# Electromagnetics I

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Vector Analysis - Part I

Topics include: Cartesian Coordinate System, Circular Cylindrical Coordinate System, Spherical Coordinate System, Circular Cylindrical to Cartesian Coordinate System Conversions, Examples of Circular Cylindrical to Cartesian Coordinate System Conversions, Distance Formula for Two Points in Cylindrical Coordinates, Exploiting Cylindrical Symmetry to Calculate Distance, Surface Area, and Volume, Spherical to Cartesian Coordinate System Conversions, Examples of Spherical to Cartesian Coordinate System Conversions, Distance Formula for Two Points in Spherical Coordinates, Scalar or Dot Product of Vectors, Vector or Cross Product of Vectors, Scalar Triple Product, Vector Triple Product, Scalar and Vector Components, Examples of Scalar and Vector Components.

01-Vector Analysis - Part I: Lecture Notes

01-Vector Analysis - Part I: Solutions Homework

Vector Analysis - Part II

Topics include: Line Integral of Vector Field Along Contour or Curve, Circulation of Vector Field Along Closed Contour, Surface Integral of Vector Field Over Surface, Flux of Vector Field from Closed Surface, Volume Integral of Scalar Volume Density, Volume Integral of Vector Volume Density, Examples of Line, Surface and Volume Integrals in Cartesian, Cylindrical, and Spherical Coordinate Systems, The Gradient of a Scalar Field, Geometric Interpretation of the Gradient of a Scalar Field, Gradient Formulas in Cartesian, Cylindrical, and Spherical Coordinate Systems, Examples of Gradient Applications.

02-Vector Analysis - Part II: Lecture Notes

02-Vector Analysis - Part II: Solutions Homework

Vector Analysis - Part III

Topics include: Divergence of a Vector Field, Divergence of a Vector Field in Cartesian, Circular Cylindrical and Spherical Coordinate Systems, Curl of a Vector Field, Curl of a Vector Field in Cartesian, Circular Cylindrical and Spherical Coordinate Systems, The Divergence Theorem, Stokes' Theorem, Classifications of Vector Fields, Conservative Vector Field, Curl-free or Irrotational Vector Field, Divergence-free or Solenoidal Vector Field, The Helmholtz Theorem, Laplacian of a Scalar Field, Laplacian of a Scalar Field in Cartesian, Circular Cylindrical and Spherical Coordinate Systems, Laplacian of a Vector Field, Laplacian of a Vector Field in Cartesian Coordinate System, Laplacian of a Vector Field in Circular Cylindrical and Spherical Coordinate Systems (in Solutions Homework).

03-Vector Analysis - Part III: Lecture Notes

03-Vector Analysis - Part III: Solutions Homework

Electrostatic Fields - Part I

Topics include: Coulomb's Law, Coulomb's Law Applied to Thin Wire (Line) of Charge of Finite Length with Uniform Line Charge Density, Coulomb's Law Applied to Thin Infinitely-long Wire with Uniform Line Charge Density, Coulomb's Law Applied to Thin Circular Disk with Uniform Surface Charge Density, Coulomb's Law Applied to Thin Infinitely-wide Plane with Uniform Surface Charge Density, Coulomb's Law Applied to Non-conducting Sphere with Uniform Volume Charge Density, Definition of Electric Field Intensity Vector, Derivation of Electric Field Intensity Vector for Thin Wire (Line) of Charge of Finite Length with Uniform Line Charge Density, Derivation of Electric Field Intensity Vector for Thin Infinitely-long Wire with Uniform Line Charge Density, Derivation of Electric Field Intensity Vector for Thin Circular Wire with Uniform Line Charge Density (in Solutions Homework), Derivation of Electric Field Intensity Vector for Thin Circular Disk with Uniform Surface Charge Density, Derivation of Electric Field Intensity Vector for Thin Infinitely-wide Plane with Uniform Surface Charge Density, Derivation of Electric Field Intensity Vector for Thin Square Plate with Uniform Surface Charge Density (in Solutions Homework), Derivation of Electric Field Intensity Vector for Non-conducting Sphere with Uniform Volume Charge Density, Electrostatic Field Postulates.

