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EEE241: Fundamentals of Electromagnetics. Introductory Concepts, Vector Fields and Coordinate Systems Instructor: Dragica Vasileska. Outline. Class Description Introductory Concepts Vector Fields Coordinate Systems. Class Description. Prerequisites by Topic: University physics
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EEE241: Fundamentals of Electromagnetics Introductory Concepts, Vector Fields and Coordinate Systems Instructor: Dragica Vasileska
Outline • Class Description • Introductory Concepts • Vector Fields • Coordinate Systems
Class Description Prerequisites by Topic: • University physics • Complex numbers • Partial differentiation • Multiple Integrals • Vector Analysis • Fourier Series
Class Description • Prerequisites: EEE 202; MAT 267, 274 (or 275), MAT 272; PHY 131, 132 • Computer Usage: Students are assumed to be versed in the use MathCAD or MATLAB to perform scientific computing such as numerical calculations, plotting of functions and performing integrations. Students will develop and visualize solutions to moderately complicated field problems using these tools. • Textbook: Cheng, Field and Wave Electromagnetics.
Class Description • Grading: Midterm #1 25% Midterm #2 25% Final 25% Homework 25%
Research Areas of Electromagnetics • Antenas • Microwaves • Computational Electromagnetics • Electromagnetic Scattering • Electromagnetic Propagation • Radars • Optics • etc …
Scalar and Vector Fields • A scalar field is a function that gives us a single value of some variable for every point in space. • Examples: voltage, current, energy, temperature • A vector is a quantity which has both a magnitude and a direction in space. • Examples: velocity, momentum, acceleration and force
Scalar Fields e.g. Temperature: Every location has associated value (number with units) 26
Scalar Fields - Contours • Colors represent surface temperature • Contour lines show constant temperatures 27
Fields are 3D • T = T(x,y,z) • Hard to visualize Work in 2D 28
Vector Fields Vector (magnitude, direction) at every point in space Example: Velocity vector field - jet stream 29
Choice is based on symmetry of problem VECTOR REPRESENTATION 3 PRIMARY COORDINATE SYSTEMS: • RECTANGULAR • CYLINDRICAL • SPHERICAL Examples: Sheets - RECTANGULAR Wires/Cables - CYLINDRICAL Spheres - SPHERICAL
Orthogonal Coordinate Systems: (coordinates mutually perpendicular) Cartesian Coordinates z P(x,y,z) y Rectangular Coordinates x P (x,y,z) z z P(r, θ, z) Cylindrical Coordinates P (r, Θ, z) y r x θ z Spherical Coordinates P(r, θ, Φ) θ r P (r, Θ, Φ) y x Φ Page 108
Parabolic Cylindrical Coordinates (u,v,z) • Paraboloidal Coordinates (u, v, Φ) • Elliptic Cylindrical Coordinates (u, v, z) • Prolate Spheroidal Coordinates (ξ, η, φ) • Oblate Spheroidal Coordinates (ξ, η, φ) • Bipolar Coordinates (u,v,z) • Toroidal Coordinates (u, v, Φ) • Conical Coordinates (λ, μ, ν) • Confocal Ellipsoidal Coordinate (λ, μ, ν) • Confocal Paraboloidal Coordinate (λ, μ, ν)
z z Cartesian Coordinates P(x,y,z) P(x,y,z) P(r, θ, Φ) θ r y x y x Φ Cylindrical Coordinates P(r, θ, z) Spherical Coordinates P(r, θ, Φ) z z P(r, θ, z) y r x θ
Coordinate Transformation • Cartesian to Cylindrical (x, y, z) to (r,θ,Φ) (r,θ,Φ)to (x, y, z)
Coordinate Transformation • Cartesian to Cylindrical Vectoral Transformation
Coordinate Transformation • Cartesian to Spherical (x, y, z) to (r,θ,Φ) (r,θ,Φ)to (x, y, z)