subtopics

▼

• Pitch: determined by frequency; high frequency = high pitch; musical notes (A4 = 440 Hz); human hearing range 20 Hz – 20 kHz
• Loudness: related to amplitude and intensity; subjective perception; same frequency can sound louder or softer
• Quality (timbre): characteristic waveform of a sound; distinguishes instruments at same pitch and loudness; due to different harmonics present
• Intensity of Sound: I = P/A (W/m²); intensity follows inverse square law: I ∝ 1/r²; threshold of hearing I₀ = 10⁻¹² W/m²
• Decibel scale: β = 10 log(I/I₀) dB; threshold of hearing 0 dB, whisper ~30 dB, normal conversation ~60 dB, pain threshold ~120 dB; Beats: periodic variation of loudness when two slightly different frequencies superpose; beat frequency f_beat = |f₁ – f₂|; applications (tuning instruments)
• Doppler Effect for sound: apparent change in frequency due to relative motion of source and observer; f' = f(v ± v_o)/(v ∓ v_s); sign rules; applications (police radar, ultrasound blood flow, astronomical redshift)
• Stationary waves in strings: nodes at fixed ends; fundamental f₁ = (1/2L)√(T/μ); harmonics f_n = nf₁; factors affecting frequency (length, tension, mass per unit length)
• Stationary waves in pipes: open pipe (antinodes at both ends): f_n = nv/2L (all harmonics); closed pipe (node at closed end, antinode at open end): f_n = nv/4L (odd harmonics only); resonance in air columns — resonance tube experiment to measure speed of sound

PHY003 — Electricity & Magnetism  |  Second Semester

20

Electrostatics

9 subtopics

▼

• Coulomb's Law: F = kq₁q₂/r² = q₁q₂/(4πε₀r²); k = 9×10⁹ N m² C⁻²; ε₀ = 8.85×10⁻¹² F/m; vector form; comparison with gravitational force
• Gauss's Law: total electric flux Φ_E = Q_enc/ε₀ = ∮E·dA; applications to spherical (point charge, shell), cylindrical (line charge), and planar (sheet charge) symmetry
• Electric field: E = F/q₀; field lines (direction, density proportional to magnitude); uniform field between parallel plates E = V/d
• Electric field due to point charge: E = kQ/r² (radially outward from +Q); superposition of fields from multiple charges
• Electric field at a specific point due to multiple charges: vector addition of individual field contributions
• Electric potential: V = kQ/r = W/q (J/C = V); potential is scalar; potential energy U = qV = kQq/r; work done W = q(V_A – V_B)
• Potential due to a point charge and a conducting sphere: outside V = kQ/r; on surface V = kQ/R; inside V = kQ/R (constant)
• Relationship between E and V: E = –dV/dr; E = –∇V; field points in direction of decreasing potential
• Equipotential surfaces: surfaces of constant potential; always perpendicular to field lines; no work done moving charge along equipotential; parallel planes (uniform field), concentric spheres (point charge)

21

Capacitors

7 subtopics

▼

• Capacitors: store electric charge; C = Q/V (Farads); parallel plate: C = ε₀A/d; factors affecting capacitance (area, separation, dielectric)
• Dielectric materials: insulating material between plates; relative permittivity εᵣ (dielectric constant); C = ε₀εᵣA/d; dielectric strength (max field before breakdown)
• Capacitors in series: 1/C_total = 1/C₁ + 1/C₂ + ... (same charge on each, voltages add); in parallel: C_total = C₁ + C₂ + ... (same voltage, charges add)
• Energy stored in a capacitor: E = ½QV = ½CV² = Q²/2C (joules); energy density in electric field = ½ε₀E²
• Effects of introducing a dielectric: with battery connected (V constant) — charge and C increase, E unchanged; with battery disconnected (Q constant) — V and E decrease, C increases
• Charging through resistance: Q = Q₀(1 – e^(–t/RC)); V_C = V₀(1 – e^(–t/RC)); I = I₀e^(–t/RC); time constant τ = RC (time for charge to reach 63.2% of final value)
• Discharging: Q = Q₀e^(–t/RC); V = V₀e^(–t/RC); I = –I₀e^(–t/RC); after 5τ, capacitor considered fully discharged; applications: timing circuits, camera flash, defibrillator, smoothing circuits

