Understanding Electromagnetic Induction: Flux and Induced e.m.f.

[accountdracula]

I'm studying electromagnetic induction and I'm trying to understand a couple of things:
Why is the flux greatest when the angle between the conductor and magnetic field is 90 degrees?
How does the induced e.m.f oppose the change which induces it?
My thoughts:
The flux is greatest when the angle between the conductor and magnetic field is 90 degrees because there is the greatest magnetic flux density within the coil when this condition is met. Is this correct and is this the only reason?

Induced e.m.f creates a current which has a magnetic field around it which is in the direction opposite to that of the magnetic field which induces the e.m.f, thus cancelling it out. Again, is this right?

 

[BvU]

I'm studying electromagnetic induction and I'm trying to understand a couple of things:
Why is the flux greatest when the angle between the conductor and magnetic field is 90 degrees?
How does the induced e.m.f oppose the change which induces it?
My thoughts:
The flux is greatest when the angle between the conductor and magnetic field is 90 degrees because there is the greatest magnetic flux density within the coil when this condition is met. Is this correct and is this the only reason?

Induced e.m.f creates a current which has a magnetic field around it which is in the direction opposite to that of the magnetic field which induces the e.m.f, thus cancelling it out. Again, is this right?

(1) Not so much the flux density as the area through which flux lines pass
(2) Yes. Whether it cancels is to be seen, but it surely opposes.
All to do with the Lorentz force (which google).