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Suppose I have a stator, where I've allocated one coil for each phase and I supply a balanced three-phase supply. So the fields, $$B_r = B_{max}\cos(\theta_{mech})\cos(\theta_{elec}) \\ B_y = B_{max}\cos(\theta_{mech}-120)\cos(\theta_{elec}-120) \\ B_b = B_{max}\cos(\theta_{mech}-240)\cos(\theta_{elec}-240)$$ whose sum ultimately gives, $$B_{res} = \dfrac{3}{2}B_{max}\,cos(\theta_{elec}-\theta_{mech}) = \dfrac{3}{2}B_{max}\,cos(\omega_{elec}t-\theta_{mech})$$ which is a rotating magnetic field with a frequency of \$\omega_{elec}\$.

Now, what happens if I've allocated 2 coils for each phase such that each coil crates 4 poles, what will be the resultant field? Will it have four poles rotating? Maybe like this\https://imgur.com/a/hWxnfOm ?

Or does the first set of RYB produce a rotating field \$B_{res1}\$ and second set of RYB produce \$B_{res2}\$ (I've no clue for what's the phase-difference between these two resultants)and the final resultant a sun of these two will be two-pole?

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    \$\begingroup\$ I think you're describing a four-pole motor? These are very common, and yes, the field (and rotor) rotate at half the speed of a two pole. \$\endgroup\$ Apr 3 '20 at 6:28
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I believe that the diagram shown below is what is described in the question. If the coils are positioned and connected correctly, you have a two-pole or a four-pole motor as shown. Six coils could be connected differently to make a two-pole motor. In either case, three phases result in a rotating magnetic field. The field has two or four poles depending on the winding. The shape of the magnetic field in space at an instant in time is something like your animation shows for a two-pole motor. It is like a rounded trapezoid. In a real motor design, there are more coils per phase distributed in more slots to make the shape of the magnetic field more sinusoidal.

enter image description here

Image from Fitzgerald, Kingsley, Umans, Electric Machinery, 4th ed.

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