Advanced Electrodynamics: Maxwell, Radiation & Momentum

Explain global and local charge conservation and derive the continuity equation, showing that ∂ρ/∂t = -∇·J follows from Q = ∫ ρ dV and the divergence theorem.

Examine energy conservation in electrodynamics by linking work on charges to changes in electric and magnetic field energy. Use J·E, energy density, and the divergence theorem to describe energy flux.

Define the poynting vector as the energy flux density, the power carried across a surface by electromagnetic fields, and relate it to energy conservation via its divergence.

Shows how Maxwell's stress tensor resolves apparent violations of Newton's third law by encoding electric and magnetic field momentum into a force as the divergence of the tensor.

Derive the force on charges via Maxwell's stress tensor, separating pressure and shear terms, in static cases, and compute Coulomb forces with boundary surface integrals.

Explore how to compute the net force on the northern hemisphere of a uniformly charged solid sphere using Maxwell's stress tensor, with boundary surfaces and spherical coordinates.

Learn momentum and angular momentum conservation in electromagnetic fields, derive the field momentum from E cross B, and apply the Maxwell stress tensor in a coaxial cable example.

Compute the electromagnetic momentum of a parallel-plate capacitor in a uniform magnetic field and introduce angular momentum density L = r × (ε0 E × B) to illustrate momentum conservation.

Analyze angular momentum in electrodynamics using two concentric charged spherical shells in a uniform magnetic field. Apply Faraday's law and torque calculations to show total angular momentum remains conserved.

Examine electromagnetic radiation by calculating the Poynting vector and radiated power around a located source. Use retarded time and a spherical surface to compare electric and magnetic dipole radiation.

Derive the electric and magnetic fields of an oscillating electric dipole from potentials using Maxwell's equations, then apply three approximations to obtain the radiation-zone field.

Derive the vector potential for an oscillating electric dipole and compute the electric and magnetic fields in the radiation zone, then obtain the pointing vector and the omega^4 power law.

Analyze magnetic dipole radiation from a circulating current loop, defining the magnetic dipole moment. Compare with electric dipole radiation and derive the vector potential in the static limit.

Explore magnetic dipole radiation, derive vector and magnetic fields under the perfect dipole approximation, compare magnetic and electric radiation powers, and relate to Maxwell's equations.