This is becoming clearer to me with a little more thought.
It all boils down to the difference between Potential and Kinetic energy.

I agree that the anvil has potential to do Work equal to the Force of gravity multiplied by the diStance that it could potentially fall.
It's when you apply your logic to the
kenetic energy of the anvil that one makes the error I did.
Here is amother way of looking at it:
When the anvil is suspended in the air by the electromagnet it is
not moving
relative to the earth.
Therefore the Work done = the Force of gravity multiplied by zero.
Therefore zero work is being done by the electromagnet to hold the anvil in the air.
If zero work is being done
and energy IS the ability to do work.
http://library.thinkquest.org/20331/physics/physics.htmlthen zero energy, in the form of electricity is needed to hold it there and it will simply float there to the amazement of everyone!
I still mantain that the laws of physics are a little vague.
The law W=FxS should be modified to:
W=Fx Potential diStance that the object could move, or is moving, due to said Force.
All I can do now is pat myself on the back for seeing the vagueness in the above law.
