Complementing the Lagrangian Density of the E. M. Field and the Surface Integral of the p-v Vector Product

Author(s)
Mirwais Rashid

ABSTRACT

Considering the Lagrangian density of the electromagnetic field, a 4 × 4 transformation matrix is found which can be used to include two of the symmetrized Maxwell’s equations as one of the Euler-Lagrange equations of the complete Lagrangian density. The 4 × 4 transformation matrix introduces newly defined vector products. In a Theorem the surface integral of one of the newly defined vector products is shown to be reduced to a line integral.

Considering the Lagrangian density of the electromagnetic field, a 4 × 4 transformation matrix is found which can be used to include two of the symmetrized Maxwell’s equations as one of the Euler-Lagrange equations of the complete Lagrangian density. The 4 × 4 transformation matrix introduces newly defined vector products. In a Theorem the surface integral of one of the newly defined vector products is shown to be reduced to a line integral.

Cite this paper

nullM. Rashid, "Complementing the Lagrangian Density of the E. M. Field and the Surface Integral of the p-v Vector Product,"*Applied Mathematics*, Vol. 2 No. 2, 2011, pp. 225-229. doi: 10.4236/am.2011.22024.

nullM. Rashid, "Complementing the Lagrangian Density of the E. M. Field and the Surface Integral of the p-v Vector Product,"

References

[1] D. H. Young and R. A. Freedman, “University Physics,” 9th Edition, Addison-Wesley Publishing Company, Inc., USA, 1996.

[2] W. E. Burcham and M. Jobes, “Nuclear and Particle Physics,” Addison Wesley Longman Limited, Singapore, 1997.

[3] E. M. Purcell, “Electricity and Magnetism,” Berkeley Physics Course, 2nd Edition, McGraw-Hill, Inc., USA, Vol. 2, 1985.

[4] T. M. Apostol, “Calculus,” 2nd Edition, John Wiley & Sons, Singapore, Vol. 2, 1969.

[5] J. B. Marion and S. T. Thornton, “Classical Dynamics of Particles and Systems,” 4th Edition, Harcourt Brace & Co., USA, 1995.

[6] I. V. Lindell, “Electromagnetic Wave Equation in Differential-Form Representation,” Progress in Electromagnetics Research, Vol. 54, 2005, pp. 321-333. doi:10.2528/PIER05021002

[7] G. R. Fowles, “Introduction to Modern Optics,” 2nd Edition, Dover Publications, Inc., New York, 1989.

[8] R. D’Inverno, “Introducing Einstein’s Relativity,” Clarendon Press, Oxford, 1995.

[9] S. Gasiorowicz, “Quantum Physics,” 2nd Edition, John Wiley & Sons, Inc., USA, 1996.

[1] D. H. Young and R. A. Freedman, “University Physics,” 9th Edition, Addison-Wesley Publishing Company, Inc., USA, 1996.

[2] W. E. Burcham and M. Jobes, “Nuclear and Particle Physics,” Addison Wesley Longman Limited, Singapore, 1997.

[3] E. M. Purcell, “Electricity and Magnetism,” Berkeley Physics Course, 2nd Edition, McGraw-Hill, Inc., USA, Vol. 2, 1985.

[4] T. M. Apostol, “Calculus,” 2nd Edition, John Wiley & Sons, Singapore, Vol. 2, 1969.

[5] J. B. Marion and S. T. Thornton, “Classical Dynamics of Particles and Systems,” 4th Edition, Harcourt Brace & Co., USA, 1995.

[6] I. V. Lindell, “Electromagnetic Wave Equation in Differential-Form Representation,” Progress in Electromagnetics Research, Vol. 54, 2005, pp. 321-333. doi:10.2528/PIER05021002

[7] G. R. Fowles, “Introduction to Modern Optics,” 2nd Edition, Dover Publications, Inc., New York, 1989.

[8] R. D’Inverno, “Introducing Einstein’s Relativity,” Clarendon Press, Oxford, 1995.

[9] S. Gasiorowicz, “Quantum Physics,” 2nd Edition, John Wiley & Sons, Inc., USA, 1996.