Electromagnetism

1. Maxwell's Equations
   1. Overview
      1. Definition and Importance
      2. Unification of Electricity and Magnetism
   2. Gauss’s Law for Electricity
      1. Mathematical Expression
      2. Physical Interpretation
         1. Flux through a Closed Surface
         2. Electric Field and Charge Distribution
      3. Applications in Electrostatics
         1. Spherical Charge Distributions
         2. Planar Charge Distributions
         3. Cylindrical Charge Distributions
      4. Computational Techniques
         1. Analytical Methods
         2. Numerical Simulations
   3. Gauss’s Law for Magnetism
      1. Mathematical Expression
      2. Physical Interpretation
         1. No Isolated Magnetic Monopoles
         2. Symmetry in Magnetic Field Lines
      3. Implications for Magnetic Fields
         1. Divergence of Magnetic Fields
         2. Conservation of Magnetic Flux
      4. Visualization Methods
         1. Magnetic Field Mapping
   4. Faraday’s Law of Induction
      1. Mathematical Expression
      2. Physical Interpretation
         1. Changing Magnetic Flux and Induced EMF
         2. Concept of Magnetic Flux Linkage
      3. Lenz’s Law
         1. Direction of Induced Current
         2. Opposition to Change in Flux
      4. Applications
         1. Electric Generators
         2. Transformers
         3. Induction Cooktops
      5. Experimentation and Demonstrations
         1. Loop and Magnet Experiments
         2. Coil Induction Setups
   5. Ampère’s Law with Maxwell’s Addition
      1. Mathematical Expression
      2. Physical Interpretation
         1. Relationship between Electric Currents and Magnetic Fields
         2. Introduction of Displacement Current
      3. Displacement Current
         1. Concept and Necessity
         2. Role in Charging Capacitors
         3. Contribution to Maxwell’s Equations
      4. Applications
         1. Electromagnetic Wave Propagation
         2. Magnetic Field Calculations in Solenoids and Toroids
      5. Computational Techniques
         1. Finite Element Analysis for Complex Geometries
   6. Integral and Differential Forms
      1. Comparison and Conversion
         1. Integral Form for Intuitive Understanding
         2. Differential Form for Localized Descriptions
      2. Usage in Different Scenarios
         1. Static vs. Dynamic Fields
         2. Boundary Conditions in Complex Systems
   7. Symmetry and Conservation Laws
      1. Symmetries of Physical Laws
      2. Conservation of Electric Charge
      3. Conservation of Magnetic Flux
   8. Theoretical Implications
      1. Foundation for Electromagnetic Theory
      2. Predictions of Electromagnetic Waves
      3. Influence on Modern Physics Theories
   9. Practical and Technological Impacts
      1. Impact on Electrical Engineering
      2. Development of Communication Systems
      3. Role in the Design of Electromagnetic Devices
   10. Advanced Topics
       1. Generalizations and Extensions
          1. Relativistic Formulation
          2. Quantum Electrodynamics Connections
       2. Contemporary Research Areas
          1. Investigations into Magnetic Monopoles
          2. Advances in Computational Electromagnetics