### Abstract

The classical theory of electrodynamics is built upon Maxwell's equations and the concepts of electromagnetic field, force, energy, and momentum, which are intimately tied together by Poynting's theorem and the Lorentz force law. Whereas Maxwell's macroscopic equations relate the electric and magnetic fields to their material sources (i.e., charge, current, polarization and magnetization), Poynting's theorem governs the flow of electromagnetic energy and its exchange between fields and material media, while the Lorentz law regulates the backand- forth transfer of momentum between the media and the fields. As it turns out, an alternative force law, first proposed in 1908 by Einstein and Laub, exists that is consistent with Maxwell's macroscopic equations and complies with the conservation laws as well as with the requirements of special relativity. While the Lorentz law requires the introduction of hidden energy and hidden momentum in situations where an electric field acts on a magnetic material, the Einstein-Laub formulation of electromagnetic force and torque does not invoke hidden entities under such circumstances. Moreover, the total force and the total torque exerted by electromagnetic fields on any given object turn out to be independent of whether force and torque densities are evaluated using the Lorentz law or in accordance with the Einstein-Laub formulas. Hidden entities aside, the two formulations differ only in their predicted force and torque distributions throughout material media. Such differences in distribution are occasionally measurable, and could serve as a guide in deciding which formulation, if either, corresponds to physical reality.

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

Volume | 8810 |

DOIs | |

State | Published - 2013 |

Event | Optical Trapping and Optical Micromanipulation X - San Diego, CA, United States Duration: Aug 25 2013 → Aug 29 2013 |

### Other

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

City | San Diego, CA |

Period | 8/25/13 → 8/29/13 |

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### 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. 8810). [88100K] https://doi.org/10.1117/12.2024808

**The force law of classical electrodynamics : Lorentz versus einstein and laub.** / Mansuripur, Masud.

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

*Proceedings of SPIE - The International Society for Optical Engineering.*vol. 8810, 88100K, Optical Trapping and Optical Micromanipulation X, San Diego, CA, United States, 8/25/13. https://doi.org/10.1117/12.2024808

}

TY - GEN

T1 - The force law of classical electrodynamics

T2 - Lorentz versus einstein and laub

AU - Mansuripur, Masud

PY - 2013

Y1 - 2013

N2 - The classical theory of electrodynamics is built upon Maxwell's equations and the concepts of electromagnetic field, force, energy, and momentum, which are intimately tied together by Poynting's theorem and the Lorentz force law. Whereas Maxwell's macroscopic equations relate the electric and magnetic fields to their material sources (i.e., charge, current, polarization and magnetization), Poynting's theorem governs the flow of electromagnetic energy and its exchange between fields and material media, while the Lorentz law regulates the backand- forth transfer of momentum between the media and the fields. As it turns out, an alternative force law, first proposed in 1908 by Einstein and Laub, exists that is consistent with Maxwell's macroscopic equations and complies with the conservation laws as well as with the requirements of special relativity. While the Lorentz law requires the introduction of hidden energy and hidden momentum in situations where an electric field acts on a magnetic material, the Einstein-Laub formulation of electromagnetic force and torque does not invoke hidden entities under such circumstances. Moreover, the total force and the total torque exerted by electromagnetic fields on any given object turn out to be independent of whether force and torque densities are evaluated using the Lorentz law or in accordance with the Einstein-Laub formulas. Hidden entities aside, the two formulations differ only in their predicted force and torque distributions throughout material media. Such differences in distribution are occasionally measurable, and could serve as a guide in deciding which formulation, if either, corresponds to physical reality.

AB - The classical theory of electrodynamics is built upon Maxwell's equations and the concepts of electromagnetic field, force, energy, and momentum, which are intimately tied together by Poynting's theorem and the Lorentz force law. Whereas Maxwell's macroscopic equations relate the electric and magnetic fields to their material sources (i.e., charge, current, polarization and magnetization), Poynting's theorem governs the flow of electromagnetic energy and its exchange between fields and material media, while the Lorentz law regulates the backand- forth transfer of momentum between the media and the fields. As it turns out, an alternative force law, first proposed in 1908 by Einstein and Laub, exists that is consistent with Maxwell's macroscopic equations and complies with the conservation laws as well as with the requirements of special relativity. While the Lorentz law requires the introduction of hidden energy and hidden momentum in situations where an electric field acts on a magnetic material, the Einstein-Laub formulation of electromagnetic force and torque does not invoke hidden entities under such circumstances. Moreover, the total force and the total torque exerted by electromagnetic fields on any given object turn out to be independent of whether force and torque densities are evaluated using the Lorentz law or in accordance with the Einstein-Laub formulas. Hidden entities aside, the two formulations differ only in their predicted force and torque distributions throughout material media. Such differences in distribution are occasionally measurable, and could serve as a guide in deciding which formulation, if either, corresponds to physical reality.

UR - http://www.scopus.com/inward/record.url?scp=84889561273&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84889561273&partnerID=8YFLogxK

U2 - 10.1117/12.2024808

DO - 10.1117/12.2024808

M3 - Conference contribution

SN - 9780819496607

VL - 8810

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

ER -