The electrobrachistochrone

The brachistochrone problem consists of finding the track of shortest travel time between given initial and final points for a particle sliding frictionlessly along it under the influence of a given external force field. Solvable variations of the standard example of a uniform gravitational field wo...

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Bibliographic Details
Published in:European journal of physics 2018-05, Vol.39 (3), p.35006
Main Authors: Lipscombe, Trevor C, Mungan, Carl E
Format: Article
Language:English
Subjects:
brachistochrone
conservation of mechanical energy
cycloid
image charge
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Summary:The brachistochrone problem consists of finding the track of shortest travel time between given initial and final points for a particle sliding frictionlessly along it under the influence of a given external force field. Solvable variations of the standard example of a uniform gravitational field would be suitable for homework and computer projects by undergraduate physics students studying intermediate mechanics and electromagnetism. An electrobrachistochrone problem is here proposed, in which a charged particle moves along a frictionless track under the influence of its electrostatic force of attraction to an image charge in a grounded conducting plane below the track. The path of least time is found to be a foreshortened cycloid and its properties are investigated analytically and graphically.
ISSN:0143-0807
1361-6404
DOI:10.1088/1361-6404/aaadf0