Magnetic moment

Taken in a break on my visit to Lichfield
I very much enjoyed appearing at the Lichfield festival on Sunday to speak about Build Your Own Time Machine. At the end of the talk, I opened things up to questions, as usual offering to discuss not only the subject of my talk, but any aspect of physics or science communication. And I came a bit of a cropper.

I'm generally able to answer the typical questions that arise on abstruse topics like relativity or quantum theory. I cope, on the whole, with the latest news stories - I've lost count of queries about the LHC and Higgs bosons or, a little while ago, faster than light neutrinos (remember them?). But the ones that tend to catch me out have a habit of being questions that rely more on the kind of basic physics I've not had to think about for a long time. And the one that tripped me up on Sunday was just such a question. It was about magnetism.

The questioner asked why is that a (permanent) magnet doesn't run out of energy. After all, it seems to be able to hold a piece of metal up against the force of gravity indefinitely.

I could answer part of the question. If you think of the magnet attracting a piece of metal up off the ground, then keeping it in the air, it only takes energy to move the metal. Keeping it in place takes no energy. It can be useful to think of what happens with gravity, as it's something we're more familiar with than magnetism. If I lift a ball off the floor and put it on a table, I do work (use energy) to lift the ball against the pull of gravity. But once the ball is on the table there is no energy being used to keep it there. How could there be? Where would it be coming from? Out of the table? Then surely the table would some how drain away?

We tend to be fooled into thinking there is an exertion of energy required just to hold something up because if we imagine holding a heavy object up for a long time ourselves, our arms would begin to ache more and more and eventually we would have to drop it - but this is all about human physiology, not physics.

That leaves us with the energy needed for the magnet to lift the piece of metal in the first place. Where did that come from? This is what threw me at the time, and I was only able to prevaricate. It's tempting to think that somehow the energy is coming out of the magnet, so if it lifted things often enough it would run out. But that's wrong. Once again this is a case where thinking of the case of gravity can be helpful.

If I lift something off the Earth, then let go, there is energy required to move that object. I put the energy into the system when I lift it, the energy is then 'released' when I let go to propel it back to Earth. Potential energy from its position in the gravitational field is translated into kinetic energy of movement. Exactly the same goes for the magnet. The potential energy the piece of metal has from its position in the magnetic field is translated into the kinetic energy of movement. The energy is not somehow sucked out of the magnet to propel the metal.

I think the reason it's fairly obvious with gravity, but less so with magnetism is that our experience tends to be inverted. On the Earth we usually lift things up against gravity's pull, then let go. The only things that get placed in the Earth's gravitational field from outside (the aspect that confuses us with a magnet) tend to be meteors and other space debris. By contrast, with the magnet we are usually putting the piece of metal in from the outside, so it is less obvious that we are giving it potential energy than if we start with the metal stuck to the magnet and drag it away before letting go.

I am sure I will be caught out again this way. When you are thinking on your feet, unless you are working in a subject day to day, it's easy to get into rabbit-in-the-headlights mode and fail to come with a sensible answer. But it won't stop me giving that open request for questions. What I've got to work on is saying 'I'm not sure, I'll check and get back to you,' rather than woffling as I tend to...