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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 $z$.
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