A charged particle in the magnetic and electric fields of a long wire, relativistic
The magnetic and electric fields of a long wire, have both azimuthal symmetry and translational symmetry. As a result, the motion of a charged particle in those is solvable. This motion is studied. In the relativistic case, this problem is transformed to the problem of motion in only the magnetic field, or only the electric field, depending on whether the ratio of the current to the charge density is larger than or smaller that a certain value.
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