22

Current Electricity

12 subtopics

▼

• Electric current I = Q/t = nAve (n = charge carrier density, A = cross-section, v = drift velocity, e = charge); conventional current opposite to electron flow
• Potential difference: V = W/Q; measured in volts; voltmeter (high resistance, connected in parallel)
• Resistance: R = V/I; Resistivity: R = ρL/A; ρ depends on material and temperature; unit (Ω·m)
• Ohm's Law: V = IR for ohmic conductors (constant R); non-ohmic: diode (one-way), filament bulb (R increases with temperature); I-V characteristics
• Resistors in series: R_total = R₁ + R₂ + ...; voltage divides; current same; in parallel: 1/R_total = Σ1/Rᵢ; current divides; voltage same
• EMF (ε): energy per unit charge from energy source; internal resistance (r); terminal voltage V = ε – Ir; short circuit current I_sc = ε/r
• Electrical power: P = IV = I²R = V²/R; maximum power transfer when R_load = r (internal resistance)
• Electrical energy: E = Pt = VIt = I²Rt; efficiency η = P_output/P_input × 100%; kilowatt-hour for billing
• Cells in series: ε_total = Σεᵢ, r_total = Σrᵢ; cells in parallel (identical): ε_total = ε, r_total = r/n
• Kirchhoff's Current Law (KCL): ΣI_in = ΣI_out at any junction; Kirchhoff's Voltage Law (KVL): sum of EMFs = sum of potential drops around any closed loop
• Temperature coefficient of resistance α: R_T = R₀(1 + αΔT); positive α (metals, increases with T); negative α (semiconductors, thermistors — decreases with T); superconductivity
• Potentiometer: null method for comparing EMFs (ε₁/ε₂ = l₁/l₂); Wheatstone Bridge: balanced when P/Q = R/S (null deflection); Galvanometer: measures small currents; conversion to ammeter (shunt in parallel) or voltmeter (high resistance in series)

23

Magnetic Field

6 subtopics

▼

• Earth's Magnetic Field: horizontal component H, vertical component Z; declination (angle between geographic and magnetic north); angle of dip/inclination (angle B makes with horizontal); magnetic equator (zero dip)
• Magnetic field B (Tesla): produced by moving charges and magnets; magnetic field lines (never cross, direction from N to S outside magnet); permeability of free space μ₀ = 4π×10⁻⁷ H/m
• Magnetic flux Φ = BA cosθ (Weber = T·m²); flux density B is the magnetic field strength
• Magnetic field of a long straight conductor: B = μ₀I/(2πr) (circles around wire, direction by right-hand grip rule)
• Magnetic field at centre of a circular coil: B = μ₀NI/(2r) (N = number of turns)
• Magnetic field inside a solenoid: B = μ₀nI (n = N/L = turns per unit length); uniform field inside; applications (electromagnets, relays, inductors)

24

Force on a Conductor & Moving Charge

7 subtopics

▼

• Force on current-carrying conductor: F = BIL sinθ (θ = angle between B and I); maximum force when B ⊥ I
• Force between two parallel conductors: F/L = μ₀I₁I₂/(2πd); attractive (currents same direction), repulsive (opposite); defines the Ampere (SI base unit)
• Fleming's Left-Hand Rule: thumb = force (motion), index = field (B), middle finger = conventional current; used for DC motors
• Torque on a rectangular current loop: τ = BANI sinθ (A = area, N = turns); for a coil in uniform field at angle θ to field; maximum torque when plane of coil parallel to B; application to galvanometer and electric motor
• Ampere's Law: ∮B·dl = μ₀I_enclosed; used to find B for symmetric configurations (solenoid, toroid, straight wire)
• Biot-Savart Law: dB = (μ₀/4π)(I dl × r̂/r²); used when Ampere's Law cannot be applied; integration to find total B
• Force on a moving charge in B field: F = qv × B = qvB sinθ; direction from right-hand rule or cross product; circular motion of charged particle: r = mv/(qB), period T = 2πm/(qB); cyclotron; Hall effect: V_H = IB/(nqd); Hall probe measurement of B

