Charge particle in magnetic field

AI Thread Summary
The discussion revolves around finding the motion of a charged particle in a magnetic field using cylindrical coordinates, specifically with the vector potential A=(0, A(r,z), 0). The participant is struggling to start the problem, which is not covered in their course book "Mechanics" by Landau and Lifshitz, nor in standard electromagnetism texts. A suggestion is made to determine the Lagrangian, which can be expressed as L = T - V - M, where M represents a generalized potential related to the electromagnetic field. The generalized potential M is defined as M = - (e/c)V⋅A, which the participant was previously unaware of. This insight provides a potential pathway to solve the problem.
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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