First law says that when current flows through a conductor, PROPORTIONAL magnetic field is produced around the conductor.
Second law says that when a conductor is kept in a CHANGING magnetic field, proportional e.m.f. is produced around the conductor.
Thus the working principle of an electric motor is based on the magnetic effects of current. A current-carrying coil experiences an angular force and rotates when placed in a magnetic field. The direction of rotation of the loop is given by the Fleming's left-hand rule.
The electric motor works on the principle of force experienced by a current carrying conductor in a magnetic field. The two forces in the opposite sides are equal and opposite. Since they act in opposite direction they can produce the rotational motion.
A device that reverses the direction of flow of current through a circuit is called a commutator. In electric motors, the split ring acts as a commutator.
Suppose there are two rotating coils used having the terminals AB and CD. Then the reversal of current also reverses the direction of force acting on the two arms AB and CD. Thus the arm AB of the coil that was earlier pushed down is now pushed up and the arm CD previously pushed up is now pushed down. Therefore the coil and the axle rotate half a turn more in the same direction. The reversing of the current is repeated at each half rotation, giving rise to a continuous rotation of the coil and to the axle.
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