25

Electromagnetic Induction

8 subtopics

▼

• Faraday's Law: induced EMF ε = –dΦ/dt; magnitude |ε| = N|dΦ/dt|; EMF proportional to rate of change of flux; greater N → greater EMF
• Lenz's Law: direction of induced current opposes the change in flux causing it (conservation of energy); induced current creates field to resist change
• Fleming's Right-Hand Rule (generator rule): thumb = motion, index = B field, middle = induced current direction
• AC Generator: rotating coil in magnetic field; EMF = NBAω sinωt; peak EMF = NBAω; sinusoidal output; slip rings and brushes for AC output
• Transformer: primary coil (N_p turns), secondary coil (N_s turns), soft iron core; V_s/V_p = N_s/N_p; ideal transformer: V_sI_s = V_pI_p (power conserved); energy losses: eddy currents (laminated core), hysteresis (soft iron core), flux leakage, resistance heating
• Eddy currents: circulating currents induced in bulk conductors by changing B; cause heating (induction cooker, eddy current braking); minimised by laminating core
• Self-inductance L: ε = –L(dI/dt) (Henrys); energy stored in inductor E = ½LI²; inductance of solenoid L = μ₀N²A/l; L-R circuit: I = I₀(1–e^(–Rt/L)) (growth), I = I₀e^(–Rt/L) (decay); time constant τ = L/R
• Mutual inductance M: ε₂ = –M(dI₁/dt); M = k√(L₁L₂) (k = coupling coefficient); energy in magnetic field per unit volume = B²/(2μ₀); DC motors (commutator converts AC to DC mechanical rotation) and AC generators (sinusoidal output)

26

Alternating Current (AC) Circuits

8 subtopics

▼

• AC characteristics: instantaneous voltage v = V₀ sinωt; period T = 1/f; peak value V₀; peak-to-peak 2V₀; RMS (root mean square) V_rms = V₀/√2 ≈ 0.707V₀; I_rms = I₀/√2; mains supply: Nigeria 240 V (rms), 50 Hz
• Purely Resistive AC circuit: V and I in phase; phasor diagram (V and I along same axis); P_av = I_rms²R = V_rms²/R = V_rmsI_rms
• Purely Capacitive circuit: current leads voltage by 90° (π/2); capacitive reactance X_C = 1/(ωC) = 1/(2πfC); V_C = IX_C; P_av = 0 (no energy dissipation); phasor: I leads V by 90°
• Purely Inductive circuit: voltage leads current by 90° (π/2); inductive reactance X_L = ωL = 2πfL; V_L = IX_L; P_av = 0; phasor: V leads I by 90°
• CR circuit: impedance Z = √(R² + X_C²); phase angle φ: tan φ = X_C/R (current leads V by φ); LR circuit: Z = √(R² + X_L²); tan φ = X_L/R (V leads I by φ); phasor diagrams
• LCR Series circuit: impedance Z = √(R² + (X_L – X_C)²); phase angle tan φ = (X_L – X_C)/R; V_R and I in phase; V_L leads I by 90°; V_C lags I by 90°; phasor diagram of voltages
• Resonance in LCR series circuit: X_L = X_C → ω₀ = 1/√(LC) → f₀ = 1/(2π√(LC)); at resonance Z = R (minimum), I = V/R (maximum), power factor = 1; sharpness of resonance Q-factor = ω₀L/R = 1/(ω₀CR); bandwidth Δω = R/L; applications: radio tuning, signal filtering
• Power in AC circuits: instantaneous p = vi; average P = V_rmsI_rms cosφ; power factor cosφ = R/Z; reactive power Q = V_rmsI_rms sinφ (VAR); apparent power S = V_rmsI_rms (VA); S² = P² + Q²; parallel LCR circuit at resonance: maximum impedance, minimum current

