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Lenz's Law (the parent / child relationship)

In 1835 Heinrich Lenz stated the law that now bears his name.  An electric current induced by a changing magnetic field will flow such that it will create its own magnetic field that opposes the magnetic field that created it.  These opposing fields occupying the same space at the same time result in a pair of forces.   These forces are felt when you turn a generator and generate electricity.  The more current you generate, the greater the force opposing you.

This force can also be felt if you try to drag a conductive, non-magnetic plate between the poles of a horseshoe magnet.  The plate sees a changing magnetic field which creates a current in the plate, which creates its own magnetic field opposing the one that created it.

steel through copper tube Another great example of Lenz's law is to take a copper tube (conductive but non-magnetic) and drop a piece of steel down through the tube.   The piece of steel will fall through, as you might expect.  It accelerates very close to the acceleration due to gravity. 
(Only air friction and some possible rubbing against the inside of the tube prevent it from reaching the acceleration due to gravity.)
magnet through tube (current being shown) Now take the same copper tube and drop a magnet through it (hopefully a strong one, Neodymium or other rare earth magnets work the best)    You will notice that the magnet falls very slowly.  This is because the copper tube "sees" a changing magnetic field from the falling magnet. This changing magnetic field induces a current in the copper tube.
induced current resists with its own magnetic field The induced current in the copper tube creates its own magnetic field that opposes the magnetic field that created it.
 
So it is slowed by the force of repulsion of the two magnetic fields.