# Energy, momentum, and force in classical electrodynamics: Application to negative-index media

Masud Mansuripur, Armis R. Zakharian

Research output: Chapter in Book/Report/Conference proceedingConference contribution

3 Citations (Scopus)

### Abstract

The classical theory of electromagnetism is based on Maxwell's macroscopic equations, an energy postulate, a momentum postulate, and a generalized form of the Lorentz law of force. These seven postulates constitute the foundation of a complete and consistent theory, thus eliminating the need for physical models of polarization P and magnetization M - these being the distinguishing features of Maxwell's macroscopic equations. In the proposed formulation, P(r,t) and M(r,t) are arbitrary functions of space and time, their physical properties being embedded in the seven postulates of the theory. The postulates are self-consistent, comply with special relativity, and satisfy the laws of conservation of energy, linear momentum, and angular momentum. The Abraham momentum density pEM(r,t)=E(r, t)×H(r,t)/c2 emerges as the universal electromagnetic momentum that does not depend on whether the field is propagating or evanescent, and whether or not the host media are homogeneous, transparent, isotropic, linear, dispersive, magnetic, hysteretic, negative-index, etc. Any variation with time of the total electromagnetic momentum of a closed system results in a force exerted on the material media within the system in accordance with the generalized Lorentz law.

Original language English (US) Proceedings of SPIE - The International Society for Optical Engineering 7392 https://doi.org/10.1117/12.825510 Published - 2009 Metamaterials: Fundamentals and Applications II - San Diego, CA, United StatesDuration: Aug 2 2009 → Aug 5 2009

### Other

Other Metamaterials: Fundamentals and Applications II United States San Diego, CA 8/2/09 → 8/5/09

### Fingerprint

Electrodynamics
Postulate
axioms
electrodynamics
Momentum
kinetic energy
momentum
macroscopic equations
Energy
Maxwell equations
electromagnetism
Maxwell's equations
Electromagnetism
Special Relativity
Relativity
Angular momentum
Physical Model
Physical property
Angular Momentum
Magnetization

### ASJC Scopus subject areas

• Applied Mathematics
• Computer Science Applications
• Electrical and Electronic Engineering
• Electronic, Optical and Magnetic Materials
• Condensed Matter Physics

### Cite this

Mansuripur, M., & Zakharian, A. R. (2009). Energy, momentum, and force in classical electrodynamics: Application to negative-index media. In Proceedings of SPIE - The International Society for Optical Engineering (Vol. 7392). [73920Q] https://doi.org/10.1117/12.825510
Proceedings of SPIE - The International Society for Optical Engineering. Vol. 7392 2009. 73920Q.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Mansuripur, M & Zakharian, AR 2009, Energy, momentum, and force in classical electrodynamics: Application to negative-index media. in Proceedings of SPIE - The International Society for Optical Engineering. vol. 7392, 73920Q, Metamaterials: Fundamentals and Applications II, San Diego, CA, United States, 8/2/09. https://doi.org/10.1117/12.825510
Mansuripur M, Zakharian AR. Energy, momentum, and force in classical electrodynamics: Application to negative-index media. In Proceedings of SPIE - The International Society for Optical Engineering. Vol. 7392. 2009. 73920Q https://doi.org/10.1117/12.825510
Mansuripur, Masud ; Zakharian, Armis R. / Energy, momentum, and force in classical electrodynamics : Application to negative-index media. Proceedings of SPIE - The International Society for Optical Engineering. Vol. 7392 2009.
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AB - The classical theory of electromagnetism is based on Maxwell's macroscopic equations, an energy postulate, a momentum postulate, and a generalized form of the Lorentz law of force. These seven postulates constitute the foundation of a complete and consistent theory, thus eliminating the need for physical models of polarization P and magnetization M - these being the distinguishing features of Maxwell's macroscopic equations. In the proposed formulation, P(r,t) and M(r,t) are arbitrary functions of space and time, their physical properties being embedded in the seven postulates of the theory. The postulates are self-consistent, comply with special relativity, and satisfy the laws of conservation of energy, linear momentum, and angular momentum. The Abraham momentum density pEM(r,t)=E(r, t)×H(r,t)/c2 emerges as the universal electromagnetic momentum that does not depend on whether the field is propagating or evanescent, and whether or not the host media are homogeneous, transparent, isotropic, linear, dispersive, magnetic, hysteretic, negative-index, etc. Any variation with time of the total electromagnetic momentum of a closed system results in a force exerted on the material media within the system in accordance with the generalized Lorentz law.

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