In cylindrical coordinate system, the potential produced by a uniform ring charge is given by $\phi = f(r, z)$ where $f$ is a continuous function of $r$ and $z$. Let $\vec{E}$ be the resulting electric field. Then the magnitude of $\nabla \times \vec{E}$
1. Increases with $r$
2. Is $0$.
3. Is $3$.
4. Decreases with $z$.