This upper-level undergraduate Electricity and Magnetism (E&M) course typically covers the foundational principles of classical electrodynamics, focusing on electrostatics, magnetostatics, and the behavior of electric and magnetic fields in vacuum and matter.
The course begins with electrostatics—Coulomb’s Law, electric fields, Gauss’s Law, and Laplace’s Equation—covering electric potential, work, and energy for both conductors and dielectrics. Magnetostatics, through Biot–Savart and Ampère’s Laws, examines magnetic fields from steady currents. Vector calculus (divergence, gradient, and curl) is used extensively throughout. The course synthesizes these concepts to express Maxwell’s equations in both differential and integral forms. Maxwell's Equation is used to discuss the production of Electromagnetic Waves and its propagation in vacuum.
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Course Outline/Summary and Lecture Notes
Electric Force and Electric Field: Point Charges, Conductors and Capacitor
Relation between Electric Field, Electric Potential, Potential Energy and Work
Calculus with Electric Field and Potential: Electric Field and Potential Continuous Charge Distribution and Gauss Law
Vector Calculus:
Vector Alzebra: Vector Addition, Vector Products (Dot, Cross and Mixed Products); representation of vectors in Cartesian, Cylindrical, and Spherical Coordinates and Coordinate Transformation
Differential Calculus: Gradient, Divergence and Curl
Integral Calculus: Line, Surface and Volume Integrals; Fundamental Theorem of Calculus
Electrostatics
Electrostatics_Part 1: Electric Force, Electric Field and Electric Potential generated by charges at rest (statics). Relation between Electric Potential, Electrostatic Work, and Energy
Electrostatics_Part 2: Boundary Values of Electric Field and Potential. Conductors and Capacitors
Poission's and Laplace's Equation: Solution to Laplace's Equation and Uniqueness Theorem
Solving Laplace's Equation: Method of Images and Seperation of Variables
Magnetostatics
Magnetostatics: Magnetism produced by charges in motion; Effect of Magnetic Field on moving charges; Work done by Magnetic Forces; Biot-Savart Law; Ampere's Law; Magnetic Dipoles
Electrodynamics
Electrodynamics_Part 1: Ohm's Law, Drift Velocity, Conductivity, Joule Heating, and Sources of EMF. Faraday's Experiments, Lenz Law and AC generators
Electrodynamics_Part 2: Maxwell's Faraday's Law; Inductance and Self-Inductance, LR circuit; Maxwell's Equation; Electromagnetic Waves (brief discussion of production of radio waves)