Electrodynamics

Electric Field

Electrostatics

• Coulomb’s Law and Electric Field $\mathbf{E}$
• Flux of Electric Field and Gauss’s Law
  • Application of Gauss’s Law in Integral Form
• Divergence of Electric Field $\nabla \cdot \mathbf{E}$
• Curl of Electric Field $\nabla \times \mathbf{E}$
• Work and Energy

Potential

• Potential $\mathbf{E} = - \nabla V$
• Properties of Potential
• Multipole Expansion of Potential and Dipole Moment
• Electric Field Created by a Dipole

Electrostatic Field in Matter

• Polarization Density and Dielectrics
• Alignment of Polar Molecules by a Uniform External Electric Field
• Alignment of Polar Molecules by a Non-Uniform Electric Field
• Bound Charges and Electric Field Created by a Polarized Object

Magnetic Field

Magnetostatics

• Lorentz Force Law and Magnetic Field $\mathbf{B}$
  • Reason for the Symbol $\mathbf{B}$ of Magnetic Field (+Which is the Magnetic Field, $\mathbf{B}$ or $\mathbf{H}$?)
• Magnetic Forces Do Not Work
• Current and Current Density
• Continuity Equation in Electromagnetism
• Steady Current and Biot-Savart Law
• Divergence (Divergence) and Curl of Magnetic Field $\nabla \cdot \mathbf{B}$, $\nabla \times \mathbf{B}$
• Ampère’s Law and Applications
• Magnetic Vector Potential $\mathbf{B} = \nabla \times \mathbf{A}$
• Multipole Expansion of Vector Potential and Magnetic Dipole Moment
• Magnetic Field Created by a Magnetic Dipole

Magnetic Field in Matter

• Magnetization Density and Magnetic Materials
• Torque on Magnetic Dipoles in an External Magnetic Field and Paramagnetism
• Changes in Electron Orbits due to an External Magnetic Field and Diamagnetism
• Bound Current Density and Magnetic Field Created by a Magnetized Object

Electrodynamics

• Electromotive Force and Motional Electromotive Force
• Faraday’s Law and Lenz’s Law
• Mutual Inductance
• Self-Inductance
• Energy in a Magnetic Field
• Maxwell’s Equations

Conservation Laws

• Poynting’s Theorem and Poynting Vector
• Maxwell Stress Tensor
• Electromagnetic Force on Charges within a Volume
• Momentum Conservation in Electrodynamics
• Angular Momentum of Electromagnetic Fields

Electromagnetic Waves

• Deriving the Speed of Electromagnetic Waves from Maxwell’s Equations

Potential and Electromagnetic Field

• Potential and Electromagnetic Field
• Gauge Transformation
• Coulomb Gauge and Lorenz Gauge
• Retarded Time, Delayed Potential for Continuous Distribution
  • Gradient of Retarded Time
• Jefimenko’s Equations
• Liénard-Wiechert Potential
  • Time Derivatives
• Electric Field Created by a Moving Point Charge
• Magnetic Field Created by a Moving Point Charge

References

• David J. Griffiths, Introduction to Electrodynamics (4th Edition, 2014)