Lecture Engineering electromagnetics: Vector analysis - Nguyễn Công Phương

Lecture Engineering electromagnetics - Vector analysis presents the following content: Scalars and vectors, the rectangular coordinate system, the Dot product and the cross product, the circular cylindrical coordinate system, the spherical coordinate system.

Nguyễn Công Phương Engineering Electromagnetics Contents I Introduction II Vector Analysis III Coulomb’s Law & Electric Field Intensity IV Electric Flux Density, Gauss’ Law & Divergence V Energy & Potential VI Current & Conductors VII Dielectrics & Capacitance VIII.Poisson’s & Laplace’s Equations IX The Steady Magnetic Field X Magnetic Forces & Inductance XI Time – Varying Fields & Maxwell’s Equations XII The Uniform Plane Wave XIII.Plane Wave Reflection & Dispersion XIV.Guided Waves & Radiation Engineering Electromagnetics - sites.google.com/site/ncpdhbkhn Introduction (1) • The study of charges (at rest or in motion) • Fundamental to electrical engineering • Why study? – – – – Electromagnetic Compatibilty High Frequency Circuits Communications etc • Applications: communication technology, computer technology, antenna technology, biomedical applications, military defense, etc • Ampere, Faraday, Gauss, Lenz, Coulomb, Maxwell, … Engineering Electromagnetics - sites.google.com/site/ncpdhbkhn Introduction (2) Electromagnetics Electrostatics ∂q =0 ∂t Magnetostatics Electromagnetic Waves ∂I =0 ∂t ∂I ≠0 ∂t Engineering Electromagnetics - sites.google.com/site/ncpdhbkhn Introduction (3) • W H Hayt, J A Buck Engineering Electromagnetics McGraw-Hill, 2007 • E J Rothwell, M J Cloud Electromagnetics CRC Press, 2001 • N B Thành, N T Quân, L V Bảng Cơ sở lý thuyết trường điện từ NXB Đại học & trung học chuyên nghiệp, 1970 • https://sites.google.com/site/ncpdhbkhn/ Engineering Electromagnetics - sites.google.com/site/ncpdhbkhn Contents I Introduction II Vector Analysis III Coulomb’s Law & Electric Field Intensity IV Electric Flux Density, Gauss’ Law & Divergence V Energy & Potential VI Current & Conductors VII Dielectrics & Capacitance VIII.Poisson’s & Laplace’s Equations IX The Steady Magnetic Field X Magnetic Forces & Inductance XI Time – Varying Fields & Maxwell’s Equations XII The Uniform Plane Wave XIII.Plane Wave Reflection & Dispersion XIV.Guided Waves & Radiation Engineering Electromagnetics - sites.google.com/site/ncpdhbkhn Vector Analysis Scalars & Vectors The Rectangular Coordinate System The Dot Product & The Cross Product The Circular Cylindrical Coordinate System The Spherical Coordinate System Engineering Electromagnetics - sites.google.com/site/ncpdhbkhn Scalars & Vectors • Scalar: refers to a quantity whose value may be represented by a single (positive/negative) real number • Ex.: distance, time, temperature, mass, … • Scalars are in italic type, e.g t, m, E,… • Vector: refers to a quantity whose value may be represented by a magnitude and a direction in space (2D, 3D, nD) • Ex.: force, velocity, acceleration, … • Vectors are in bold type, e.g A • A may be written as A Engineering Electromagnetics - sites.google.com/site/ncpdhbkhn Vector Analysis Scalars & Vectors The Rectangular Coordinate System The Dot Product & The Cross Product The Circular Cylindrical Coordinate System The Spherical Coordinate System Engineering Electromagnetics - sites.google.com/site/ncpdhbkhn The Rectangular Coordinate System (1) z y x Engineering Electromagnetics - sites.google.com/site/ncpdhbkhn 10 The Cross Product (4) Ex Given A = ax – 2ay + 3az and B = –4ax + 5ay – 6az Find the angle between A & B? Method 2: A • B = A B cos θ → cos θ = A•B A B A • B = 1( −4) − 2(5) + 3( −6) = −32 A = 12 + 22 + 32 = 3.74 B = + 52 + 62 = 8.75 −32 → cos θ = = −0.97 → θ = a cos( −0.97) = 12.9o 3.74 × 8.75 Engineering Electromagnetics - sites.google.com/site/ncpdhbkhn 24 Ex The Cross Product (5) Given A = ax – 2ay + 3az, B = –4ax + 5ay – 6az, and C = ax – ay + az Find: a) A ± B, B ± C, C ± A b) A.B, B.C, C.A c) A B, B C, C A d) (A B).C, A.