04-Electrostatic Fields - Part I: Lecture Notes

04-Electrostatic Fields - Part I: Solutions Homework

Electrostatic Fields - Part II

Topics include: Electric Flux Density, Gauss' Law, Derivation of Gauss' Law, Gauss' Law Applied to Cylindrical Surface of Infinite Length and Uniform Surface Charge Density, Gauss' Law Applied to "Long" Non-conducting Cylinder with Uniform Volume Charge Density, Gauss' Law Applied to "Long" Non-conducting Cylinder with Non-uniform Volume Charge Density (in Solutions Homework), Gauss' Law Applied to Infinite Plane with Uniform Surface Charge Density, Gauss' Law Applied to Two Equally "Large" Parallel Planes with Equal and Opposite Uniform Surface Charge Densities, Gauss' Law Applied to Concentric Spherical Surfaces with Equal and Opposite Uniform Surface Charge Densities, Gauss' Law Applied to Non-conducting Sphere with Uniform Volume Charge Density, Gauss' Law Applied to Infinite Line of Charge with Uniform Line Charge Density (in Solutions Homework), Gauss' Law Applied to Infinite Non-conducting Slab with Uniform Volume Charge Density (in Solutions Homework).

05-Electrostatic Fields - Part II: Lecture Notes

05-Electrostatic Fields - Part II: Solutions Homework

Electrostatic Fields - Part III

Topics include: Electric Scalar Potential Difference, Electric Scalar Potential, Zero-potential Reference, Equipotential Surface, Example: Electric Scalar Potential Difference Formula for Infinite Line of Charge with Uniform Line Charge Density, Example: Electric Scalar Potential Difference Formula for Hollow, Cylindrical Conductor of Infinite Span with Uniform Surface Charge Density, Example: Electric Scalar Potential Difference Formula Between Thin, Concentric, Conductive Spheres with Uniform Surface Charge Density (in Solutions Homework), Example: Electric Scalar Potential Difference Formula for Infinite Sheet of Charge with Uniform Surface Charge Density (in Solutions Homework), Example: Electric Scalar Potential Formula for Two Thin, Parallel, and Infinitely Long Wires with Uniform Line Charge Density (in Solutions Homework), Example: Electric Scalar Potential Formula for Thin, Circular Loop with Uniform Line Charge Density (in Solutions Homework), Poisson's and Laplace's Equations, Superposition Principle of Electric Scalar Potential, Electric Scalar Potential Due to Point Charges, Lines of Electric Force (or Electric Flux Lines) and Equipotential Surfaces for Point Charge, Pair of Unlike Charges, and Pair of Positive Charges, The Electric Dipole and Dipole Moment, Electric Scalar Potential Due to Charge Distributions, Example: Electric Scalar Potential Formula for Thin Circular Disk with Uniform Surface Charge Density, Stored Energy, Example: Formula for Stored Energy Between Hollow, Coaxial, Cylindrical Conductors of Infinite Span with Uniform Surface Charge Density, Example: Formula for Stored Energy Between Thin, Concentric, Conductive Spheres with Uniform Surface Charge Density (in Solutions Homework).

06-Electrostatic Fields - Part III: Lecture Notes

06-Electrostatic Fields - Part III: Solutions Homework

Electrostatic Fields and Materials

Topics include: Perfect Conductor, Perfect Conductors at Electrostatic Equilibrium, Perfect Dielectric, Polarization of a Dielectric, Polarization Vector, Polarization and Bound Charge in Dielectrics, Electric Flux Density and Gauss' Law With Dielectrics, Permittivity, Relative Permittivity or Dielectric Constant, Electric Susceptibility, Linear, Isotropic, and Homogeneous Dielectrics, Interface Relations of Tangential Field Components, Interface Relations of Normal Field Components, Summary Table of Interface Relations for Static Fields, Examples of Interface Relations of Static Fields, Electrostatic Field Postulates or Maxwell's Equations With Dielectrics.

