Problem 1.3. Find a vector field \(\vec{E}(\vec{r})\) in \(\mathbb{R}^2\) such that:
\(\nabla \times \vec{E} = \vec{0}\), \(\nabla \cdot \vec{E} = \rho\),
where \(\rho\) represents a point of charge \(2\pi\) placed at the origin,
\(\rho(\vec{r}) = 0\) for \(\vec{r} \neq \vec{0}\), and \(\iint_{\mathbb{R}^2} \rho dA = 2\pi\).