Faraday closed the switch between battery and primary in his transformer. See diagram . A Transverse Electromagnetic Wave proceeded towards the primary. It contained magnetic as well as electric field (actually a single electromagnetic field). When it reached the front face of the secondary, some of this field leaked out into the secondary as indicated in the second trace of Figure 36 . The front end of the secondary being shorted, no voltage was apparent there (although there was energy), but it developed later, further down the secondary as shown in the second trace. Again looking at the diagram , on reaching the end of the secondary, some of the energy travelling in the secondary continued towards the galvanometer. This energy was also in the form of a TEM Wave, and contained magnetic as well as electric field. However, the galvanometer only measured voltage.
At every stage in this process, a TEM Wave was involved, There was no transfer between electric and magnetic fields. Electric current was not involved.
The energy builds up in the primary of the transformer in a manner similar to the way a capacitor is charged, as in the Figure 3 in my article "Displacement Current" .
The second article; "The Inductor as a Transmission Line" is also relevant.
Ivor Catt 18 September 2012
I have written this for you.
Faraday did not discover electromagnetic induction. He discovered crosstalk. http://www.ivorcatt.co.uk/x147.pdf . My article mainly deals with crosstalk to a second pair of conductors open circuit at the front end. However, Figure 36 shows what happens as in a transformer, when the pair of wires in the secondary are shorted together at the front end. Still, some of the TEM Wave leaks out into the secondary.
The key point is that it is impossible for a TEM Wave to travel along down a pair of parallel conductors (e.g. transformer primary) and leave a second pair of parallel conductors (e.g. transformer secondary) unaffected. The conventional maths at the end of the article proves this, using classical theory