# Homework Help: I am having trouble understanding how to find symmetries given a

1. Oct 15, 2011

### 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?

2. Oct 15, 2011

### capandbells

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?

3. Oct 15, 2011

### berra

Re: symmetry

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

4. Oct 15, 2011

### capandbells

Re: symmetry

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

5. Oct 15, 2011

Re: symmetry