EASA Module 3.12 · DC Motor Theory
A current-carrying armature in a magnetic field feels a force F = B·I·L. Switch the commutator off and watch the torque reverse every half turn — the motor stalls and rocks instead of running.
Each side of the armature carries current in the opposite direction, so the two forces form a couple that turns the coil. Torque is proportional to B·I·cos θ — greatest when the coil plane lies along the field, and momentarily zero as it passes through the vertical.
The commutator reverses the armature connections at exactly that zero-torque point, so the current in each limb flips just as it crosses from one pole to the other. The torque therefore always acts the same way round. Turn it off and the raw torque follows cos θ, averaging to nothing.
Notice the back-EMF. As speed rises it opposes the supply, so armature current falls: I = (V − E_b) / R_a. At the instant of starting the speed is zero, there is no back-EMF, and only the small armature resistance limits the current — which is exactly why starting current is so high. Use Fleming's LEFT hand for a motor (right hand is for a generator).