Motion of a charged particle in the static fields of an infinite straight wire

Abstract

The nonrelativistic trajectory of a point charge q in the magnetic field of a steady line current I is characterized by the three components of its initial velocity. The motion is periodic in the cylindrical coordinates s, [Formula: see text], and [Formula: see text], describing, in the generic case, a kind of “double helix,” with one helix serving as a guide while the other winds around it. A positive charge “drifts” in the direction of the current (a negative charge goes the other way). The inclusion of a uniform line charge λ (coinciding with the current) does not alter the motion qualitatively, but it does change the drift velocity, and can even reduce it to zero, collapsing the trajectory to the surface of a toroid. The relativistic treatment modifies and illuminates these results.