Electromagnetism

1. Theoretical Concepts in Electromagnetism
   1. Electromagnetic Field Theory
      1. Classical Electrodynamics
         1. Coulomb’s Law
            1. Inverse Square Law
            2. Electric Force and Point Charges
         2. Biot-Savart Law
            1. Magnetic Field due to Current
            2. Application in Solenoids and Toroids
         3. Lorentz Force Law
            1. Forces on Charges in Electric and Magnetic Fields
            2. Applications in Particle Accelerators
         4. Poynting Vector
            1. Energy Transfer in Electromagnetic Fields
            2. Power Flow in Electromagnetic Radiation
      2. Quantum Electrodynamics (QED)
         1. Photon as the Force Carrier
            1. Particle-Wave Duality
            2. Compton Scattering
         2. Feynman Diagrams
            1. Visualizing QED Interactions
            2. Calculating Amplitude of Quantum Events
         3. Renormalization
            1. Handling Infinities in QED
            2. Contributions to the Fine-Structure Constant
         4. Casimir Effect
            1. Zero-Point Energy
            2. Experimental Realizations
   2. Special Relativity and Electromagnetism
      1. Lorentz Transformations
         1. Transformation of Electric and Magnetic Fields
         2. Time Dilation and Length Contraction
      2. Relativistic Electrodynamics
         1. Lorentz Invariant Formulation
         2. Four-Vectors in Electrodynamics
         3. Electromagnetic Field Tensor
            1. Covariant Electromagnetic Field Equations
            2. Dual Tensor and its Applications
         4. Relativistic Effects in Magnetic Forces
            1. Relativistic Dynamics of Charged Particles
            2. Magnetism as a Relativistic Phenomenon
      3. Einstein's mass-energy equivalence
         1. Implications for Charged Particles
         2. Relation to Rest Mass Energy and Photons
   3. Advanced Theoretical Concepts
      1. Gauge Symmetry
         1. Gauge Transformations and Potentials
         2. Role in the Standard Model of Particle Physics
      2. Electromagnetic Duality
         1. Electric-Magnetic Dualism
         2. Theoretical Implications in String Theory
      3. Topological Considerations
         1. Topological Insulators
         2. Aharonov-Bohm Effect
      4. Quantum Field Theory Extensions
         1. Spin and Helicity of Photons
         2. Virtual Particles and Vacuum Polarization