There is a use for curl - Faraday's Law!

Faraday's Law in integral form is the following: $$ \oint_C \vec{E} \circ d\vec{l} = -\frac{d}{dt} \int_S \vec{B} \circ \hat{n}dA $$

It states that the circulation of an electric field \( \vec{E} \) around a closed path \( C \) is equal to the negative time derivative of the flux of the magnetic field through the surface \( S \) bounded by \( C \).

In other words, changing magnetic flux induce electric fields which form closed loops.