# Does the magnetic field move with the current element that induced it?

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?

$$\nabla \times E = -\frac{\delta B}{\delta t}$$

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?