Who or What is Doing Work on the Rod in a Superconducting MRI Magnet?

[vabamyyr]

Suppose I have a superconducting solenoid MRI magnet (cooled with liquid helium) producing a static magnetic field around it. I approach the magnet bore with a steel rod in my hand. The rod starts to pull towards the magnet and i have to work against the pull in order not to let it attach onto the machine. Now my question is, have I reduced the energy of the static magnetic field when I've pulled the rod away from the magnet or is there some sort of compensatory mechanism that keeps the static field fixed to its nominal value? I know that the pull is largely due to the spatial gradient of the magnetic field but what or who is doing the work on the rod?

 

[tiny-tim]

Hi vabamyyr!

It's the same as carrying a rod downstairs …

the potential energy of the rod (gravitational or magnetic) changes, but since PE is just another name for work done by a conservative field, that's another way of saying that work is done by the field.

Work is also done by you, and so long as the two cancel, the KE remains zero, and the rod stays in your hand.

 

[Bob S]

When a steel rod is inserted into a magnetic field, the stored energy in the magnetic field decreases. The stored energy is the integral

Stored magnetic energy = 1/2 ∫B·H dV where integral is over all space.

Air can store more magnetic energy than steel for a specific B. So inserting a steel rod reduces strored energy.

Bob S

 

[arithmetix]

I am very, very uncomfortable with the idea that a field does work. Next thing, we'll have to say that a field has energy.

I think the situation is exactly that of a susceptible object in any other field, say the gravitational field about the Earth. Drop something, pick it up... where did the energy come from? Was it in the gravitational field or was it a property of the object which was raised on high?

In your magnetic field, a magnet and a steel bar find themselves attracted to one another; if you had collected all the energy converted in the approach you could use it again to get yourself out.

 

[vabamyyr]

does that mean when I repeatedly let the magnet pull the rod and me pulling it back ultimately reduce the field strength to 0?

 

[Dale]

does that mean when I repeatedly let the magnet pull the rod and me pulling it back ultimately reduce the field strength to 0?

No. Every time you insert the rod work is done on the rod and the energy of the field decreases. Every time you pull the rod back out the rod does work and the energy of the field increases back to where it was.

 

[Dale]

I am very, very uncomfortable with the idea that a field does work. Next thing, we'll have to say that a field has energy.

The field does have energy. See: http://farside.ph.utexas.edu/teaching/em/lectures/node89.html"

 

[vabamyyr]

thank you DaleSpam