# Problem: find power required to keep metal attached to electromagnet

Suppose I need to find out the efficiency of electromagnet (solenoid) mounted on the table.

I energize it so that $$1\text{lb}$$ steel object gets attached to it. I energize it with DC current from a battery so that object only barely kept attached but does not press against the e-magnet, in other words the power provided to e-magnet produces only equal to the gravitational force of the object, no more. Assuming that the vectors of forces are fully vertical, force developed by e-magnet is equal to the weight of the object.

To calculate efficiency I know the input power $$V\cdot I$$ = $$36\ \text W$$ supplied to e-magnet but how to get the mechanical power required to keep the object attached up to e-magnet?

In larger retrospect I want to know how to find the mechanical power required to maintain object's potential energy in a static position without motion.