07-Electrostatic Fields and Materials: Lecture Notes

07-Electrostatic Fields and Materials: Solutions Homework

Capacitance

Topics include: Capacitor, Definition of Capacitance, Stored Energy, Finding Capacitance with a Homogeneous Dielectric, Finding Capacitance of a Spherical Capacitor, Finding Capacitance of an Isolated Sphere, Finding Capacitance of a Parallel Plate Capacitor, Finding Capacitance of an Infinite Structure, Finding Capacitance of a Coaxial Cable, Finding Capacitance of a Cylindrical Capacitor, Finding Capacitance of a Two Wire Transmission Line, Finding Capacitance of a Capacitor with Piecewise Homogeneous Dielectric.

08-Capacitance: Lecture Notes

08-Capacitance: Solutions Homework

Current and Current Density

Topics include: Conduction Current and Conduction Current Density, Local or Point Form of Ohm's Law, Conductivity, Current, Classifications of Conductive Materials, Linear, Isotropic, and Homogeneous Conducting Medium, Convection Current and Convection Current Density, The Continuity Equation, Relaxation Time, Steady Current Density Field Postulates, Resistance, Conductance, Duality Relationship of Resistance and Capacitance, Resistor, Circuit Element Form of Ohm's Law, Resistance of Uniform Rectangular Conducting Medium, Resistivity, Effect of Temperature on Resistivity and Resistance, Conductance of Spherical Capacitor, Conductance Per Unit Length of Coaxial Cable or Cylindrical Capacitor, Joule's Law, and Steady Current Density Interface Relations.

09-Current and Current Density: Lecture Notes

09-Current and Current Density: Solutions Homework

Magnetostatic Fields - Part I

Topics include: Ampere's Force Law in Terms of Moving Charges, Ampere's Force Law in Terms of Current-carrying Elemental Volumes, Ampere's Force Law in Terms of Current-carrying Elemental Filaments, Ampere's Force Law in Terms of Current-carrying Elemental Surfaces, Ampere's Force Law Applied to a Two-conductor Transmission Line with Long, Straight, and Thin Conducting Wires, Ampere's Force Law Applied to a Two-conductor Transmission Line Composed of an Infinitely Long, Straight, and Thin Conducting Wire Located Midway Above an Infinitely Long, Straight, and Thin Conducting Strip of Finite Width, Magnetic Flux Density, Biot-Savart Law, Magnetic Field Intensity, Magnetic Permeability, Magnetic Field Intensity of a Circular Loop of Thin Conducting Wire at Field Points on the Axis of the Loop, Magnetic Field Intensity of a Solenoid (Cylindrical Coil) at Field Points on the Axis of the Solenoid, Magnetic Field Intensity of a Straight and Thin Conducting Wire of Finite Length at Arbitrary Field Point, Magnetic Field Intensity of a Straight and Thin Conducting Wire of Infinite Length at Arbitrary Field Point, Magnetic Field Intensity at Midpoint on Common Axis Between Two Flat Coils of Thin Conducting Wire (Solutions Homework), Magnetic Field Intensity Above, Between, and Below a Pair of Infinitely Long and Infinitely Wide Conducting Sheets (Solutions Homework), Magnetic Field Intensity at a Height Above the Center of a Square Loop of Thin Conducting Wire (Solutions Homework), Magnetic Field Intensity of Infinitely Long, Straight, and Thin Conducting Wire Bent at a Right Angle (Solutions Homework), Magnetic Force on a Current-carrying Rectangular Loop of Thin Conducting Wire in the Same Plane as a Current-carrying Infinitely Long, Straight, and Thin Conducting Wire (Solutions Homework), Magnetic Field Intensity of a Circular Arc Segment of Thin Conducting Wire (Solutions Homework).

