Homopole: Faraday Paradox

Electromagnetism & Plasma arc, page 79 of 193. Back to The Pixelated Physics Universe

Who they are

Homopole spins a copper war-wheel between magnet poles, and sparks jump from rim to axle.

Homopole 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

Michael Faraday built the copper-disk generator in his first Experimental Researches in Electricity, Phil. Trans. 122, 125 (1832).

$$ \begin{gathered} \mathcal{E} = \int (\mathbf{v}\times\mathbf{B})\cdot d\mathbf{r} = \tfrac{1}{2} B\,\omega R^{2} \end{gathered} $$

Symbol Meaning SI unit
$\mathcal{E}$ EMF between axle and rim V
$\mathbf{v}$ velocity of a point of the disk m/s
$\mathbf{B}$ magnetic flux density, along the axis T
$d\mathbf{r}$ radial line element m
$\omega$ disk angular speed rad/s
$R$ disk radius m

Sources

Crossovers

Homopole meets The Spark Herald (Electromagnetism / Lightning Command). The Spark Herald's energy flows through the fields around a wire, along the Poynting vector. Homopole's spinning copper disk makes an EMF from motion in a magnetic field. In both, the circuit's energy is carried by electric and magnetic fields together.

Homopole meets Lumidisk (Feynman's Disk Paradox). Homopole and Lumidisk are both spinning-disk puzzles in induction. Homopole's EMF depends on the disk moving through the field. Lumidisk's spin comes from a changing magnetic flux inducing an electric field. In both, total angular momentum and energy are conserved once the fields are counted.

Wear the lore

Concept keywords: Faraday Paradox, Homopole, Electromagnetism & Plasma, physics lore, Pixelated Physics