PHY004 — Modern Physics  |  Second Semester

27

Atomic Structure

10 subtopics

▼

• The Nucleus: composed of protons (Z, charge +e = +1.6×10⁻¹⁹ C, mass ≈ 1.673×10⁻²⁷ kg) and neutrons (N = A–Z, neutral, mass ≈ 1.675×10⁻²⁷ kg); atomic number Z, mass number A = Z + N; nuclide notation ᴬ_Z X
• The Electron: charge –e = –1.6×10⁻¹⁹ C; rest mass m_e = 9.11×10⁻³¹ kg; electron shells (K, L, M...) and subshells; quantised energy levels
• Specific charge of electron: e/m_e = 1.76×10¹¹ C/kg; Thomson's cathode ray tube experiment — crossed E and B fields to measure e/m
• Isotopes: nuclides with same Z but different A (different N); examples: ¹H, ²H (deuterium), ³H (tritium); ¹²C, ¹³C, ¹⁴C; chemical properties same (same Z), physical properties differ
• Millikan's Oil Drop Experiment: fine oil drops in electric field; balancing gravitational and electric forces to find charge; quantisation of charge in multiples of e = 1.6×10⁻¹⁹ C
• Cathode Ray Oscilloscope (CRO): electron gun (cathode, anode, accelerating voltage), deflection plates (X and Y), fluorescent screen; uses: measuring voltage, frequency, time; displaying waveforms
• Types of spectra: continuous spectrum (hot solids/liquids — all wavelengths); line emission spectrum (hot gas — specific wavelengths); line absorption spectrum (cool gas absorbs specific wavelengths → dark lines on continuous background)
• Hydrogen emission spectrum: visible series (Balmer: n₂≥3 → n₁=2); UV (Lyman: n₂≥2 → n₁=1); infrared (Paschen: n₁=3, Brackett: n₁=4, Pfund: n₁=5)
• Rydberg formula: 1/λ = R_H(1/n₁² – 1/n₂²); Rydberg constant R_H = 1.097×10⁷ m⁻¹; calculation of wavelengths of spectral lines
• Evidence for quantisation of energy from atomic spectra: only specific wavelengths emitted/absorbed → electrons occupy discrete energy levels only

28

Elements of Modern Physics

9 subtopics

▼

• Failure of classical (wave) theory: couldn't explain blackbody radiation curve (predicted UV catastrophe — infinite energy at high frequencies) or photoelectric effect
• Planck's quantum hypothesis: energy emitted/absorbed in discrete quanta E = hf (h = 6.63×10⁻³⁴ J·s = Planck's constant); solved blackbody problem
• Photoelectric effect: emission of electrons from metal surface when illuminated by light above threshold frequency; Einstein's explanation using photons; ½mv²_max = hf – φ (φ = work function = hf₀); stopping potential V_s: eV_s = ½mv²_max; photoelectric equation confirms particle nature of light
• Bohr's model postulates: (1) electrons orbit nucleus in stationary circular orbits without radiating; (2) angular momentum quantised: L = nℏ = nh/2π; (3) energy emitted/absorbed when electron changes orbit: hf = E_upper – E_lower
• Energy levels of hydrogen: E_n = –13.6/n² eV (n = 1, 2, 3...); ground state n=1 (E = –13.6 eV); ionisation energy = 13.6 eV; orbital radius r_n = n²a₀ (a₀ = 0.053 nm = Bohr radius)
• Excitation: electron absorbs photon of exact energy ΔE = hf and jumps to higher energy level; collisional excitation also possible; atom in excited state is unstable
• Emission: electron falls to lower level; photon emitted with hf = E_upper – E_lower; spontaneous emission (random) and stimulated emission (triggered by passing photon)
• Fraunhofer Lines: dark absorption lines in solar spectrum; atoms in cooler solar atmosphere absorb specific wavelengths from continuous spectrum of hot interior; used to identify elements in the Sun and other stars
• Laser principle: Light Amplification by Stimulated Emission of Radiation; requires population inversion (more atoms in excited than ground state); stimulated emission produces coherent photons; optical cavity (mirrors) provides positive feedback; properties: monochromatic, coherent, collimated, high intensity; applications (surgery, barcode scanners, fibre optic communication, DVD players)

