Loss of energy due to creation of electromagnetic waves

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?

• a) yes b) It is stored in the current, i.e. kinetic energy of electrons c) The emitted electromagnetic field will propagate outwards. This is roughly how antennas work – Jannick Aug 22 '18 at 13:51
• @Jannick How exactly will the field/energy propagate outwards? – Rutwik Aug 22 '18 at 14:01

The direction in which the wave propagates will vary depending on the wire. If you have a straight wire with $l$ >> $\lambda$, one could approximate that the wave will radiate outwards from the wire equal in all directions (of course this does not hold for the edges of the wire, but hey, it's an approximation)