Electric Field Inside a Cylindrical Gaussian Surface: Exploiting Symmetry

[jaejoon89]

What is the electric field inside a cylindrical Gaussian surface in terms of volume charge density?

 

[Defennder]

What is the charge configuration ie. how are the charges distributed? Or are you referring to $$\nabla \cdot \mathbf{D} = p_V$$?

 

[jaejoon89]

I'm not familiar with that notation (the upside down triangle). I was given volume charge density and needed to find the electric field inside an infinitly long cylinder. I know rho (vol. charge density) = Q/V but don't know what to use for the volume, since it's infinite.

 

[Defennder]

Okay, then in that case just ignore the notation above. Now, exploit symmetry here. Do this by considering a cylindrical Gaussian surface in the cylinder with the same geometrical axis. How do you find the flux through the closed surface and hence the field? Never mind if it's infinite. That is just a hint to ignore some parts of the Gaussian surface.