Suppose I have a conducting wire attached to a battery and it carries some current. As a result there also exists a magnetic field around the wire. If I then detach the wire ends from the battery, the current ceases to flow and subsequently, there is a varying magnetic field around the conductor which acts as a source to create an electric field in the surrounding. This varying electric field in turn produces a magnetic field and the cycle will continue. My questions are as follows,
(1) Is the above reasoning correct? Does this actually happen?
(2) If yes then from where did the energy now stored in the electromagnetic field come from?
(3) Also, will this energy propagate outwards in space or will it remain localized in the surroundings?