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.
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