1. Electrostatics: Coulomb's Law, Electric Field & Potential

Coulomb's Law in vacuum: F = [1 / (4πε0)] · (|q1 q2| / r^2), where 1/(4πε0) ≈ 8.99 × 10^9 N·m^2/C^2. In dielectric medium of relative permittivity K (dielectric constant): F_med = F_vac / K. Electric Field due to point charge: E = F/q0 = [1 / (4πε0)] · (q / r^2). Electrostatic Potential: V = W/q0 = [1 / (4πε0)] · (q / r). Relation between Field and Potential: E = -dV/dr (field points along maximum potential decrease). Electrostatic Potential Energy of two charges: U = [1 / (4πε0)] · (q1 q2 / r). Gauss's Law: Electric flux through closed surface Φ = ∮ E · dA = q_enclosed / ε0.

2. Capacitance & Energy Stored in Capacitors

Definition of capacitance: C = Q / V (SI unit: Farad, F). Parallel plate capacitor with plate area A and separation d: In vacuum: C0 = ε0 A / d. With dielectric slab of constant K completely filling space: C = K C0 = (K ε0 A) / d. Energy stored in charged capacitor: U = (1/2) C V^2 = (1/2) Q V = Q^2 / (2C). Energy density in electric field: u = (1/2) ε0 E^2. Grouping of capacitors: (1) In Series: 1/C_eq = 1/C1 + 1/C2 + ... (charge Q is identical on all capacitors); (2) In Parallel: C_eq = C1 + C2 + ... (voltage V is identical across all capacitors).

3. Current Electricity & Kirchhoff's Circuit Laws

Current: I = dq/dt = n·e·A·vd (where n is electron density, vd is drift velocity). Drift velocity: vd = (e E τ) / m. Ohm's Law: V = I R, where resistance R = ρ(l / A) = (m / n e^2 τ) · (l / A). Resistivity ρ depends on material and temperature (ρ_T = ρ0[1 + α(T - T0)]). Electrical Power: P = V I = I^2 R = V^2 / R. Kirchhoff's First Law (Junction Rule / KCL): Σ I = 0 at any node (conservation of electric charge). Kirchhoff's Second Law (Loop Rule / KVL): Σ ΔV = 0 around any closed mesh (conservation of energy). Wheatstone Bridge balance condition: P/Q = R/S (no current flows through galvanometer).

4. Magnetism, Lorentz Force & Electromagnetic Induction (EMI)

Magnetic force on moving charge (Lorentz Force): F = q(v × B), magnitude F = q v B sin θ. Force on current-carrying conductor: F = I(L × B). Biot-Savart Law: dB = [μ0 / (4π)] · (I dl sin θ / r^2), where μ0 / (4π) = 10^-7 T·m/A. Magnetic field at center of circular coil of N turns: B = (μ0 N I) / (2R); along axis of circular coil: B = (μ0 N I R^2) / [2(R^2 + x^2)^(3/2)]; inside long ideal solenoid: B = μ0 n I (where n = N/l turns per meter). Faraday's Law of Induction: induced EMF e = -dΦ/dt = -d(B·A cos θ)/dt. Lenz's Law: the induced current opposes the change in flux causing it (justifying the negative sign, conservation of energy). Motional EMF: e = B l v for a rod sliding perpendicular to B.

5. Modern Physics: Photoelectric Effect & Matter Waves

Planck's quantum hypothesis: Energy of photon E = hν = hc/λ (hc ≈ 1240 eV·nm). Einstein's Photoelectric Equation: K_max = hν - Φ0 = hν - hν0 = e V_s, where Φ0 = hν0 is the work function of the metal and V_s is the stopping potential. Maximum kinetic energy depends purely on frequency ν of incident radiation, independent of intensity; photoelectric current is directly proportional to intensity. de Broglie wavelength for matter waves: λ = h / p = h / (m v) = h / √(2 m K). For an electron accelerated through potential difference V volts: λ = 12.27 / √V Ångströms (Å) = 1.227 / √V nm.

6. Bohr's Atomic Model & Nuclear Decay Formulas

Bohr's postulates for hydrogen-like atoms (atomic number Z): (1) Angular momentum quantization: L = m v r = n h / (2π); (2) Radius of nth orbit: r_n = (0.529 Å) · (n^2 / Z); (3) Velocity in nth orbit: v_n = (2.18 × 10^6 m/s) · (Z / n); (4) Total Energy in nth orbit: E_n = -13.6 eV · (Z^2 / n^2). Rydberg formula for spectral line emission: 1/λ = R_H · Z^2 [1/n1^2 - 1/n2^2], where R_H ≈ 1.097 × 10^7 m^-1. Radioactive decay law: N(t) = N0 e^(-λt). Half-life: T_1/2 = ln(2) / λ ≈ 0.693 / λ. Mean life: τ = 1/λ = T_1/2 / 0.693 ≈ 1.44 T_1/2.