An exact formula for electromagnetic momentum in terms of the charge density and the Coulomb gauge vector potential

The electromagnetic momentum p = 1 ( 4 π c ) ∫ E × B d V is sometimes approximated by p 0 = ( 1 c ) ∫ A d V , where is the charge density and A is the Coulomb gauge vector potential. Here, we show that p 0 is the first term in an exact two-term expression p = p 0 + p 1 where the second term refers t...

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Bibliographic Details
Published in:European journal of physics 2018-03, Vol.39 (2), p.25202
Main Author: Essén, Hanno
Format: Article
Language:English
Subjects:
canonical momentum
Coulomb gauge
Darwin Lagrangian
electromagnetic momentum
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Summary:The electromagnetic momentum p = 1 ( 4 π c ) ∫ E × B d V is sometimes approximated by p 0 = ( 1 c ) ∫ A d V , where is the charge density and A is the Coulomb gauge vector potential. Here, we show that p 0 is the first term in an exact two-term expression p = p 0 + p 1 where the second term refers to radiation. When the charge density is zero, p = p 1 is the momentum of fields propagating in vacuum. In the presence of charged particles, however, p 0 normally dominates. We argue that p 0 is the natural formula for the electromagnetic momentum when radiation can be neglected. It is shown that this term may in fact be much larger than the purely mechanical contribution from mass times velocity.
ISSN:0143-0807
1361-6404
1361-6404
DOI:10.1088/1361-6404/aa9051