volume | PIER Journals

Abstract

In this paper, the independence, completeness of Maxwell's equations and uniqueness theorems in electromagnetics are reviewed. It is shown that the four Maxwell's equations are independent and complete. A complete uniqueness theorem is proposed and proven for the first time by pointing out logic mistakes in the existing proof and presenting a truth table. Therefore, electrostatics and magnetostatics can be reduced from dynamical electromagnetics in all aspects including not only the equations as subsets of Maxwell's equations but also the corresponding uniqueness theorems. It is concluded that the axiomatic system of electromagnetic theory must consist of all four Maxwell's equations.

1. Maxwell, J. C., A Treatise on Electricity and Magnetism, Dover Publications, 1954.

2. Stratton, J. A., Electromagnetic Theory, John Wiley & Sons, 1941.

3. Arfken, G. B. and H. J. Weber, Mathematical Methods for Physicists, Academic Press, 1995.

4. Chew, W. C., Waves and Fields in Inhomogenous Media, Van Nostrand Teinhold, 1990.

5. Kong, J. A., Maxwell Equations, EMW Publishing, 2002.

6. Feynman, R. P. and R. B. Leightonand M. Sands, The Feynman Lectures on Physics, Addison-Wesley, 1989.

7. Elliott, R. S., Electromagnetics: History, Theory, 1993.

8. Jackson, J. D., Classical Electrodynamics, 3rd edition, 1998.

9. Rigden, J. S., Macmillan Encyclopedia of Physics, Simon & Schuster and Prentice Hall International, 1996.

10. Pozar, D., Microwave Engineering, Addison-Wesley, 1993.

11. Cheng, D. K., Field and Wave Electromagnetics, Addison-Wesley Pub. Co., 1989.

12. Collin, R. E., Field Theory of Guided Waves, IEEE Press, 1991.

13. Schelkunoff, S. A., Electromagnetic Fields, Blaisdell Pub. Co., 1963.

14. Jin, J. M., The Finite Element Method in Electromagnetics, John Wiley & Sons, 1993.

15. Taflove, A., Computational Electrodynamics: The Finite- Difference Time-Domain Method, Artech House, 1995.

16. Senior, T. B. A. and J. L. Volakis, Approximate Boundary Conditions in Electromagnetics, The Institute of Electrical Engineers, 1995.

17. Kong, J. A., Electromagnetic Wave Theory, 2nd edition, 1990.

18. Cessenat, M., Mathematical Methods in Electromagnetism: Linear theory and applications, World Scientific, 1996.

19. Someda, C. G., Electromagnetic Waves, Chapman & Hall, 1998.

20. Bossavit, A., Computational Electromagnetism: Variational Formulations, Complementarity, 1998.

21. Courant, R., Methods of Mathematical Physics, Vol. 2, Vol. 2, 1962.

22. Landau, L. D. and E. M. Lifshitz, The Classical Theory of Fields, Pergamon Press, 1962.

23. Balanis, C. A., Advanced Engineering Electromagnetics, John Wiley & Sons, 1989.

24. Kong, J. A., Electromagnetic Wave Theory, John Wiley & Sons, 1986.

25. Losungender, E., "Maxwellschen Gleichungen," Physik. Z., Vol. 27, No. 22, 707-710, 1926.

26. Korn, G. A. and T. M. Korn, Mathematical Handbook for Scientists and Engineering (Definition, formulas, 1968.

27. Weisstein, E. W., CRC Concise Encyclopedia of Mathematics, CRC Press, 1999.

28. Wylie, C. R. and L. C. Barrett, Advanced Engineering Mathematics, McGraw-Hill, 1995.

29. Knops, R. J. and L. E. Payne, Uniqueness Theorems in Linear Elasticity, Springer-Verlag, 1971.

30. Keller, F. J. and W. E. Gettysand M. J. Skove, Physics: Classical and Modern, McGraw-Hill, 1993.

31. Solow, D., How to Read and Do Proofs: An introduction to mathematical thought processes, 2nd edition, 1990.

32. Velleman, D. J., How to Prove It: A structured approach, Cambridge University, 1994.

33. Lakhtakia, A., Essays on the Formal Aspects of Electromagnetic Theory, World Scientific, 1993.

34. Van Bladel, J., Electromagnetic Fields, Hemisphere Pub. Corp., 1965.

35. Schwartz, M., S. Green, and W. A. Rutledge, Vector Analysis, with Applications to Geometry and Physics, 1960.

36. Zahn, M., Electromagnetic Field Theory: A problem solving approach, Wiley, 1979.

Dr. Xingling Zhou