29

X-Rays

6 subtopics

▼

• Nature of X-rays: transverse EM waves; wavelength λ = 10⁻¹⁰ – 10⁻¹² m (0.001–0.1 nm); frequency 10¹⁷–10²⁰ Hz; travel at speed c; high penetrating power; cause ionisation; affect photographic film; can cause fluorescence
• Production of X-rays: Coolidge tube — electrons accelerated through high voltage V; strike tungsten anode; (1) Bremsstrahlung (braking radiation): continuous spectrum; minimum wavelength λ_min = hc/eV; (2) Characteristic X-rays: discrete wavelengths from electron transitions in inner shells of target atoms
• Crystal structure: regular 3D arrangement of atoms; unit cell (cubic, hexagonal, etc.); lattice parameter (interplanar spacing d)
• Bragg's Law: constructive interference when 2d sinθ = nλ (θ = glancing angle, n = order); used in X-ray crystallography to determine crystal structure (DNA structure, protein folding); Moseley's Law: √f = a(Z – b); linear relationship between √(X-ray frequency) and atomic number Z; used to establish correct ordering of elements in periodic table
• X-ray imaging: radiography (bones, chest); contrast media (barium meal, iodine); computed tomography (CT scan = 3D cross-sections from multiple X-ray images); fluoroscopy (real-time X-ray imaging); radiation dose (mSv); radiation protection (lead aprons, limiting exposure time)
• X-ray and gamma absorption: I = I₀e^(–μx) (μ = linear attenuation coefficient); mass attenuation coefficient μ/ρ; half-value thickness; energy-dependent absorption; photoelectric effect dominates at low energies, Compton scattering at medium energies, pair production at high energies

30

Wave-Particle Duality

6 subtopics

▼

• Electron Diffraction: Davisson-Germer experiment (1927) — electrons diffracted by crystal lattice of nickel; diffraction pattern confirms wave nature of electrons; confirmed de Broglie hypothesis; Thomson's experiment (electron diffraction through thin gold foil)
• de Broglie Hypothesis: matter has wave properties; de Broglie wavelength λ = h/p = h/mv; applicable to all matter but observable only for very small masses; calculation: λ of electron accelerated through voltage V: λ = h/√(2meV)
• Wave-particle duality of matter: large objects (λ too small to observe); electrons, protons, neutrons — observable diffraction; wave function gives probability of finding particle; |ψ|² = probability density
• Compton Effect: X-ray photon (wavelength λ) collides with free electron; scattered photon has longer wavelength λ'; wavelength shift Δλ = λ' – λ = (h/m_ec)(1 – cosθ) = 0.00243(1 – cosθ) nm; recoil electron gains kinetic energy; proof that photons have momentum p = h/λ = E/c
• Heisenberg's Uncertainty Principle: Δx·Δp_x ≥ ℏ/2 (position-momentum); ΔE·Δt ≥ ℏ/2 (energy-time); fundamental limit — not due to experimental imperfection; consequence: electron cannot have precisely defined position and momentum simultaneously; explains why electrons don't spiral into nucleus
• Applications: electron microscope (wavelength of electrons much smaller than light → greater resolving power); quantum tunnelling (scanning tunnelling microscope, nuclear fusion in stars, tunnel diode); natural linewidth of spectral lines (ΔE·Δt ≥ ℏ)

