What is Lenz's law, explaining all variables?

Lenz's law, physical law, discovered by the German scientist H. F. E. Lenz in 1834, that states that the electromotive force induced in a conductor moving perpendicular to a magnetic field tends to oppose that motion. When an electric motor is in operation, the armature is turning in a magnetic field, and an emf is thus induced in it. Lenz's law requires that this emf, called back emf or counter emf, oppose the motion of the armature and also the original emf, causing the motor to operate. As a result, the speed of the motor changes in such a way that the energy supplied by the original voltage source less the energy required to overcome the back emf is always exactly equal to the sum of the energy used to drive the mechanism to which the motor is attached and the energy lost as heat within the motor. Lenz's law may thus be seen as a consequence of the law of conservation of energy.

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A law of electromagnetism which states that, whenever there is an induced electromotive force in a conductor, it is always in such a direction that the current it would produce would oppose the change which causes the induced emf. If the change is the motion of a conductor through a magnetic field, the induced current must be in such a direction as to produce a force opposing the motion. If the change causing the emf is a change of flux threading a coil, the induced current must produce a flux in such a direction as to oppose the change.