I think the magnetic field is assumed to be uniform B=B[sub]0[/sub].

The magnetic flux pass through the coil depends on the angle ,

assume the coil rotate at constant angular velocity .

i.e.

From Faraday's law, induced voltage

So the voltage is a sine wave (without commutator).

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i agree with the above analysis that AC generator (without commutator) the emf induced in the coil is a sine wave.

so is it that with a commutator, which flip the current in half cycle rotation, therefore emf induced in the coil will be a |sine| wave?

if that is true, then i understand why the emf induced is |sine| wave.

By the way,

i am certain http://hyperphysics.phy-astr.gsu.edu/HBASE/magnetic/motdct.html is accurate for torque vs time is a |sine| wave.

[img]http://hyperphysics.phy-astr.gsu.edu/HBASE/magnetic/imgmag/dcmtorv.gif[/img]