I have studied that curl of electrostatic field is zero Or $\nabla \times \mathbf E =\mathbf 0$ and hence we can say that E has a electrostatic potential $(v)$ but why the curl of this electrostatic field is zero? Rather $\nabla\times \mathbf E=\mathbf 0$ implies that the electric field is irrotational.
But why can't electric field be a rotational vector ?
Can I any how make an electric field rotational so that $\nabla\times \mathbf E\ne \mathbf 0$ like $\mathbf E= (q/4\pi\varepsilon)(y~\mathbf i+x~\mathbf j)\,?$
Here it has non-zero curl
On the other hand $\nabla\cdot \mathbf E=\rho/\varepsilon\ne 0$
So this implies that electric field has non zero divergence.
So in the nature of electric field vector something is coming out or coming in.
So I can't understand why the curl of electric field is zero and divergence of electric field is non zero, in the sense of physical significance of curl and divergence.