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Advanced MechanicsFrom Euler's Determinism to Arnold's Chaos$
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S. G. Rajeev

Print publication date: 2013

Print ISBN-13: 9780199670857

Published to Oxford Scholarship Online: December 2013

DOI: 10.1093/acprof:oso/9780199670857.001.0001

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Magnetic fields

Magnetic fields

Chapter:
(p.103) 13 Magnetic fields
Source:
Advanced Mechanics
Author(s):

S. G. Rajeev

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199670857.003.0013

The Hamiltonian of a charged particle moving in a static magnetic field consists only of kinetic energy: the magnetic field appears in the Poisson brackets of velocities. This allows a way to solve for the orbit of a charged particle in the field of a magnetic monopole. The conserved angular momentum includes a surprising contribution from the electromagnetic field. Quantization implies that the product of electric and magnetic monopoles must be an integer multiple of a fundamental constant of nature. The stability of charged particles in a Penning trap is shown to be explained by the same theory as that of a Lagrange point.

Keywords:   magnetic field, magnetic monopoles, Penning trap

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