An electromagnetic induction question

[herich]

There is a soft iron bar, with two coils wound at the two end. A current source is connected to the primary coil. A resistor is connected to the secondary coil.

So, the question is:
"Whether increasing the area of the secondary coil but keeping the area of the primary coil unchanged can increase the induced voltage across the resistor connected the secondary coil?"

My attempt:
Correct,
since according to Faraday's Law, induced emf is proportional to the area of the secondary coil.

But the answer is incorrect. Actually why? Thanks

 

[marcusl]

The reason is that the iron core has such high permeability \mu that most all the flux from the first coil is found in the core and virtually none is in the air. Increasing the 2nd coil's area therefore doesn't increase the flux enclosed. In fact, the flux in the 2nd coil decreases a little because its bigger area now encloses some of the return flux that exits the end of the rod and bends back into the end of the rod at the 1st coil. The field lines of the return flux point opposite to those in the core so the net flux in coil 2 drops as its area increases.

 

[herich]

I see. That means however the secondary coil 's area change, B-field only exists along the iron core. So, the "effective" area of the area of the secondary coil is still the same. Thanks!