Question

What is back-emf equal to when there is no resistance?

Answer 1

For real motors, back EMF and source voltage come closest to being equal when there is minimum friction in the motor and it is not driving a torque load. Then the current draw is very low and the voltage loss in the motor windings is minimal. 

Answer 2

If the emf due to the solenoid is assumed to oppose the applied voltage and have equal magnitude (in volts), there is zero electromotive intensity in the wire. Since current is assumed to be present, this means the current flows even while total electromotive force vanishes.

This is possible for wire made of perfect conductor (superconductor). In practice, there is always some resistance to current so the coil emf cannot exactly cancel the applied voltage at all times.