In this paper, we discuss two well known definitions of electromagnetic momentum, ρA and \epsilon0[E x B]. We show that the former is preferable to the latter for several reasons which we will discuss. Primarily, we show in detail|and by example|that the usual manipulations used in deriving the expression \epsilon0[E x B] have a serious mathematical flaw. We follow this by presenting a succinct derivation for the former expression. We feel that the fundamental definition of electromagnetic momentum should rely upon the interaction of a single particle with the electromagnetic field. Thus, it contrasts with the definition of momentum as \epsilon0[E x B] which depends upon a (defective) integral over an entire region, usually all space.
2. Rousseaux, G., "On the physical meaning of the gauge conditions of Classical Electromagnetism: The hydrodynamics analogue viewpoint," Annales de la Fondation Louis de Broglie, Vol. 28, 2, 2003.
3. Semon, M. D. and J. R. Taylor, "Thoughts on the magnetic vector potential," Am. J. Phys., Vol. 64, 1361, 1996.
4. Pfeifer, R. N. C., et al., "Momentum of an electromagnetic wave in dielectric media," Rev. Mod. Phys., Vol. 79, No. 4, 1197, 2007.
5. Griffiths, D. J., Introduction to Electrodynamics, 3rd Ed., Prentice-Hall Inc., 1999.
6. Panofsky, W. K. H. and M. Phillips, Classical Electricity and Magnetism, 2nd Ed., Ch. 14, Addison-Wesley, Reading, MA, 1962.
7. Tikhonov, A. N. and A. A. Samarski, Equations of Mathematical Physics, Ch. IV.5.5, Dover Publications, Inc., New York, 1990.
8. Darwin, C. G., "The dynamical motion of charged particles," Phil. Mag., Vol. 39, 537, 1920.
9. Page, L., N. I. Adams, and Jr., "Action and reaction between moving charges," Am. J. Phys., Vol. 13, 141, 1945.
10. Landau, L. D. and E. M. Lifshitz, The Classical Theory of Fields, Section 65, Pergamon Press, 1971.