Electromagnetism

Electromagnetism is one of the four fundamental forces of nature, describing the interaction between electrically charged particles through electric and magnetic fields. It unifies what were once considered separate phenomena, revealing that a moving electric charge generates a magnetic field, and a changing magnetic field generates an electric field. Governed by Maxwell's equations, this foundational principle explains a vast range of phenomena, from the propagation of light—which is an electromagnetic wave—to the forces that hold atoms and molecules together, and it forms the basis for modern technologies like electric motors, generators, and all electronics.

1. Fundamental Concepts and Mathematical Preliminaries
   1. Vector Calculus in Electromagnetism
      1. Coordinate Systems
         1. Cartesian Coordinates
            1. Unit Vectors
            2. Position Vector
            3. Coordinate Transformations
            4. Applications in Electromagnetism
         2. Cylindrical Coordinates
            1. Unit Vectors
            2. Position Vector
            3. Coordinate Transformations
            4. Applications in Electromagnetism
         3. Spherical Coordinates
            1. Unit Vectors
            2. Position Vector
            3. Coordinate Transformations
            4. Applications in Electromagnetism
      2. Vector Operations
         1. Scalar Fields
            1. Definition and Examples
            2. Level Surfaces
         2. Vector Fields
            1. Definition and Examples
            2. Field Lines
            3. Visualization Techniques
         3. Gradient Operation
            1. Definition and Notation
            2. Physical Interpretation
            3. Calculation in Cartesian Coordinates
            4. Calculation in Cylindrical Coordinates
            5. Calculation in Spherical Coordinates
            6. Properties and Rules
         4. Divergence Operation
            1. Definition and Notation
            2. Physical Interpretation
            3. Calculation in Cartesian Coordinates
            4. Calculation in Cylindrical Coordinates
            5. Calculation in Spherical Coordinates
            6. Properties and Rules
         5. Curl Operation
            1. Definition and Notation
            2. Physical Interpretation
            3. Calculation in Cartesian Coordinates
            4. Calculation in Cylindrical Coordinates
            5. Calculation in Spherical Coordinates
            6. Properties and Rules
         6. Laplacian Operator
            1. Scalar Laplacian
               1. Definition and Notation
               2. Calculation in Different Coordinates
            2. Vector Laplacian
               1. Definition and Notation
               2. Calculation in Different Coordinates
      3. Integral Theorems
         1. Line Integrals
            1. Definition and Calculation
            2. Path Dependence
            3. Path Independence
            4. Conservative Fields
         2. Surface Integrals
            1. Definition and Calculation
            2. Orientation of Surfaces
            3. Area Elements in Different Coordinates
         3. Volume Integrals
            1. Definition and Calculation
            2. Volume Elements in Different Coordinates
         4. Fundamental Theorem for Gradients
            1. Statement and Proof
         5. Stokes' Theorem
            1. Statement and Proof
            2. Physical Interpretation
            3. Applications in Electromagnetism
         6. Divergence Theorem
            1. Statement and Proof
            2. Physical Interpretation
            3. Applications in Electromagnetism
      4. Dirac Delta Function
         1. Definition and Properties
         2. One-Dimensional Delta Function
         3. Three-Dimensional Delta Function
         4. Representations of Delta Function
         5. Applications in Charge Distributions
         6. Applications in Current Distributions
   2. Core Physical Concepts
      1. Electric Charge
         1. Nature of Electric Charge
         2. Properties of Charge
            1. Additivity
            2. Conservation
            3. Invariance under Lorentz Transformations
         3. Elementary Charge
         4. Quantization of Charge
         5. Charge Conservation Law
            1. Local Conservation
            2. Global Conservation
      2. Charge Distributions
         1. Point Charges
         2. Linear Charge Density
            1. Definition and Units
            2. Examples and Applications
         3. Surface Charge Density
            1. Definition and Units
            2. Examples and Applications
         4. Volume Charge Density
            1. Definition and Units
            2. Examples and Applications
      3. Electric Current
         1. Definition of Current
         2. Units and Measurement
         3. Conventional Current Direction
         4. Microscopic View of Current
      4. Current Density
         1. Definition and Units
         2. Relationship to Current
         3. Current Density Vector
      5. Continuity Equation
         1. Physical Meaning
         2. Mathematical Formulation
         3. Derivation from Charge Conservation