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Physics 704/804 Electromagnetic Theory II

This lecture by Professor A.G. Krafft explores the use of symmetry in Green function for efficient field evaluation, including Jefimenko Expressions and conservation of energy in electromagnetic fields. Discussions on Heavyside-Feynman fields, power considerations, and momentum conservation are covered, emphasizing the importance of understanding vector forms and energy density. Suitable for advanced students and researchers in physics.

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Physics 704/804 Electromagnetic Theory II

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  1. Physics 704/804ElectromagneticTheory II G. A. Krafft Jefferson Lab Jefferson Lab Professor of Physics Old Dominion University

  2. Retarded Solutions for Fields Evaluation can be expedited by noting and using the symmetry of the Green function and using relations such as

  3. Direct computation, using the unprimed variables, gives Jefimenko Expressions (Jackson 6.55 and 6.56)

  4. For time independent distributions reproduce Jackson 1.5 and 5.14 (Coulomb’s Law or the Biot-Savart Law for magnetic field). Heavyside-Feynman fields for a point particle are found in the homework problem.

  5. Energy/Power considerations Units of electric field , electric displacement, and current density Power delivered from electromagnetic field to a current element per unit volume involves E and J forms (magnetic fields cannot do work on a current because the force is perpendicular to the current). Power per unit volume must be

  6. Energy Conservation Energy/volume involves (exterior) multiplication of E and D. The exact formula comes from the Maxwell Equations: The RHS terms define the [1] Poynting (Energy Flux) form For linear materials have [2] energy density form

  7. In Vector Form Energy Density (J/m3) Poynting Vector (J/sec m2)

  8. Momentum Conservation Momentum is a vector quantity. To describe momentum densities need (what could be more natural) vector valued forms. Mechanical momentum delivered to a load by an electromagnetic field is Define the vector 3-form force density to be Momentum Flux density must have nine components

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