Magnetron Twins: Electromagnetism / Polarity Lock

Electromagnetism & Plasma arc, page 76 of 193. Back to The Pixelated Physics Universe

Who they are

By classical physics, there should be no magnets. Magnetism in matter comes mainly from electron spin, about one Bohr magneton each; in iron, the exchange interaction lines the spins up. Two dipoles attract nose to tail, and side by side, pointing the same way, they repel. Magnetron Twins on a pixel-art unisex tee; equation, symbols and sources in the panel below.

Magnetron Twins is a character of the Electromagnetism & Plasma arc: drawn in pixels, ruled by one piece of real physics, and never allowed to break it.

The physics

The energy of two small magnets depends on both their distance and how they are oriented relative to the line joining them. Aligned end to end they attract, and side by side and parallel they repel, with the energy falling off as one over r cubed.

$$ \begin{gathered} U = -\frac{\mu_0}{4\pi r^{3}}\left[3(\vec m_1\cdot\hat r)(\vec m_2\cdot\hat r) - \vec m_1\cdot\vec m_2\right] \end{gathered} $$

Symbol Meaning SI unit
$U$ interaction energy J
$\mu_0$ vacuum permeability N/A²
$\vec m_1, \vec m_2$ magnetic dipole moments A·m²
$r$ separation m
$\hat r$ unit vector between dipoles 1

Sources

Crossovers

Magnetron Twins meets Monopola (Dirac's Monopole). The Magnetron Twins are dipoles: north and south always come together, because every known magnet is made of spinning electrons and currents. Monopola would be a lone pole, and no one has ever confirmed finding one.

Magnetron Twins meets Remanenza (Magnetic Hysteresis Loop). The Magnetron Twins line up their electron spins through exchange. Remanenza remembers the field that lined them up: drive the field back to zero and some magnetisation stays, which traces out a hysteresis loop.

Wear the lore

Concept keywords: Electromagnetism / Polarity Lock, Magnetron Twins, Electromagnetism & Plasma, physics lore, Pixelated Physics