Physics / advanced
Radiation from moving charges
Derive electromagnetic radiation using retarded fields, multipole expansions, angular distributions, and carefully delimited radiation-reaction models.
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Module 01 advanced
Radiation from moving charges
Derive electromagnetic radiation using retarded fields, multipole expansions, angular distributions, and carefully delimited radiation-reaction models.
- 01
Select causal solutions with retarded Green functions
Derive retarded potentials in SI units and distinguish a causal boundary condition from the differential wave equation.
32 min - 02
Retardation for a moving point charge
Derive the moving-source Jacobian and evaluate the Liénard–Wiechert potentials at the correct emission event.
32 min - 03
Separate bound fields from outgoing radiation
Identify the inverse-square and inverse-distance parts of the point-charge field and test their large-sphere flux.
32 min - 04
Normalize electric dipole radiation
Derive the sin-squared pattern, its total power, and the distinction between peak and cycle-averaged radiation.
32 min - 05
Continue beyond the electric dipole
Use source symmetry and a controlled long-wavelength expansion to identify magnetic dipole and electric quadrupole emission.
32 min - 06
Match radiation power to the kinematic regime
Connect Larmor power to its relativistic extension and preserve the distinction between emission time and reception time.
32 min - 07
Follow radiation from a relativistic bend
Relate curvature, relativistic beaming, short received pulses, and the limits of classical synchrotron formulas.
32 min - 08
Estimate radiation from a weak encounter
Integrate Larmor power along an approximately straight Coulomb encounter while testing deflection, recoil, and energy-loss assumptions.
32 min - 09
Balance momentum carried by radiation
Compute vacuum radiation pressure from incoming and outgoing momentum, including absorption, reflection, transmission, and finite pulses.
32 min - 10
Use radiation reaction as a controlled approximation
Diagnose runaway solutions and derive a weak reduced-order self-force while keeping near-field energy in the balance.
32 min