If I had a simple transformer Core with Primary on the left and
secondary on the right. If I sliced the core in half seperating the
primary from the secondary would the two sections repel or attract?
The physical forces always act to attempt to shorten the magnetic
path.
You talk about a 'simple' transformer with windings on the left and
the right. I have to assume you are describing a U-U structure or a
torus, both fairly special structures in real life, and seldom wound
as you describe.
For a start, for a transformer to be a transformer, the circuit must
be completed - this usually involves a load and a source. Without
either, you have a mock-up-only science project, or an unneccessarily
complex inductor.
Once the circuit is complete, you can actually have transformer
action.
The shortened magnetic path could be achieved in your 'simple' circuit
if the ends of the winding structures were closer together - a force
will therefor be applied to attract these ends together.
If they were wound side by side on the same axis, the force would be
exerted to pull distant ends together - if this is equal in all
directions the result is force impelling the coils towards each other.
As few things are really as equal or symmetrical as they seem, in real
life the axial winding will try to bend, under extreme applications of
external energy.
This effect can be seen for common-mode impulses applied to cheap
common-mode EMI chokes wound on E-E structures, using partitioned
bobbins. A hefty common-mode surge (lightning) will cause them to fold
over like a sandwich made from a single slice of bread - folding axis
being the core joint in line with the bobbin's partition.
RL