I was studying how electromagnetic waves (EM waves) were generated and propagated. I was shown a dipole antenna with an AC source sloshing charges back and forth.

To my understanding, when the charges are accelerated their field lines change and "update" the existing field lines, effectively creating a pulse of electric field lines, shown below (credit to Alfred Centauri here) which race off to infinity

As this was a current in the wire, it also would create a matching magnetic field, which also races off to infinity on it's own right? So with these two elements we have completed the electric and magnetic part of the EM wave.

However, the textbook also talks about how there are changing electric fields which induce magnetic fields (and vice versa). Where does that happen? I don't think that the electric field needs anything to "induce" the front of it right? Don't the electric and magnetic fields just keep on propagating because they're field lines?

I was studying how electromagnetic waves (EM waves) were generated and propagated. I was shown a dipole antenna with an AC source sloshing charges back and forth.

To my understanding, when the charges are accelerated their field lines change and "update" the existing field lines, effectively creating a pulse of electric field lines, shown below (credit to Alfred Centauri here) which race off to infinity

As this was a current in the wire, it also would create a matching magnetic field, which also races off to infinity on it's own right? So with these two elements we have completed the electric and magnetic part of the EM wave.

However, the textbook also talks about how there are changing electric fields which induce magnetic fields (and vice versa). Where does that happen? I don't think that the electric field needs anything to "induce" the front of it right? Don't the electric and magnetic fields just keep on propagating because they're field lines?

So my question is, how does this "induction" occur and how does it produce the next segment of the wave?