EECS 220 Handouts
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CHAPTER 2: VECTOR ANALYSIS
Section 2-2: Physical Quantities and Units
(pp. 7-11)
Examples of Physical Quantities
Section 2-3: Vector Algebra (pp. 11-16)
Arithmetic Operations of Vectors
Multiplicative Operations of Vectors and
Scalars
Orthogonal and Orthonormal Vector Sets
Section 2-4: Orthogonal Coordinate Systems
(pp. 16-33)
Example: Coordinate Transformations
Vector Expansion using Base Vectors
Vector Algebra using Orthonormal Base Vectors
Example: Expressing Vector Fields with
Coordinate Systems
Section 2-5: The Calculus of Scalar and Vector
Fields (pp. 33-55)
The Line Integral
Differential Line Vector Elements
The Differential Line Vector for Coordinate
Systems
Line Integrals with Complex Contours
Steps for Analyzing Line Integrals
The Surface Integral
The Differential Surface Vector for
Coordinate Systems
Integrals with Complex Surfaces
Steps for Analyzing a Surface Integral
The Volume Integral
The Differential Volume Element
The Gradient
The Gradient Operator in Other Coordinate
Systems
Example: Line Integrals of Conservative
Fields
Divergence
The Divergence of a Vector Field
Divergence in Cylindrical and Spherical
Coordinate Systems
Curl
Curl in Cylindrical and Spherical Coordinate
Systems
The Curl of a Conservative Field
CHAPTER 3: ELECTROMAGNETIC SOURCES,
FORCES, AND FIELDS
Section 3-2: Charge and Charge Density (pp.
62-63)
Section 3-3: Current and Current Density (pp.
63-68)
The Current I through Surface S
Charge Velocity and Current Density
Section 3-4: The Law of Charge Conservation
(pp. 68-71)
The Point Form of the Continutiy Equation
Section 3-5: Two Action-at-a-Distance Force Laws (pp.
71-75)
Vector Form of Coulomb’s Law of Force
Example: Ampere’s Law of Force
Section 3-6: The Lorentz Force Law and the Field
Concept of Electromagnetics (pp. 75-81)
The Differential Form of the Lorentz Force
Law
Section 3-7: Maxwell’s Equations (pp. 81-84)
CHAPTER 4: ELECTROSTATIC FIELDS IN FREE
SPACE
Section 4-2: Maxwell’s Equations for
Electrostatics in Free Space (pp. 88-90)
The Integral Form of Electrostatics
Section 4-3: Coulomb’s Law (pp. 90-93)
Coulomb's Law for Charge Density
Section 4-4: E-field Calculations Using Coulomb’s
Law (pp. 93-98)
The Uniform Infinite Line Charge
Section 4-5: Field Computation Using Gauss’s Law (pp.
98-107)
Spherically Symmetric Charge Densities
Cylindrically Symmetric Charge Densities
Example Using Gauss Law to Determine the
Electric Field
Section 4-6: Voltage and Electric Potential (pp.
107- 116)
Voltage and Electric Potential
Electric Potential for Point Charge
Electric Potential Function for Charge
Densities
Section 4-7: Poisson’s and Laplace’s Equations
(pp. 116-117)
Poisson’s and Laplace’s Equations
CHAPTER 5: ELECTROSTATIC FIELDS IN
MATERIAL MEDIA
Section 5-2: Conductors (pp. 123-132)
Section 5-3: Dielectrics (pp. 132-149)
Polarization Charge Distributions
Electrostatic Field Equations in Dielectrics
Boundary Conditions on Perfect Conductors
Section 5-4: Electrostatic Boundary Value
Problems (pp. 149-157)
Example: The Electrostatic Fields of a
Coaxial Line
Example: Dielectric Filled Parallel Plates
Example: Charge Filled Parallel Plates
Example: Solutions Inolving Imhogeneous
Dielectrics
CHAPTER 6: CAPACITANCE AND ELECTRIC
ENERGY
Section 6-2: Capacitance (pp. 180-195)
Capacitance of a Coaxial Transmission Line
Section 6-3: The Energy Contained in an
Electrostatic Charge Distribution (pp.195-200)
The Stored Energy of Charge Distributions
Section 6-4: Energy Storage in Capacitors (pp.
200-201)
CHAPTER 7: MAGNETOSTATIC FIELDS IN FREE
SPACE
Section 7-2: Maxwell’s Equatons for
Magnetostatics in Free Space (pp. 206-207)
Maxwells Equations for Magnetostatics
The Integral Form of Magnetostatics
Section 7-3: The Biot-Savart Law and the Magnetic
Vector Potential (pp. 208-218)
Example An Infinite Line of Current
B-field from an Infinite Sheet of Current
Section 7-4: Field Calculations Using Ampere’s Law (pp. 218-227)
B-field from Cylindrically Symmetic Current
Distributions
Example: A Hollow Tube of Current
Example: The B-field of a Coaxial Cable
Section 7-5: Magnetic Potentials (pp.
227-236)
The Integral Definition of Magnetic Vector
Potential
CHAPTER 8: MAGNETOSTATIC FIELDS IN
MATERIAL MEDIA
Section 8-3: Magnetic Materials (244-260)
The Magnetic Dipole in B field
Field Equations in Magnetic Materials
Section 8-4: Magnetic Boundary Value Problems (pp.
260-263)
Example: A Magnetic Boundary Value Problem
Section 8-5: Permantent Magnets and Magnetic
Recording (pp.265-267)
CHAPTER 9: MAGNETIC INDUCTANCE, ENERGY, AND FORCES
Section 9-2: Faraday’s Law of Induction (pp.
278-290)
Section 9-3:
Inductance (pp. 290-307)
Example The Inductance of a Solenoid
The Inductance of a Coaxial Transmission Line
Section 9-4:
Magnetic Forces and Torques (pp. 310-318)
CHAPTER 10: TIME-VARYING ELECTROMAGNETIC
FIELDS
Section 10-2:
Displacement Current (pp. 326-330)
Maxwell’s Equations (Yet Again)
Section 10-3: Maxwell’s Equations for
Time-Varying Fields (pp. 330-331)
Propagation of Electromagnetic Waves