(B C) e) What is the angle between B and C A? Engineering Electromagnetics - sites.google.com/site/ncpdhbkhn 25 The Rectangular Coordinate System (6) z ax.ay = ax.ax = az x ax ax ax = ay ax ay = az Engineering Electromagnetics - sites.google.com/site/ncpdhbkhn 26 Vector Analysis Scalars & Vectors The Rectangular Coordinate System The Dot Product & The Cross Product The Circular Cylindrical Coordinate System The Spherical Coordinate System Engineering Electromagnetics - sites.google.com/site/ncpdhbkhn 27 The Circular Cylindrical Coordinate System (1) z y ρ x z φ ρ, φ, z Engineering Electromagnetics - sites.google.com/site/ncpdhbkhn 28 The Circular Cylindrical Coordinate System (2) dS = ρdρdφaz z dρ dz z+dz z dS= dρdzaφ x φ φ+dφ ρ ρ+dρ dS = ρdφdzaρ y ρdφ dV = ρdρdφdz Engineering Electromagnetics - sites.google.com/site/ncpdhbkhn 29 The Circular Cylindrical Coordinate System (3) az z aφ y aρ ρ x z φ aρ.aφ = aρ.aρ = aρ aρ = aρ aφ = az Engineering Electromagnetics - sites.google.com/site/ncpdhbkhn 30 Vector Analysis Scalars & Vectors The Rectangular Coordinate System The Dot Product & The Cross Product The Circular Cylindrical Coordinate System The Spherical Coordinate System Engineering Electromagnetics - sites.google.com/site/ncpdhbkhn 31 The Spherical Coordinate System (1) z r y x r, θ, φ Engineering Electromagnetics - sites.google.com/site/ncpdhbkhn 32 The Spherical Coordinate System (1) z θ y x r, θ, φ Engineering Electromagnetics - sites.google.com/site/ncpdhbkhn 33 The Spherical Coordinate System (1) z y φ x r, θ, φ Engineering Electromagnetics - sites.google.com/site/ncpdhbkhn 34 The Spherical Coordinate System (2) z θ r y φ x r, θ, φ Engineering Electromagnetics - sites.google.com/site/ncpdhbkhn 35 The Spherical Coordinate System (3) z dS = rsinθdrdφaθ dS = r2sinθdθdφar dr dS = rdrdθaφ y rdθ rsinθdφ x dV = r2sinθdrdθdφ Engineering Electromagnetics - sites.google.com/site/ncpdhbkhn 36 The Spherical Coordinate System (4) z ar.aθ = aφ θ φ y r ar aθ x ar.ar = ar ar = ar aθ = aφ r, θ, φ Engineering Electromagnetics - sites.google.com/site/ncpdhbkhn 37 RECTANGULAR CYLINDRICAL SPHERICAL x ρ cos ϕ r sin θ cos ϕ y ρ sin ϕ r sin θ sin ϕ z z r cos θ CYLINDRICAL RECTANGULAR SPHERICAL ρ r sin θ ϕ x2 + y atan( y / x) z z r cos θ SPHERICAL RECTANGULAR SPHERICAL x2 + y + z2 ρ + z2 r θ ϕ ϕ acos( z / x + y + z ) acos( z / ρ + z ) acot( x / y ) ϕ Engineering Electromagnetics - sites.google.com/site/ncpdhbkhn 38 ... Its components? b) Its magnitude? c) Its unit vector ? Engineering Electromagnetics - sites.google.com/site/ncpdhbkhn 14 Vector Analysis Scalars & Vectors The Rectangular Coordinate System The... Vectors are in bold type, e.g A • A may be written as A Engineering Electromagnetics - sites.google.com/site/ncpdhbkhn Vector Analysis Scalars & Vectors The Rectangular Coordinate System The Dot Product... Reflection & Dispersion XIV.Guided Waves & Radiation Engineering Electromagnetics - sites.google.com/site/ncpdhbkhn Vector Analysis Scalars & Vectors The Rectangular Coordinate System The Dot Product