I am having trouble understanding how to find symmetries given a

[berra]

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?

 

[capandbells]

Can't you argue that since the potential is not dependent on z or phi, the z and phi components of E vanish?

 

[berra]

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

 

[capandbells]

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

 

[berra]

Okay, thanks for your answer!