Electromagnetics

Electromagnetics is a fundamental branch of electrical engineering that studies the interactions between electric fields and magnetic fields. Governed by Maxwell's equations, this discipline explains how electric charges and currents create these fields, and how changing fields can propagate through space as electromagnetic waves, such as radio waves and light. This foundational knowledge is critical for the design and analysis of a vast range of technologies, including antennas, wireless communication systems, transmission lines, electric motors, generators, and optical devices.

1. Foundations of Electromagnetics
   1. Historical Development of Electromagnetic Theory
      1. Ancient Observations of Electric and Magnetic Phenomena
      2. Coulomb's Contributions
      3. Faraday's Experimental Work
      4. Maxwell's Theoretical Unification
      5. Modern Developments
   2. Physical Quantities and Units
      1. SI Units in Electromagnetics
         1. Base Units
         2. Derived Units for Electric Quantities
         3. Derived Units for Magnetic Quantities
      2. Dimensional Analysis
         1. Dimensional Consistency
         2. Unit Conversions
   3. Vector Analysis
      1. Vector Algebra
         1. Scalars and Vectors
            1. Definition and Properties
            2. Vector Representation
         2. Vector Addition and Subtraction
            1. Geometric Methods
            2. Component Methods
         3. Scalar Product
            1. Definition and Properties
            2. Geometric Interpretation
         4. Vector Product
            1. Definition and Properties
            2. Geometric Interpretation
         5. Scalar Triple Product
            1. Definition and Properties
            2. Geometric Interpretation
         6. Vector Triple Product
            1. Definition and Properties
            2. Vector Identities
         7. Physical Interpretation of Vector Operations
      2. Coordinate Systems
         1. Cartesian Coordinates
            1. Unit Vectors
            2. Position Vector Representation
            3. Differential Elements
         2. Cylindrical Coordinates
            1. Unit Vectors
            2. Position Vector Representation
            3. Differential Elements
         3. Spherical Coordinates
            1. Unit Vectors
            2. Position Vector Representation
            3. Differential Elements
         4. Vector Transformations Between Systems
            1. Transformation Equations
            2. Applications in Electromagnetics
      3. Vector Calculus
         1. The Del Operator
            1. Definition in Different Coordinate Systems
            2. Operator Properties
         2. Gradient of a Scalar Field
            1. Definition and Physical Meaning
            2. Calculation in Cartesian Coordinates
            3. Calculation in Cylindrical Coordinates
            4. Calculation in Spherical Coordinates
         3. Divergence of a Vector Field
            1. Definition and Physical Meaning
            2. Calculation in Cartesian Coordinates
            3. Calculation in Cylindrical Coordinates
            4. Calculation in Spherical Coordinates
         4. Curl of a Vector Field
            1. Definition and Physical Meaning
            2. Calculation in Cartesian Coordinates
            3. Calculation in Cylindrical Coordinates
            4. Calculation in Spherical Coordinates
         5. Laplacian of a Scalar Field
            1. Definition and Physical Meaning
            2. Calculation in Cartesian Coordinates
            3. Calculation in Cylindrical Coordinates
            4. Calculation in Spherical Coordinates
      4. Integral Theorems
         1. Line Integrals
            1. Definition and Evaluation
            2. Path Independence
         2. Surface Integrals
            1. Definition and Evaluation
            2. Orientation of Surfaces
         3. Volume Integrals
            1. Definition and Evaluation
         4. Divergence Theorem
            1. Statement and Proof
         5. Stokes's Theorem
            1. Statement and Proof