I am having trouble understanding how to find symmetries given a

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Homework Help Overview

The discussion revolves around understanding how to find symmetries in electrostatics, specifically for a cylindrical conductor that is infinite in the z-direction. The original poster is exploring the implications of a homogeneous charge distribution on the electric field and its components.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to reason through the symmetry of the electric field based on the charge distribution and questions how to handle the components of the electric field. Some participants suggest that the potential's independence from certain variables implies that corresponding components of the electric field may vanish. Others inquire about more general approaches, such as symmetry groups.

Discussion Status

The discussion is ongoing, with participants exploring different interpretations of the problem. Some guidance has been offered regarding the implications of the potential's dependence on variables, but there is no explicit consensus on a comprehensive method or approach.

Contextual Notes

There is a mention of using Helmholtz theorem and Faraday's law, indicating a focus on the mathematical relationships governing the electric field components. The original poster expresses uncertainty about the conventions used in this context.

berra
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I am having trouble understanding how to find symmetries given a problem.
Ex:
Cylinder, infinite in z, that is a conductor in electrostatics.
My reasoning is: assuming a homogenous charge distribution, the E-field should be symmetric for translations in z and phi so those derivatives are zero. But how do I do for the components? My only guess was to take the divergence and curl and use helmholtz theorem, but in the curl I still have dEz/drho and an Ephi term. Is the convention to use faradays law and assuming Ez and Ephi are the trivial solutions to the PDE so the Efield only has a rho component?
 
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Can't you argue that since the potential is not dependent on z or phi, the z and phi components of E vanish?
 


Ah yes! That would take care of it! Nice. Is there any other more general approach? Like symmetry groups somehow?
 


I don't really know enough about symmetry groups in this context to answer that. Hopefully someone more knowledgeable will drop by!
 


Okay, thanks for your answer!
 

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