10-Magnetostatic Fields - Part I: Lecture Notes

10-Magnetostatic Fields - Part I: Solutions Homework

Magnetostatic Fields - Part II

Topics include: Magnetic Flux, Conservation Law of Magnetic Flux, Ampere's Circuital Law, Using Ampere's Law to Find the Static Magnetic Field of an Infinite, Straight, Solid Conductor of Circular Cross Section, Using Ampere's Law to Find the Static Magnetic Field of an Infinite, Straight, Coaxial Transmission Line, Using Ampere's Law to Find the Static Field of an Infinite Current Sheet with Uniform Surface Current Density, Using Ampere's Law to Find the Static Field of an Infinitely Long Solenoid with Circular Cross Section, Using Ampere's Law to Find the Static Field of a Torus with Rectangular Cross Section, Magnetostatic Field Postulates (Maxwell's Equations).

11-Magnetostatic Fields - Part II: Lecture Notes

11-Magnetostatic Fields - Part II: Solutions Homework

Magnetostatic Fields - Part III

Topics include: Magnetic Scalar Potential, Laplace's Equation for Scalar Potential, Magnetic Vector Potential, Coulomb Gauge, Poisson's Equation for Magnetic Vector Potential, Superposition Principle for Magnetic Vector Potential, Magnetic Vector Potential Due to Source Current Distribution, Magnetic Flux Expressed in Terms of Magnetic Vector Potential, Magnetic Vector Potential Approach to Find Magnetic Field Due to Straight Filament of Short Length Carrying Steady Current, Magnetic Vector Potential Approach to Find Magnetic Field Due to Circular Filament of Small Radius Carrying Steady Current, Magnetic Dipole Moment of Circular Current Loop, Torque on Circular Current Loop in Uniform Magnetic Field, Torque on Square Current Loop in Uniform Magnetic Field (Solutions Homework), Derivation of General Formulas of Magnetic Dipole Moment and Magnetic Vector Potential at a Far Distant Point From a Small Loop Carrying Steady Current (Solutions Homework).

12-Magnetostatic Fields - Part III: Lecture Notes

12-Magnetostatic Fields - Part III: Solutions Homework

Magnetostatic Fields and Materials

Topics include: Magnetic Behavior of Materials, Diamagnetic Materials, Paramagnetic Materials, Ferromagnetism, Ferromagnetic Materials, Hysteresis, Saturation, Normal Magnetization Curve, Remanent Flux Density, Coercive Field Intensity, Magnetization Vector, Bound Current Densities, Ampere's Law with Magnetic Materials, Linear, Isotropic and Homogeneous Magnetic Materials, Permeability, Relative Permeability, Magnetic Susceptibility, Interface Relations of Magnetostatic Fields, Stored Energy in Terms of Field Quantities, Magnetostatic Field Postulates or Maxwell's Equations With Magnetic Materials.

13-Magnetostatic Fields and Materials: Lecture Notes

13-Magnetostatic Fields and Materials: Solutions Homework

Inductance

Topics include: Self-inductance, Mutual Inductance, Neumann Formula, Self-inductance of Infinitely Long Solenoid, Self-inductance of Long Solenoid, Mutual Inductance Between Solenoid with Two Concentric Windings, Mutual Inductance Between Two Coaxial Coils, Self-inductance of Toroid, Self-inductance of Thin Toroid, Self-inductance Per Unit Length of Long Coaxial Line with Thin-walled Tubular Inner and Outer Conductors, Self-inductance Per Unit Length of Long Two-wire Line with Thin Solid Conductors, Total Self-inductance Per Unit Length of Long Coaxial Line with Solid Inner Conductor and Thin-walled Tubular Outer Conductor.

14-Inductance: Lecture Notes

14-Inductance: Solutions Homework

Magnetic Circuit Analysis

Topics include: Basic Assumptions, Analysis of a Simple Magnetic Circuit, Complex Magnetic Circuit Analysis Under Basic Assumptions, Magnetic Circuit Analysis Using Piecewise-linear Magnetization Curve.

15-Magnetic Circuit Analysis: Lecture Notes

15-Magnetic Circuit Analysis: Solutions Homework