1. Classical Electrodynamics Jingbo Zhang Harbin Institute of Technology

2. Chapter 1 Classical Electrodynamics Section 1 Electrostatics Section 2 Magnetostatics Section 3 Electrodynamics Section 4 Electromagnetodynamics

3. Jingbo Zhang Section 4 EletromagnetodynamicsChapter 1 Aug 30, 2004 Classical Electrodynamics Review  Maxwell’s Equations for Electrodynamics We should discuss some important point here.

4. Jingbo Zhang Section 4 EletromagnetodynamicsChapter 1 Aug 30, 2004 Classical Electrodynamics 1 Electromagnetic Duality  Dirac’s assumption of existence magnetic charges or magnetic monopoles. Now, Dirac-Maxwell Equations show the electromagnetic symmetric again.

5. Jingbo Zhang Section 4 EletromagnetodynamicsChapter 1 Aug 30, 2004 Classical Electrodynamics  Introduce the speed of light in vacuum, then, we have

6. Jingbo Zhang Section 4 EletromagnetodynamicsChapter 1 Aug 30, 2004 Classical Electrodynamics  Continuity Equation for Magnetic Monopoles which has the same form as that for the electric charges, and means the same physics that the time rate of change of magnetic charge density is auto balanced by the divergence of magnetic current density.

7. Jingbo Zhang Section 4 EletromagnetodynamicsChapter 1 Aug 30, 2004 Classical Electrodynamics 2 Duality Transformation

8. Jingbo Zhang Section 4 EletromagnetodynamicsChapter 1 Aug 30, 2004 Classical Electrodynamics  General case which leaves the symmetrised Maxwell equations and the physics they described invariant.

9. Jingbo Zhang Section 4 EletromagnetodynamicsChapter 1 Aug 30, 2004 Classical Electrodynamics Example 1 Faraday’s Law  Use continuity equation for magnetic charges and Dirac-Maxwell’s equations to derive Faraday’s Law. Coulomb-like’s Law Finally, we have

10. Jingbo Zhang Section 4 EletromagnetodynamicsChapter 1 Aug 30, 2004 Classical Electrodynamics Example 2 Duality Transformation  Show that the symmetric, electromagnetodynamic form of Maxwell’s equations are invariant under the duality transformation.

11. Jingbo Zhang Section 4 EletromagnetodynamicsChapter 1 Aug 30, 2004 Classical Electrodynamics Example 3 Mixing Angle  Show that for a fixed mixing angle, the symmetrised Maxwell’s equations reduce to usual Maxwell equtions. For the duality transformation, we have the inverse of the transformation,

12. Jingbo Zhang Section 4 EletromagnetodynamicsChapter 1 Aug 30, 2004 Classical Electrodynamics  Symmetric Discussion IV sencond time broken Symmetrised Maxwell’s equation

13. Jingbo Zhang Section 4 EletromagnetodynamicsChapter 1 Aug 30, 2004 Classical Electrodynamics Perfect Beautiful Symmetric Super-Theory  Another set of symmetric