Electrodynamics is the study of time-varying electric and magnetic fields and their interactions with charges and currents. It forms the foundation of modern physics, underlying everything from electromagnetic waves and radiation to the relativistic structure of spacetime and the workings of astrophysical jets.
This section presents a pedagogical yet rigorous development of classical electrodynamics, with emphasis on its foundational equations, physical implications, and applications in both static and dynamic regimes — including relativistic contexts relevant to high-energy astrophysics.
Maxwell's Equations
The central pillars of classical electrodynamics in differential form.
Lorentz Force Law
Describes how electric and magnetic fields exert forces on charged particles.
Charge Continuity Equation
A statement of local charge conservation derived from Maxwell's equations.
Gauss's Law
Relates electric flux through a surface to enclosed charge.
Faraday's Law
Connects changing magnetic flux to induced electric fields.
Ampère–Maxwell Law
Generalizes Ampère's law by including displacement current.
Ohm's Law
Phenomenological relation between current density and electric field in conductors.
Potential Formulism
Expresses fields in terms of scalar and vector potentials, laying groundwork for wave solutions.
Retarded Potentials
Causal solutions to the inhomogeneous wave equations incorporating finite signal speed.
Multipole Expansion
A systematic method for approximating potentials from extended sources.
Magnetic Moments
Origin, definition, and field structures associated with magnetic dipoles.
Poynting Flux and Energy Density
Energy conservation in electromagnetic fields; flow of EM energy.
Maxwell Stress Tensor
Encodes electromagnetic pressure and tension — useful in field momentum and forces.
Relativistic Frame Transformations
How electric and magnetic fields mix under Lorentz boosts.
Faraday Tensor
Covariant expression of the electromagnetic field in special relativity.