he field induced will have ideally, shape of the source variation, (temporal nature) with a damping on a time scale by coil damping factor. Ex. If temporal variation is linearlly moving up and down with a periodic time of t, the induced field will also vary with the same nature assuming no damping or else, it can have shape with alongation on a rise and fall time.
Raul, I suggest that an electric field is not created - unless the loop is gaining charge as well as carrying current - and I suggest that a toroidal magnetic field is created.
The things are a little bit more complex that Zotan said or I have understood him. Let me try to explain it.
I f you have a coil with an AC current this produces a variable magnetic field that induces an electromotive force (Faraday law) between the coils and no in besides in the central axis. But this also translates to oppose one current (Lenz law) trying to avoid the change of magnetic flux. And finally you have a new flux opposing the original one between each two coils which is equivalent to have a resistive impedance. Finally this is simple to take into account just giving the self induction L equivalent of the coil.
Sorry, I want to say the interaction between each two wire loops within the coil. I know that you have only one coil. No between two coils.
The thing is that the current which goes to the wire loops of the coil creates a variable magnetic field or variable magnetic flux. This creates also an electromotive force which an opposite current to the initial one in such a form that you have a kind of resistance where the current diminished: resistive impedance. This is in fact larger convergent process because you create a variable magnetic field which produces electric one (Faraday) but variable magnetic field again creates a new magnetic field (Ampere) and so on. The form to take into account all this process and if we have only one coil (no coupling between coils) can be summarized introducing the self induction paramete L which tells us that
V/L =deritative with respect to time of the current i initial.