Since magnetic fields and magnetic force are caused by motion relative to an electric field, how can a static bar magnet create a magnetic field and exert a magnetic force on another static object, and how can a magnetic force from a bar magnet do work when magnetic force cannot do work? (Bar magnets can do work...
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answers:
YKhan say: The short answer is that there are moving electrical charges within a permanent magnet, they just circulate within the domains of the magnetic material itself.
Magnetic charges are created by moving electrical charges and where the movement creates a length contraction through Special Relativity. The SR's length contraction makes certain charges (i.e. negative or positive) less dense or more dense than the other charge within a given volume of the magnetic material.
https://youtu.be/hFAOXdXZ5TM
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Andrew Smith say: Energy can be stored in many ways.
It takes energy to line up the magnetic domains to form the magnet.
That energy IS available to do work.
Now if you bring a piece of steel nearby and the magnet attracts that steel it does some work.
But you then try to pick up some paper clips with the result. It can't pick up anywhere near as many so we know that the field has been reduced.
Every time the bar magnet does work the resultant field is lessened.
Of course if you pull the steel away the magnetic field strength is restored.
But then you have put the energy back into the field by doing work on the magnet.
To that extent the magnets do no net work other than the work that is stored in them by their very creation.
In your example of one magnet lifting another the magnet does NOT do work.
There is no movement between the magnets so that it exerts a static force .
Work = force * distance = force * zero = no work.