Initially, a point($P$) is defined in space, with a magnetic field($-B\hat{k}$) produced by a current element ($Idl$). If the wire begins to move in the $-v\hat{i}$ direction, would that produce an electric field around $P$ since the magnetic field is changing?
$$ \nabla \times E = -\frac{\delta B}{\delta t}$$
I ask this because, I've been pondering with Faraday's paradox, and remembered this experiment:
One of the steps states the following result:
The disc is held stationary while the magnet is spun on its axis. The result is that the galvanometer registers no current.
The reason(which was very insightful) for that is; rotating the magnet(and the dipoles within) does not cause the magnetic field to move.
Which made me consider the case of a current carrying elements. I know that system is not applying the Lorentz force(specifically the the magnetic force ($v\times B$)).
In addition, if the wire(or $Idl$) moves in any other direction would it still yield an non-conservative $E_{ns}$?
How is the current element and it's relation to the magnetic field produce by it, dynamically different than the rotating magnet with a stationary magnetic field produced by the magnet?