# How is there not an infinite regress in the emf of a motor?

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?

Thanks.

• Worth looking at? physics.stackexchange.com/questions/233089/… – Farcher Jul 6 '16 at 9:54
• Is your question essentially how can your simple motor reach (or have) a steady state? – Alfred Centauri Jul 6 '16 at 10:24
• In part, yes, it is. – Gauri Jul 6 '16 at 11:04
• The sign of the emf opposes the battery voltage until the current trough the coil's resistance is just enough to make up for the loss of energy due to friction and torque (load) of the motor. See en.wikipedia.org/wiki/Motor_constants – CuriousOne Jul 6 '16 at 13:34