Introduction 2018 mk

Nguyễn Công Phương Engineering Electromagnetics Contents I II III IV V VI VII VIII IX X XI XII XIII XIV XV Introduction Vector Analysis Coulomb’s Law & Electric Field Intensity Electric Flux Density, Gauss’ Law & Divergence Energy & Potential Current & Conductors Dielectrics & Capacitance Poisson’s & Laplace’s Equations The Steady Magnetic Field Magnetic Forces & Inductance Time – Varying Fields & Maxwell’s Equations Transmission Lines The Uniform Plane Wave Plane Wave Reflection & Dispersion Guided Waves & Radiation Engineering Electromagnetics - sites.google.com/site/ncpdhbkhn Introduction (1) https://kimrendfeld.wordpress.com/2012/11/ 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) Electromagnetic compatibility Antenna Biomedical engineering ELECTROMAGNETICS Wireless communication Remote sensing Laser engineering Electric machines Military defense Engineering Electromagnetics - sites.google.com/site/ncpdhbkhn Introduction (4) Electromagnetic compatibility http://w ww.aysamakses.com/en/bilgi-bankasi/elektromanyetik-uyumluluk-emc/ Engineering Electromagnetics - sites.google.com/site/ncpdhbkhn Introduction (5) Biomedical engineering https://biomedical.njit.edu/mri/ Engineering Electromagnetics - sites.google.com/site/ncpdhbkhn Introduction (6) Laser engineering https://w ww.shutterstock.com/video/clip-3748037-stock-footage-masked-ninjas-strike-variousdramatic-poses-at-the-bottom-of-the-screen-plenty-of-space-for.html Engineering Electromagnetics - sites.google.com/site/ncpdhbkhn Introduction (7) Antenna http://www.intertronicsolutions.com/my-product/12m-antenna/ Engineering Electromagnetics - sites.google.com/site/ncpdhbkhn Introduction (8) Electric machines http://gibbonsgroup.blogspot.com/2014/05/3-problems-youll-face-if-your-electric.html 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 = A B cosθ → cos θ = A B A • B = 1( −4) − 2(5) + 3( −6) = −32 A = 12 + 22 + 32 = 3.74 B = 42 + 52 + = 8.75 −32 → cos θ = = −0.97 → θ = a cos(− 0.97) = 12.9 o 3.74 × 8.75 Engineering Electromagnetics - sites.google.com/site/ncpdhbkhn 37 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 38 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 39 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 40 The Circular Cylindrical Coordinate System (1) z y ρ x z φ ρ, φ, z Engineering Electromagnetics - sites.google.com/site/ncpdhbkhn 41 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 42 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 43 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 44 The Spherical Coordinate System (1) z r y x r, θ, φ Engineering Electromagnetics - sites.google.com/site/ncpdhbkhn 45 The Spherical Coordinate System (1) z θ y x r, θ, φ Engineering Electromagnetics - sites.google.com/site/ncpdhbkhn 46 The Spherical Coordinate System (1) z y φ x r, θ, φ Engineering Electromagnetics - sites.google.com/site/ncpdhbkhn 47 The Spherical Coordinate System (2) z θ r y φ x r, θ, φ Engineering Electromagnetics - sites.google.com/site/ncpdhbkhn 48 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 49 The Spherical Coordinate System (4) z ar.aθ = aφ θ φ y ar ar = r ar aθ x ar.ar = ar aθ = aφ r, θ, φ Engineering Electromagnetics - sites.google.com/site/ncpdhbkhn 50 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 x2 + y r sin θ ϕ atan( y / x ) ϕ z z r cos θ SPHERICAL RECTANGULAR CYLINDRICAL x2 + y + z ρ + z2 r θ ϕ acos( z / x + y + z ) acos( z / ρ + z ) acot( x / y ) ϕ Engineering Electromagnetics - sites.google.com/site/ncpdhbkhn 51 ... - sites.google.com/site/ncpdhbkhn Introduction (1) https://kimrendfeld.wordpress.com/2012/11/ Engineering Electromagnetics - sites.google.com/site/ncpdhbkhn Introduction (2) Electromagnetics... sites.google.com/site/ncpdhbkhn Introduction (4) Electromagnetic compatibility http://w ww.aysamakses.com/en/bilgi-bankasi/elektromanyetik-uyumluluk-emc/ Engineering Electromagnetics - sites.google.com/site/ncpdhbkhn Introduction. .. sites.google.com/site/ncpdhbkhn Introduction (7) Antenna http://www.intertronicsolutions.com/my-product/12m-antenna/ Engineering Electromagnetics - sites.google.com/site/ncpdhbkhn Introduction (8) Electric