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I am having trouble understanding how to find symmetries given a

  1. Oct 15, 2011 #1
    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?
     
  2. jcsd
  3. Oct 15, 2011 #2
    Re: symmetry

    Can't you argue that since the potential is not dependent on z or phi, the z and phi components of E vanish?
     
  4. Oct 15, 2011 #3
    Re: symmetry

    Ah yes! That would take care of it! Nice. Is there any other more general approach? Like symmetry groups somehow?
     
  5. Oct 15, 2011 #4
    Re: symmetry

    I don't really know enough about symmetry groups in this context to answer that. Hopefully someone more knowledgable will drop by!
     
  6. Oct 15, 2011 #5
    Re: symmetry

    Okay, thanks for your answer!
     
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