Transformer with Single Turn Secondary in an Induction heater

I was thinking of a circuit which essentially has a series LC circuit connected in between an H bridge. There were certain things, I wasn't sure if I understand correctly, and would appreciate any input about it.

Neglecting the details of the L & C values. Now if I was to turn on M1 and M4 at the same time, while turning off M2 and M3 and the other way around in the other cycle.

I would expect an AC square wave, which when passes through the LC low pass filter, I would expect a Sine wave in the middle of L and C.

Here is the part I want to confirm I understand correctly: Now if I was to run this at resonance, then the voltage in the middle will have the highest peak at that frequency.

If my Inductance was actually a work coil(that is used in an induction heater) and I was to play a steel rod in between or across it, then am I correct in assuming that this will behave like a step down transformer ?

So my work coil will be the primary with the high voltage, and the steel rod would be the single turn secondary, thus voltage steps down and CUrrent multiplies and causes eddy currents in the rod to heat it up.

Thanks for looking.