Back emf in Motors

Lenz’s Law can be used to explain an interesting effect in electric motors.  In an electric motor, a current supplied to a coil sitting in a magnetic field causes it to turn.  However, while the coil of the motor is rotating, it experiences a change in magnetic flux with time and by Faraday’s Law an emf is induced in the coil.  By Lenz’s Law this induced emf must oppose the supplied emf driving the coil.  Thus, the induced emf is called a back emf.  As the coil rotates faster, the back emf increases and the difference between the constant supplied emf and the back emf gets smaller.  Clearly, this difference between the two emf’s is equal to the potential difference across the motor coil and hence determines the actual current in the coil.

It's the back EMF that sets the speed for a particular voltage, which is why DC motors can easily be speed controlled by varying the supply voltage.
That will keep happening (more torque loading = less speed & more current) all the way down until the motor stalls and it is taking the full current allowed by the resistance of the circuit with zero back EMF.

When the motor is first turned on and the coil begins to rotate, the back-emf is very small, since the rate of cutting flux is small.  This means that the current passing through the coil in the forward direction is very large and could possibly burn out the motor.  To ensure that this does not happen, adjustable starting resistors in series with the motor are often used, especially with large motors.  Once the motor has reached its normal operating speed, these starting resistors can be switched out, since by then the back emf has reached a maximum and has thereby minimised the current in the coil.

If the load on the motor is increased at some time, the motor will slow down, reducing the back-emf and allowing a larger current to flow in the coil.  Since torque is proportional to current, an automatic increase in torque will follow an increase in load on the motor.