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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:

ac generator

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:

concave poles

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

user3407319
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  • 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 00:28
  • @nielsnielsen what does this mean? – user3407319 Dec 17 '18 at 07:01
  • it makes the geometry of the motor and field magnets easier for you to understand. – niels nielsen Dec 17 '18 at 07:10
  • 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
  • their "degree of uselessness" varies with the angle of rotation of the rotor. the pull exerted on the wires is at a maximum when the wires are at the center of the two pole pieces and nearly zero when the wires are all the way out of the gap. – niels nielsen Dec 17 '18 at 16:47
  • @nielsnielsen so the graph isn’t really a very accurate sine curve? – user3407319 Dec 17 '18 at 19:30
  • it's close, so OK for our purposes.. – niels nielsen Dec 17 '18 at 19:52
  • @nielsnielsen thanks. I just have one more question, why don’t we use a magnet like the one in this photo: https://goo.gl/images/CE9fzy ? That way it will be more uniform i guess? – user3407319 Dec 17 '18 at 19:57
  • easier to "shape" the field through the use of clever pieces of iron stuck to the magnet faces. these are called "pole pieces" and they guide the field lines where you want them to go. iron is lots easier to cut and form than the stuff the magnets are made from. – niels nielsen Dec 17 '18 at 20:10

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