Magnetic Torque

A magnetic field exerts a torque on a loop of wire that carries current. The magnetic torque causes the loop of wire to spin around a fixed axis.

Motor

In the above orientations, the loop of wire twists counterclockwise. In the above orientations, the loop of wire twists clockwise.

Equilibrium

When the loop of wire is perpendicular to the magnetic field, the motion of wire loop may be in unstable equilibrium and a slight deviation does not return to the equilibrium state as following Besides, the loop of wire is perpendicular to the magnetic field, the motion of wire loop may be in stable equilibrium and a slight deviation returns to the equilibrium state as following

Commutator

In order to to prevent the stable equilibrium state of the loop of wire and to maintain the loop of wire twists counterclockwise, a commutator is used.

Force on a Magnetic Dipole

Magnetic force 𝑑𝐹=𝐼𝑑𝑙×𝐵, is not point to the left. Therefore using a sneaky way to find the net force to the left 𝐹_magnet by equating the magnetic force pulling the coil to the left due to moving the coil to the right by an external force. 𝑊=∆𝑈, 𝑈=−𝜇⋅𝐵
∆𝑈=𝑊by hand=𝐹by hand∆𝑥=−𝐹magnet∆𝑥
𝐹magnet=−∆𝑈∆𝑥→𝐹magnet=−𝑑𝑈𝑑𝑥
if 𝜇 is constant (typical case), then 𝐹magnet=𝜇𝑑𝐵𝑑𝑥
if 𝐵 is constant, then net 𝐹magnet=0

Generator

Generator converts mechanical energy into electrical energy.

Source and Reference

https://www.youtube.com/watch?v=82TYIjuSi-U&list=PLZ6kagz8q0bvxaUKCe2RRvU_h7wtNNxxi&index=21