Test as per wattsup's description.
Long and boring for most,but it is interesting to see the difference the core makes when i slide it into the primary coil.
What you observed is exactly as expected. But before going into detail may I try to steer you away from what appears to me to be some incorrect perceptions. You keep mentioning flux lines "cutting" the secondary which suggests to me that you believe the flux lines have to touch the conductor. Wrong!! It is the flux lines that don't touch the conductor that do the work, it is the flux lines that pass through the coil, with is why I used the term "threading".
You might ask how is it that flux that doesn't actually impinge on the conductor can create a voltage in it, and that requires a more detailed answer that goes into the realms of another type of field known as the vector magnetic potential which is given the symbol A
. In reality the current flowing in the primary coil, plus any atomic current circulations flowing in the core if it is present, create circular A
field lines both within the coil and outside the coil. Because the primary current is AC then so are these circular A
fields, and the time rate of change of the A
field then creates the circular E
field that can drive electrons around a circular wire. That A
is now considered to be the primary field which then produces the magnetic B
field that we are all familiar with. The B
field comes from the manner in which the A
field changes spatially, and in particular how the A
field changes value if you take an observation point by moving sideways from the field line. There is a vector function of space known as the "Curl" that describes the spatial change in A
needed to create B
, and we end up with the formula B
). So current scientific philosiphy is that B
comes from A
, that E
comes from a time-changing A
, and therefore if you have that E
there must also be a time-changing B
present that is related to E
If you find all this confusing then just forget it and go back to the simpler viewpoint that it is the time changing B
that produces circular E
. Those circular E
lines exist within the B
flux in the primary coil having zero value at the centre rising to a maximum at the inside edge of the coil. Then outside the coil the value decreases as you move to ever larger radii. For any given radius the value of E multiplied by the circumference gives you the volts-per-turn for a coil of that radius. And that volts-per-turn is equal to the rate of change of total flux passing through the coil (not flux cutting or touching the conductor). That is usually just the primary flux but for the coils you are playing with some of that primary flux can return through your large radius secondary so that the total flux gets reduced. This effect would not be very noticeable with your very long primary coil because your secondary is quite close to the primary. Only when your secondary is at a radius comparable to the primary coil length would you get any significant flux loss.
That brings me onto your video. Without the core your "transformer" is a poor one (at 50Hz) because the primary inductance is not high enough. The input is mainly resistive so the input current is in phase with the voltage (which you show at the end of your video). That primary current creates flux, then since output voltage comes from rate-of-change of flux you get a secondary voltage that is almost 90 degree shifted from the primary voltage. If you did any power measurements you would have an inefficient transformer.
With the core in place the primary inductance has increased so now it works much better as a transformer. You find that primary and secondary voltage are almost in phase (or anti-phase depending on the polarity of the coil connections). In that "good transformer" condition the flux that is creating the secondary voltage is the magnetizing flux that comes from the "magnetizing current" in the primary and that current is 90 degree shifted from primary voltage. Electrically it does not represent a power flow from primary to secondary (although in the magnetic domain the magnetizing flux does represent power flow along the magnetic circuit). With no load on the secondary the 90 degree shifted magnetizing current is the only current flowing (that ignores primary coil loss, in reality there will be a little in-phase current). When there is a secondary load you get an in-phase component of current flowing in the primary, and electrically that (multiplied by the primary voltage) represents the power being transferred to the secondary. IMO your tests agreed with all this transformer action.
The increase in secondary voltage as you moved the core into the primary coil is fully explicable and what would be expected. The primary inductance value gradually increased, and since flux for a given current is proportional to L, this resulted in increased flux hence increased secondary voltage.
As regards the air cored tests showing maximum voltage with the secondary coil at the centre, this fully demonstrates the typical flux pattern in a solenoid.