joule per tesla

The joule per tesla answers a slightly odd-sounding question, how much energy a magnet trades against a field, and the equivalence in the definition is the whole trick: one joule per tesla is one ampere square metre, the moment of a one-amp current circulating around a one-square-metre loop. Torque in a field follows $\tau = mB\sin\theta$ and the alignment energy $U = -mB\cos\theta$, so the same number states both how hard a compass needle is twisted and how much energy it gives up by swinging north.

Magnitudes in this unit span more of nature than almost any other on the site. An electron's intrinsic moment is about $9.3 \times 10^{-24}$ J/T, the Bohr magneton listed beside this entry; a proton's is roughly 660 times smaller still, and that tiny moment is the signal MRI machines coax out of the body. A one cubic centimetre neodymium magnet carries about 1 J/T, and the Earth's core currents amount to a dipole of about $8 \times 10^{22}$ J/T. That is some forty-six orders of magnitude between electron and planet, all quoted in one unit without a prefix change looking strange at either end.

In the laboratory the unit's CGS rival is still alive: magnetometer output is routinely labelled emu, the erg per gauss, exactly one thousandth of a joule per tesla, and that entry beside this one carries the conversion and its traps.