31

Principles of Radioactivity

10 subtopics

▼

• Radioactivity: spontaneous, random emission of radiation by unstable nuclei; discovered by Becquerel (1896); studied by Curie; not affected by temperature, pressure, or chemical state
• Types and properties: α particles (⁴₂He, +2e, stopped by paper, highly ionising, range ~5 cm in air); β⁻ (electron, –e, stopped by 3 mm Al, moderately ionising); β⁺ (positron, +e, annihilation with electron → 2 gamma); γ rays (EM radiation, very penetrating, requires thick lead/concrete, weakly ionising)
• Mass defect and nuclear binding energy: Δm = (Zm_p + Nm_n) – M_nucleus; BE = Δm·c²; BE per nucleon peaks at ⁵⁶Fe → most stable nucleus; fission releases energy for heavy nuclei (splitting); fusion releases energy for light nuclei (combining)
• Nuclear fission: ²³⁵U + n → fission fragments + 2-3 neutrons + energy (≈200 MeV); chain reaction (controlled in reactor, uncontrolled in bomb); critical mass; moderator slows neutrons; control rods absorb neutrons
• Nuclear fusion: ²H + ³H → ⁴He + n + 17.6 MeV; requires extreme temperature and pressure (stellar cores, thermonuclear bombs); promising clean energy source (ITER project)
• Geiger-Müller tube: cylindrical tube with central anode; argon gas + halogen quencher; ionising radiation produces ion pairs → current pulse; connected to counter; dead time (tube insensitive for ~100 μs after each count); plateau region on characteristic curve
• Radioactive decay law: N = N₀e^(–λt); A = λN = A₀e^(–λt) (activity in Becquerels: 1 Bq = 1 decay/s; or Curie: 1 Ci = 3.7×10¹⁰ Bq); λ = decay constant (probability of decay per second)
• Half-life T½: time for activity (or number of undecayed nuclei) to halve; T½ = ln2/λ = 0.693/λ; N = N₀(½)^(t/T½); range: milliseconds (²¹²Po) to billions of years (²³⁸U)
• Nuclear equations — conservation laws: mass number A conserved, atomic number Z conserved, charge conserved, mass-energy conserved; α decay: ᴬ_Z X → ᴬ⁻⁴_{Z-2}Y + ⁴₂He; β⁻ decay: ᴬ_Z X → ᴬ_{Z+1}Y + e⁻ + ν̄_e; γ emission: no change in A or Z, nucleus loses energy
• Einstein's mass-energy equivalence: E = mc²; c = 3×10⁸ m/s; 1 amu = 931.5 MeV/c²; energy released in nuclear reactions; radiocarbon dating (¹⁴C, T½ = 5730 years); medical isotopes (⁹⁹ᵐTc for imaging, ¹³¹I for thyroid treatment); industrial tracers

Half-life calculations and balancing nuclear equations are very commonly examined. Practice both types thoroughly.

32

Introduction to Semiconductors

7 subtopics

▼

• Intrinsic semiconductors: pure Si or Ge; valence 4 — covalent bonds; thermally generated electron-hole pairs; n_i = concentration of electrons = concentration of holes; conductivity increases with temperature (unlike metals); band gap ~1.1 eV (Si), ~0.7 eV (Ge)
• Energy band theory: valence band (filled at 0 K), conduction band (empty at 0 K), band gap E_g; conductors (overlapping bands or partially filled), semiconductors (small E_g), insulators (large E_g ~5 eV); Fermi level position determines type
• Doping: n-type — add pentavalent donor impurity (P, As, Sb) → extra free electron, donor energy level just below conduction band; majority carriers: electrons, minority: holes; p-type — add trivalent acceptor impurity (B, Al, Ga) → extra hole, acceptor level just above valence band; majority: holes, minority: electrons
• p-n junction diode: depletion region at junction (space charge); built-in electric field; potential barrier ~0.6 V (Si), ~0.3 V (Ge); forward bias reduces barrier → current flows exponentially; reverse bias increases barrier → only tiny leakage current; breakdown voltage; I-V characteristics curve
• Half-wave rectification: single diode in series with load; only positive half-cycles passed; output: pulsating DC; efficiency 40.6%; ripple frequency = supply frequency; smoothing: large capacitor in parallel with load reduces ripple
• Full-wave rectification: bridge rectifier (4 diodes) — both half-cycles used; output: pulsating DC with ripple frequency = 2× supply frequency; higher efficiency (~81%); bridge rectifier circuit diagram and operation; smoothing capacitor
• Bipolar Junction Transistor (BJT — NPN or PNP): emitter, base, collector; common emitter configuration; base current I_B controls collector current I_C; current gain hFE = β = I_C/I_B (typically 50–300); transistor as amplifier: small base current → large collector current, voltage gain = –β(R_C/R_E); transistor as switch: cut-off (I_B = 0, transistor OFF), saturation (transistor fully ON, V_CE ≈ 0); logic gates using transistor switches

