Why are there two concave poles in an AC generator

If we suppose that the magnetic poles in the AC generator are regular rectangular bar magnets, then the field lines are supposed to be straight lines as in the photo below:

And then the direction of velocity will be inclined with an angle to flux lines, so we will need to multiply by sinθ as in the following equation:

ℰ=NABωsinθ

But the poles are actually concave so I suppose that the direction of velocity will always be perpendicular to the flux lines as in the following photo:

So if the concave poles are the ones really used, why do we need sinθ in the equation?

• Note that in a real-life generator, the gap between the loops and the pole piece faces is very small. – niels nielsen Dec 17 '18 at 0:28
• @nielsnielsen what does this mean? – user3407319 Dec 17 '18 at 7:01
• it makes the geometry of the motor and field magnets easier for you to understand. – niels nielsen Dec 17 '18 at 7:10
• I still don’t get what does the gap distance have to do with the shape of the flux lines – user3407319 Dec 17 '18 at 13:24
• I mean even if the gap is small, aren’t the flux lines still supposed to be perpendicular to the lateral sides making multiplying by sine the angle useless? – user3407319 Dec 17 '18 at 13:26