Say we have a coil connected to a battery in a uniform magnetic field, perpendicular to the magnetic moment of the coil. This is a simple motor. There is a torque on the coil that varies with the angle θ between the field and the moment. Clearly, the angular velocity ω is not constant.
Here is my concern: since the flux through the coil is changing in time, there is a back emf in it. This will reduce the net emf, which will reduce the current. That will reduce the torque on the coil which in turn will change the angular velocity in time (I imagine it is the angular velocity that determines dΦ/dt in the first place) and that should change the back emf...one can see where this is going.
What is happening here? And how does one calculate dΦ/dt?