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Physics78

Work, Energy & Power5

The Work–Energy Theorem — Wₙₑₜ = ΔK → Positive, Negative and Zero Work — the Sign of W = F·d·cos θ → Work Done by a Constant Force — W = F·d·cos θ → Kinetic Energy — K = ½mv² → Conservative vs Non-Conservative Forces — the Round-Trip Test →

Laws of Motion10

Free Body Diagram — Isolate One Body, Draw Every Force → Newton's First Law (Law of Inertia) → Connected Bodies — One Rope, One Tension, One Shared Acceleration → Normal Force — N Is Not Always mg → Block on an Incline — Static Friction Adjusts Until Grip Fails at tan θ = μₛ → Newton's Second Law (F = ma) → Tension Force — Set by the Motion, Not the Same in Every String → Newton's Third Law (Action-Reaction) → Friction Force — Static Friction Matches the Push, Up to a Maximum → Rolling Friction — Rolling Resists Motion Far Less Than Sliding →

Chapter 1 — Electric Charges & Fields11

Coulomb's Law — Force Between Two Point Charges → Electric Field due to a Point Charge (and its Field Lines) → Force on a Charge in an Electric Field (F = qE) → Electric Field due to an Electric Dipole → Charge Densities (λ, σ, ρ) and the dq-Superposition Idea → Field of a Charged Spherical Shell: E=0 inside, kq/r² outside → Field of a Uniformly Charged Solid Sphere: E ∝ r inside, kq/r² outside → Field of an Infinite Charged Sheet: E = σ/(2ε₀), a CONSTANT field → Field of an Infinite Line Charge: E = λ/(2πε₀r), a 1/r falloff → Electric Flux Φ = E·A and Net Flux Through a Closed Surface → Gauss's Law: Φ = q_enc/ε₀ →

Chapter 2 — Electrostatic Potential & Capacitance9

Electric Potential — Work Done per Unit Charge (V = W/q) → Potential of a Point Charge — V = kQ/r (falls off as 1/r) → Potential of a Dipole — V = kp cosθ/r² (zero on the equator, falls as 1/r²) → Potential of a System of Charges — V = Σ k qᵢ/rᵢ (a scalar sum of signed numbers) → Equipotential Surfaces — Same-V Shells, ⟂ to the Field, No Work Along Them → Potential Energy in an External Field — U = qV (a charge), U = q₁V₁+q₂V₂ (a system), U = −p·E (a dipole) → Potential Energy of a System of Charges — U = Σ k qᵢqⱼ/rᵢⱼ (the work to assemble them) → Capacitance — C = Q/V = ε₀A/d, the Fixed Ratio of a Capacitor → Parallel-Plate Capacitor Field — Uniform E = V/d Between the Plates, ≈0 Outside →

Chapter 3 — Current Electricity13

Ohm's Law — the Straight Line That Is V = IR → Drift Velocity — the Tiny Collective Crawl Behind Every Current (v_d = eEτ/m, i = neAv_d) → Resistivity — Shape Times Material (R = ρL/A, ρ = m/ne²τ, ρ_T = ρ₀(1+αΔT)) → Electrical Power in a Resistor — P = VI = I²R = V²/R → Combination of Resistors — Series Adds Resistance, Parallel Opens New Paths → EMF — the Energy a Cell Gives Each Charge → Internal Resistance — the Hidden r Inside Every Real Cell → Combination of Cells — Series Adds, Parallel Shares → Kirchhoff's Junction Rule (KCL) — Σi_in = Σi_out → Kirchhoff's Loop Rule (KVL) — ΣV = 0 → Wheatstone Bridge — Balance Condition P/Q = R/S → Potentiometer — Measuring True EMF by Nulling (E = k·l) → Meter Bridge — Finding an Unknown Resistance by Nulling on a Slide Wire (X = R·(100 − l₁)/l₁) →

Chapter 4 — Moving Charges & Magnetism9

How Big Is the Circle? — r = mv/qB for a Charge in a Uniform Field → Lorentz Force on a Moving Charged Particle (F = q v × B) → Same Lap Every Time — T = 2πm/qB Is Independent of Speed → Which Way Does the Force Point? — the Right-Hand Rule for F = q v × B → Why a Magnetic Force Can't Speed You Up — F ⊥ v Means No Work → Magnetic Force on a Current-Carrying Wire (F = I L × B) → What Is a Magnetic Field? — B as a Vector Field Sourced by Moving Charge → The Helix — a Charge Entering a Uniform Field at an Angle → Force Between Two Parallel Currents →

Chapter 5 — Magnetism & Matter5

A Bar Magnet in a Uniform Field (τ = m × B, U = −m·B, T = 2π√(I/mB)) → The Bar Magnet as a Magnetic Dipole — closed-loop field, no monopole, m, 1/r³ → Gauss's Law for Magnetism: ∮B·dA = 0 → The Earth's Magnetism: declination D, dip I, B = √(H²+V²) → Magnetisation & Magnetic Intensity — B = μ₀(H + M) →

Chapter 6 — Electromagnetic Induction6

Magnetic Flux — Φ = B·A·cosθ → Faraday's Law of Induction — ε = −N dΦ/dt → Motional EMF — ε = Bvl → Eddy Currents → Inductance — Self & Mutual → AC Generator →

Chapter 7 — Alternating Current8

AC Voltage Applied to a Resistor → AC Voltage Applied to an Inductor → AC Voltage Applied to a Capacitor → Phasors — Rotating Vectors for AC → Series LCR Circuit — Impedance and Resonance → Power in AC Circuits — The Power Factor → LC Oscillations — The Circuit's Own Rhythm → Transformer — Trading Voltage for Current →

Chapter 8 — Electromagnetic Waves2

Displacement Current — I_d = ε₀ dΦ_E/dt, the Ampère–Maxwell Correction → Electromagnetic Wave Propagation — Self-Regenerating E and B at c = 1/√(μ₀ε₀) →

Chemistry12

Some Basic Concepts of Chemistry1

Law of Conservation of Mass — Atoms Rearranged, Never Destroyed →

Structure of Atom2

Bohr Model — Discrete Energy Levels and the Line Spectrum → Atomic Orbitals: s, p and d Shapes Are Regions of Probability, Not Paths →

Chemical Bonding & Molecular Structure5

Bond Polarity and Dipole Moment — Shape Determines Molecular Polarity → Hybridisation: One Dial — s-Character — Sets Both the Orbital's Shape and Its Angle → VSEPR — Electron Domains Repel, and That Is the Molecule's Shape → σ and π Bonds: One Overlap Survives a Twist, the Other Doesn't → Hydrogen Bonding — Why Water Boils Far Higher Than Expected →

States of Matter1

Kinetic particle theory of gases →

Equilibrium2

Dynamic equilibrium → Le Chatelier's principle →

Chemical Kinetics1

Collision theory and activation energy →

Mathematics6

Relations and Functions1

Graph Transformations — a·f(b(x−h))+k →

Trigonometric Functions1

The Unit Circle Unrolled into Sine and Cosine →

Limits and Derivatives1

The Derivative as the Limit of a Secant Slope →

Integrals1

The Definite Integral as Accumulated Area →

Application of Integrals1

Solids of Revolution: Spinning a Flat Region and Finding Its Volume →

Three Dimensional Geometry1

Lines and Planes in Space: Equations and the Shortest Distance →