# Magnet and needle

When I place a needle near a clamped magnet and let it go, it moves towards the magnet. Since magnetic field cannot work on individual charge particles, we must conclude that the needle loses its overall internal energy and hence cools down! Is this true?

• Why "must we conclude" the energy loss in the needle? – Kyle Kanos Nov 5 '15 at 0:36
• Dr, it is not the force between a magnetic field and a charge, but between two magnetic fields.en.wikipedia.org/wiki/… – user83548 Nov 5 '15 at 0:51
• @KyleKanos If you think of a needle as a collection of ions, isn't it clear that the individual speeds of the ions do not change in the magnetic field. But the needle accelerates as a whole system so it must lose internal energy. – user97646 Nov 5 '15 at 1:02
• think of each ion as a little magnet too – user83548 Nov 5 '15 at 1:22

## 2 Answers

The total energy stored in the magnetic field goes down - that's where the energy to move the needle comes from. The "internal energy" of the atoms inside the needle has nothing to do with it.

• What is the "Energy stored in magnetic field"? Sorry for my ignorance. Also, if we view the magnet + needle + table (on which the magnet is clamped + earth etc.) as a mechanical system, who loses energy in the end? – user97646 Nov 5 '15 at 1:26
• Magnetic field lines in space contain energy - $\frac12 \frac{B^2}{\mu}$ see for example this link. As the needle approaches the magnet, the shape of the magnetic field lines changes - while they will be closer together in some areas (thus higher energy per unit volume), other (larger) regions will have a lower magnetic field. The net result is that there will be less energy stored in the magnetic field. – Floris Nov 5 '15 at 1:30

Yeah I think that's right, put spins in a magnetic field and they fall into the lower energy state, (with a time given by T1) it's the first step in magnetic cooling.

Edit: As Floris pointed out I got this backwards. As the spins go into a lower energy state the energy they had has to go somewhere.. into the lattice (or needle in this case.)

• In magnetic cooling, the cooling happens when you remove the magnetic field and the ordered atoms become disordered again. – Floris Nov 5 '15 at 1:31
• @Floris, Right! (my mistake) I'll edit my answer. (That's what I get for thinking too fast.) – George Herold Nov 5 '15 at 15:54