*title: “00 Master Glossary & Formula Sheet for ECE 2105” aliases:
- ECE 2105 Master Glossary
- ECE 2105 Formula Sheet
- Electromagnetic Fields Reference Sheet tags:
- ece2105
- electromagnetics
- cheatsheet
- master-reference type: uni-note course: “ECE 2105 - Electromagnetic Fields and Waves” chapter: 1-5 term: 2-1 teacher: Mashuk Sir / Sanglap Sir status: enhanced*
00 Master Glossary & Formula Sheet for ECE 2105 (Electromagnetic Fields & Waves)
Overview: Complete exam-ready master reference sheet containing all core definitions (with PYQ appearance years) and mathematical formulas for ECE 2105: Electromagnetic Fields and Waves covering Vector Calculus, Electrostatics, Dielectrics, Magnetostatics, Time-Varying Fields, Maxwell’s Equations, Wave Propagation, and Radio Propagation*.*
1. Master Formula & Coordinate Transformation Sheet
1.1 Vector Differential Operators in 3D Coordinates
| Operator | Cartesian (x, y, z) | Cylindrical (r, φ, z) | Spherical (R, θ, φ) |
|---|---|---|---|
| Gradient (∇V) | â_x ∂V/∂x + â_y ∂V/∂y + â_z ∂V/∂z | â_r ∂V/∂r + â_φ (1/r)∂V/∂φ + â_z ∂V/∂z | â_R ∂V/∂R + â_θ (1/R)∂V/∂θ + â_φ (1/(R sinθ))∂V/∂φ |
| Divergence (∇ · A) | ∂A_x/∂x + ∂A_y/∂y + ∂A_z/∂z | (1/r)∂/∂r(r A_r) + (1/r)∂A_φ/∂φ + ∂A_z/∂z | (1/R²)∂/∂R(R² A_R) + (1/(R sinθ))∂/∂θ(A_θ sinθ) + (1/(R sinθ))∂A_φ/∂φ |
| Laplacian (∇²V) | ∂²V/∂x² + ∂²V/∂y² + ∂²V/∂z² | (1/r)∂/∂r(r ∂V/∂r) + (1/r²)∂²V/∂φ² + ∂²V/∂z² | (1/R²)∂/∂R(R² ∂V/∂R) + (1/(R² sinθ))∂/∂θ(sinθ ∂V/∂θ) + (1/(R² sin²θ))∂²V/∂φ² |
1.2 Electrostatic & Dielectric Formulas
- Coulomb’s Force: F₁₂ = â_R (q₁ q₂)/(4πε₀ R²)
- Gauss’s Law: ∮_S D · dŝ = Q_enclosed
- Electric Potential: V = -∫ E · dl ⇒ E = -∇V
- Dipole Potential & Field: V = (p cosθ)/(4πε₀ r²), E = p/(4πε₀ r³)(2cosθ â_r + sinθ â_θ)
- Polarization Bound Charges: ρ_ps = P · â_n, ρ_p = -∇ · P
- Flux Density in Dielectric: D = ε₀ E + P = ε E
- Dielectric Boundary Conditions: E₁t = E₂t, D₁n - D₂n = ρ_s, tanα₁/tanα₂ = ε₁/ε₂
- Poisson & Laplace Equations: ∇²V = -ρ_v/ε (ρ_v ≠ 0), ∇²V = 0 (ρ_v = 0)
1.3 Magnetostatic & Magnetic Material Formulas
- Lorentz Force: F = q(E + u x B)
- Biot-Savart Law: B = (μ₀ I)/(4π) ∮ (dl’ x â_R)/R²
- Finite Straight Wire Field (2L): B = â_φ (μ₀ I L)/(2π r √(r² + L²))
- Circular Loop Axis Field: B_z = (μ₀ I b²)/(2(b² + z²)^(3/2))
- Vector Magnetic Potential: B = ∇ x A, ∇²A = -μ₀ J
- Bound Current Densities: J_ms = M x â_n, J_m = ∇ x M
- Magnetic Boundary Conditions: B₁n = B₂n, H₁t - H₂t = J_s, tanθ₁/tanθ₂ = μ₁/μ₂
- Hall Voltage: V_H = (B I)/(n q w)
1.4 Maxwell’s Equations & Wave Propagation Formulas
- Continuity Equation: ∇ · J = -∂ρ_v/∂t
- Displacement Current Density: J_d = ∂D/∂t = ε ∂E/∂t
- Poynting Vector & Power Flow: S = E x H [W/m²]
- Complex Propagation Constant: γ = α + jβ = √(jωμ(σ + jωε))
- Good Conductor Approximations (σ/ωε >> 1): α = β = √(π f μ σ), δ = 1/α = 1/√(π f μ σ)
- Normal Incidence Reflection & Transmission: Γ = (η₂ - η₁)/(η₂ + η₁), τ = 2η₂/(η₂ + η₁), 1 + Γ = τ, SWR = (1+|Γ|)/(1-|Γ|)
- Ionospheric Sky-Wave: n = √(1 - 81N/f²), f_c ≈ 9√N_max, MUF = f_c secθ_i