### Abstract

The macroscopic equations of Maxwell combined with a generalized form of the Lorentz law are a complete and consistent set; not only are these five equations fully compatible with the special theory of relativity, they also conform with the conservation laws of energy, momentum, and angular momentum. The linear momentum density associated with the electromagnetic field is p _{EM}(r,t)=E(r,t)×H(r,t)/c^{2}, whether the field is in vacuum or in a ponderable medium. [Homogeneous, linear, isotropic media are typically specified by their electric and magnetic permeabilities ε_{o} ε(ω) and μ_{o}μ(ω).] The electromagnetic momentum residing in a ponderable medium is often referred to as Abraham momentum. When an electromagnetic wave enters a medium, say, from the free space, it brings in Abraham momentum at a rate determined by the density distribution p_{EM}(r,t), which spreads within the medium with the light's group velocity. The balance of the incident, reflected, and transmitted (electromagnetic) momenta is subsequently transferred to the medium as mechanical force in accordance with Newton's second law. The mechanical force of the radiation field on the medium may also be calculated by a straightforward application of the generalized form of the Lorentz law. The fact that these two methods of force calculation yield identical results is the basis of our claim that the equations of electrodynamics (Maxwell + Lorentz) comply with the momentum conservation law. When applying the Lorentz law, one must take care to properly account for the effects of material dispersion and absorption, discontinuities at material boundaries, and finite beam dimensions. This paper demonstrates some of the issues involved in such calculations of the electromagnetic force in magnetic dielectric media.

Original language | English (US) |
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Title of host publication | Proceedings of SPIE - The International Society for Optical Engineering |

Volume | 7038 |

DOIs | |

State | Published - 2008 |

Event | Optical Trapping and Optical Micromanipulation V - San Diego, CA, United States Duration: Aug 10 2008 → Aug 13 2008 |

### Other

Other | Optical Trapping and Optical Micromanipulation V |
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Country | United States |

City | San Diego, CA |

Period | 8/10/08 → 8/13/08 |

### Fingerprint

### Keywords

- Electromagnetic theory
- Momentum of light
- Optical trapping
- Radiation pressure

### ASJC Scopus subject areas

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

### Cite this

*Proceedings of SPIE - The International Society for Optical Engineering*(Vol. 7038). [70381T] https://doi.org/10.1117/12.796530

**Generalized Lorentz Law and the force of radiation on magnetic dielectrics.** / Mansuripur, Masud.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings of SPIE - The International Society for Optical Engineering.*vol. 7038, 70381T, Optical Trapping and Optical Micromanipulation V, San Diego, CA, United States, 8/10/08. https://doi.org/10.1117/12.796530

}

TY - GEN

T1 - Generalized Lorentz Law and the force of radiation on magnetic dielectrics

AU - Mansuripur, Masud

PY - 2008

Y1 - 2008

N2 - The macroscopic equations of Maxwell combined with a generalized form of the Lorentz law are a complete and consistent set; not only are these five equations fully compatible with the special theory of relativity, they also conform with the conservation laws of energy, momentum, and angular momentum. The linear momentum density associated with the electromagnetic field is p EM(r,t)=E(r,t)×H(r,t)/c2, whether the field is in vacuum or in a ponderable medium. [Homogeneous, linear, isotropic media are typically specified by their electric and magnetic permeabilities εo ε(ω) and μoμ(ω).] The electromagnetic momentum residing in a ponderable medium is often referred to as Abraham momentum. When an electromagnetic wave enters a medium, say, from the free space, it brings in Abraham momentum at a rate determined by the density distribution pEM(r,t), which spreads within the medium with the light's group velocity. The balance of the incident, reflected, and transmitted (electromagnetic) momenta is subsequently transferred to the medium as mechanical force in accordance with Newton's second law. The mechanical force of the radiation field on the medium may also be calculated by a straightforward application of the generalized form of the Lorentz law. The fact that these two methods of force calculation yield identical results is the basis of our claim that the equations of electrodynamics (Maxwell + Lorentz) comply with the momentum conservation law. When applying the Lorentz law, one must take care to properly account for the effects of material dispersion and absorption, discontinuities at material boundaries, and finite beam dimensions. This paper demonstrates some of the issues involved in such calculations of the electromagnetic force in magnetic dielectric media.

AB - The macroscopic equations of Maxwell combined with a generalized form of the Lorentz law are a complete and consistent set; not only are these five equations fully compatible with the special theory of relativity, they also conform with the conservation laws of energy, momentum, and angular momentum. The linear momentum density associated with the electromagnetic field is p EM(r,t)=E(r,t)×H(r,t)/c2, whether the field is in vacuum or in a ponderable medium. [Homogeneous, linear, isotropic media are typically specified by their electric and magnetic permeabilities εo ε(ω) and μoμ(ω).] The electromagnetic momentum residing in a ponderable medium is often referred to as Abraham momentum. When an electromagnetic wave enters a medium, say, from the free space, it brings in Abraham momentum at a rate determined by the density distribution pEM(r,t), which spreads within the medium with the light's group velocity. The balance of the incident, reflected, and transmitted (electromagnetic) momenta is subsequently transferred to the medium as mechanical force in accordance with Newton's second law. The mechanical force of the radiation field on the medium may also be calculated by a straightforward application of the generalized form of the Lorentz law. The fact that these two methods of force calculation yield identical results is the basis of our claim that the equations of electrodynamics (Maxwell + Lorentz) comply with the momentum conservation law. When applying the Lorentz law, one must take care to properly account for the effects of material dispersion and absorption, discontinuities at material boundaries, and finite beam dimensions. This paper demonstrates some of the issues involved in such calculations of the electromagnetic force in magnetic dielectric media.

KW - Electromagnetic theory

KW - Momentum of light

KW - Optical trapping

KW - Radiation pressure

UR - http://www.scopus.com/inward/record.url?scp=56249147827&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=56249147827&partnerID=8YFLogxK

U2 - 10.1117/12.796530

DO - 10.1117/12.796530

M3 - Conference contribution

AN - SCOPUS:56249147827

SN - 9780819472588

VL - 7038

BT - Proceedings of SPIE - The International Society for Optical Engineering

ER -