Charge particle in magnetic field

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Discussion Overview

The discussion revolves around the motion of a charged particle in a magnetic field, specifically in the context of analytical mechanics. Participants explore the formulation of the Lagrangian and the challenges associated with integrating motion in a cylindrical coordinate system.

Discussion Character

  • Technical explanation, Conceptual clarification, Homework-related

Main Points Raised

  • One participant expresses difficulty in finding the motion and integrals for a charged particle in a magnetic field, referencing the potential in cylindrical coordinates.
  • Another participant asks for clarification on whether the goal is to determine the Lagrangian.
  • A participant explains that the Lagrangian can be expressed as T - V - M, where M is a generalized potential related to the electromagnetic field, specifically noting its dependence on coordinates, velocity, and possibly time.
  • The initial poster acknowledges the new information about the generalized potential and expresses intent to explore it further.

Areas of Agreement / Disagreement

Participants appear to agree on the relevance of the Lagrangian formulation, but the discussion remains unresolved regarding the specific application to the problem at hand.

Contextual Notes

The discussion does not clarify the specific assumptions or definitions related to the generalized potential or the integration process in cylindrical coordinates.

liran avraham
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i have a problem to find the motion of motion and integrals in a magnetic field given the potential in cylinder quardinate A=(0,A(r,z),0) and i have trouble to even begin with.
its part on a course called analitical mechanics with the course book ''mechanics'' by landau lifhsitz'
the problem even don't mention in the book and i looked it in e.m book to no avail (jackson , greiner, griffiths)
help please
 
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Could you be more specific. Are you looking to determine the Lagrangian for example?
 
yes
 
Are you aware that the Lagrangian L can be written as T - V - M where M is referred to as a generalized potential not derivable from an ordinary potential as V which depends only on the coordinates and maybe time. M is a function of the coordinate, and velocity,and maybe time For a charged particle in a EM field
M= - (e/c)V⋅A.
 
no i didnt know, i will try it
thank you
 

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