# Interaction of Two Charges in a Uniform Magnetic Field: II. Spatial Problem

@article{Pinheiro2008InteractionOT,
title={Interaction of Two Charges in a Uniform Magnetic Field: II. Spatial Problem},
author={Diogo Pinheiro and Robert S. MacKay},
journal={Journal of Nonlinear Science},
year={2008},
volume={18},
pages={615-666}
}
• Published 29 April 2008
• Physics
• Journal of Nonlinear Science
The interaction of two charges moving in ℝ3 in a magnetic field B can be formulated as a Hamiltonian system with six degrees of freedom. Assuming that the magnetic field is uniform and the interaction potential has rotation symmetry, we reduce this system to one with three degrees of freedom. For special values of the conserved quantities, choices of parameters or restriction to the coplanar case, we obtain systems with two degrees of freedom. Specialising to the case of Coulomb interaction…
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