33

Applied Physics

5 subtopics

▼

• Physics in life sciences: biomechanics — levers in the human body (jaw, forearm, foot), mechanical advantage; fluid mechanics — blood flow in vessels (Poiseuille's equation), blood pressure measurement (sphygmomanometer); surface tension and lung function (surfactant reduces surface tension in alveoli)
• Ultrasound diagnostics: frequency >20 kHz (medical: 1–20 MHz); produced by piezoelectric transducer; pulse-echo technique; acoustic impedance Z = ρv; reflection at boundaries (Z mismatch); A-scan (depth information), B-scan (2D image); Doppler ultrasound — measures blood flow velocity using frequency shift; foetal imaging, abdominal scans; advantages over X-rays: no ionising radiation, real-time, portable
• X-ray medical applications: conventional radiography (contrast from differential absorption); fluoroscopy (real-time imaging with contrast media — barium meal, iodine); CT scan (computed tomography — 3D reconstruction from multiple projections, Hounsfield units); dental X-rays; mammography; radiation dose (effective dose in mSv); ALARA principle; biological effects of radiation
• Nuclear Magnetic Resonance (NMR) & MRI: proton (¹H nucleus) has spin → magnetic moment; in external magnetic field B₀, protons precess at Larmor frequency f = γB₀/2π (γ = gyromagnetic ratio); RF pulse at resonant frequency tips magnetisation; relaxation (T₁ and T₂ times) produces detectable signal; MRI (Magnetic Resonance Imaging): maps proton density and relaxation times; soft tissue contrast superior to X-ray; no ionising radiation; contraindications (metallic implants, pacemakers)
• Radiation therapy and safety: gamma rays and high-energy X-rays used to kill cancer cells; targeted delivery (stereotactic radiosurgery, brachytherapy); radiation protection principles: time (reduce exposure duration), distance (I ∝ 1/r²), shielding (lead, concrete); dose units — gray (Gy): absorbed dose 1 J/kg; sievert (Sv): equivalent dose = absorbed dose × radiation weighting factor; background radiation sources (cosmic, radon, medical, nuclear industry)

Grading System

Marks (%)	Grade	Grade Points	Remark
70 – 100	A	5	Excellent
60 – 69	B	4	Very Good
50 – 59	C	3	Good
45 – 49	D	2	Merit
40 – 44	E	1	Pass
39 and below	F	0	Fail

Point Calculation: A = 5, B = 4, C = 3, D = 2, E = 1, F = 0. A bonus point (+1) is added for candidates with no F grade in their result.
Example: CCC = 3+3+3+1 = 10 points. Maximum AAA = 5+5+5+1 = 16 points.
Note: JUPEB results are released within 60 days of the final examination. Examinations are held annually in June.

Recommended Textbooks

• 01Ike, E.E. (2014). Essential Principles of Physics. Jos: ENIC Publishers.
• 02Ike, E.E. (2014). Numerical Problems and Solutions in Physics. Jos: ENIC Publishers.
• 03Nelson, M. (1977). Fundamentals of Physics. Great Britain: Hart Davis Education.
• 04Nelson, M. & Parker, S. (1989). Advanced Level Physics (6th ed.). Heinemann.
• 05Okeke, P.N. & Anyakoha, M.W. (2000). Senior Secondary School Physics. Lagos: Pacific Printers.
• 06Olumuyiwa, A. & Ogunkoya, O.O. (1992). Comprehensive Certificate Physics. Ibadan: University Press Plc.

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