Monopola: Dirac's Monopole
Electromagnetism & Plasma arc, page 77 of 193. Back to The Pixelated Physics Universe
Who they are
Monopola carries a single magnetic pole, field lines bursting out like a sunburst. If she exists anywhere, every charge in the universe has to fall in line.
Monopola 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
Paul Dirac showed that if even one magnetic monopole exists, quantum mechanics forces all electric charge to come in whole-number steps. That would explain why charge is quantised. The monopole needs a singular line, the Dirac string, which cannot be seen if the condition holds. Dirac published it in 1931. B. Cabrera (Stanford) recorded one candidate event on 14 Feb 1982 in 151 days of running; it was never repeated.
$$ \begin{gathered} e\,g = \frac{n\hbar c}{2} \qquad (\text{Gaussian units},\ n = 0, \pm1, \pm2, \dots) \\ \mathbf{B} = \frac{g\,\hat{\mathbf{r}}}{r^{2}}, \qquad \nabla\cdot\mathbf{B} = 4\pi\rho_m \quad (\text{hypothetical}) \end{gathered} $$
| Symbol | Meaning | SI unit |
|---|---|---|
| $e$ | electric charge (Gaussian units, statC) | statC |
| $g$ | magnetic charge of the monopole (Gaussian units) | statC |
| $n$ | integer | 1 |
| $\hbar$ | reduced Planck constant (Gaussian: erg·s) | erg·s |
| $c$ | speed of light, 2.997 924 58 × 10¹⁰ cm/s (exact) | cm/s |
| $\mathbf{B}$ | magnetic field (Gaussian units) | G |
| $r,\ \hat{\mathbf{r}}$ | distance from the monopole and unit vector away from it | cm |
| $\rho_m$ | magnetic charge density (hypothetical) | statC/cm³ |
Honest caveat: No magnetic monopole has ever been confirmed. The monopole field shown on the back is hypothetical.
Status: part of this topic is unsolved, unconfirmed or debated. The text above says which part; treat it as an open question, not settled fact.
Sources
- Dirac (1931) Quantised Singularities in the Electromagnetic Field, Proc. R. Soc. Lond. A 133, 60
- Cabrera (1982) First Results from a Superconductive Detector for Moving Magnetic Monopoles, Phys. Rev. Lett. 48, 1378
- Jackson (1999) Classical Electrodynamics, 3rd ed., Wiley, §6.11
Crossovers
Monopola meets Magnetron Twins (Electromagnetism / Polarity Lock). 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.
Monopola meets Secundar (Gauge Invariance). Monopola's existence would make electric charge quantised, through Dirac's condition. Secundar notes the subtle price: describing her with a vector potential needs a singular "string" that no gauge choice removes, only moves, and it must be invisible.
Wear the lore
Concept keywords: Dirac's Monopole, Monopola, Electromagnetism & Plasma, physics lore, Pixelated Physics