How to calculate Electric field curl in loop by dipole charge?

Let us consider that two charges $q^+$ and $q^-$ are placed at the ends of a rod and attached to its ends,
Now the question says if we pass this rod inside a metal loop and take it out, as in Faraday’s experiment, but here we did not use a magnetic field but an electric field but its spacing is zero
$$vec{nabla}cdot{vec{E}} =0$$

I write the curl of the electric field created in the loop
$$vec{nabla}timesvec{E}_{text{ring}}=-frac{partial {vec{E}}_{text{charge}} }{partial t}$$
I do not know if I am on the right path or not, and I do not know where the error is.