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, , and , 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.
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July 2022
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July 01 2022
Motion of a charged particle in the static fields of an infinite straight wire
Joel Franklin
;
Joel Franklin
a)
Department of Physics, Reed College
, Portland, Oregon 97202
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David J. Griffiths
;
David J. Griffiths
b)
Department of Physics, Reed College
, Portland, Oregon 97202
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Nelia Mann
Nelia Mann
c)
Department of Physics, Union College
, Schenectady, New York 12308
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a)
Electronic address: jfrankli@reed.edu, ORCID: 0000-0002-9073-5507.
b)
Electronic address: griffith@reed.edu, ORCID: 0000-0002-4406-4781.
c)
Electronic address: mannn@union.edu
Am. J. Phys. 90, 513–519 (2022)
Article history
Received:
October 29 2021
Accepted:
February 28 2022
Citation
Joel Franklin, David J. Griffiths, Nelia Mann; Motion of a charged particle in the static fields of an infinite straight wire. Am. J. Phys. 1 July 2022; 90 (7): 513–519. https://doi.org/10.1119/5.0077042
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