1 / 11

Classical Electrodynamics

Classical Electrodynamics. Jingbo Zhang Harbin Institute of Technology. Chapter 3 Electromagnetic Potentials. Section 1 Electrodynamic Potentials. Section 2 Gauge Transformations. Review. Field Equations. Fields and Potentials. Potential Equations. 1 Lorentz Gauge. In Lorentz gauge.

charlotte-walton
Download Presentation

Classical Electrodynamics

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Classical Electrodynamics Jingbo Zhang Harbin Institute of Technology

  2. Chapter 3Electromagnetic Potentials Section 1Electrodynamic Potentials Section 2Gauge Transformations

  3. Review Field Equations Fields and Potentials Potential Equations Classical Electrodynamics

  4. 1 Lorentz Gauge In Lorentz gauge uncoupled imhomogeneous wave equations coupled imhomogeneous wave equations Classical Electrodynamics

  5. Introducing d’Alembert operator Lorentz equations for potentials Classical Electrodynamics

  6. Retarded Potentials the solutions of Lorentz potential equations The solutions at time t at field point x are dependent on the behaviour at an early time t’ of the source point x’. Classical Electrodynamics

  7. 2 Coulomb Gauge In Coulomb gauge coupled imhomogeneous wave equations Poisson equation and imhomogeneous wave equations Classical Electrodynamics

  8. solution of Poisson equation • solution of imhomogeneous wave equation The scalar potential is only dependent on charge density source at time t. The retardation effects occur only in the vector potential. Classical Electrodynamics

  9. 3 Gauge Transformations • Turning the potentials simultaneously into the new one according to the following transformation, where, is an arbitrary differentiable scalar function is called the gauge function. A transformation of the potentials which leaves the fields and Maxwell’s equations invariant is called a gauge transformation. A physical law or quality which doesn’t change under a gauge transformation is said to be gauge invariant. Classical Electrodynamics

  10. Gauge invariant of Lorentz wave equations, If we require the gauge function itself be restricted to fulfill the following equation, such transformation would keep the Lorentz equations invariant. Classical Electrodynamics

  11. Homework 3.2 • (Textbook page 46)Example 3.1 In Dirac’s symmetrised form of electrodynamics, derive the inhomogeneous wave equations with introducing the potentials. Classical Electrodynamics

More Related