The Spark HeraldElectromagnetism / Lightning Command
The Spark Herald – Electromagnetism / Lightning Command Physics T-Shirt
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- White · Black
- Size
- S–5XL
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Size & fitS–5XL
Unisex heavy cotton (Gildan 5000), classic fit.
| Size | Width | Length | Sleeve |
|---|---|---|---|
| S | 18 | 28 | 15.1 |
| M | 20 | 29 | 16.5 |
| L | 22 | 30 | 18 |
| XL | 24 | 31 | 19.5 |
| 2XL | 26 | 32 | 21 |
| 3XL | 28 | 33 | 22.4 |
| 4XL | 30 | 34 | 23.7 |
| 5XL | 32 | 35 | 25 |
Measurements in inches, ±1.5 in tolerance.
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∂ The physics
The Spark Herald sends energy down a wire. The strange part is that almost none of it travels in the wire.
The four equations on this page are Maxwell's, the full theory of electricity and magnetism, and the last line gives the speed of the waves they predict: light. One consequence took until 1884 to spell out. John Henry Poynting showed that electromagnetic energy flows wherever there are electric and magnetic fields together, at a rate given by the new line added to this page: the cross product of E and B, divided by μ₀.
Apply that to a simple circuit, a battery and a lamp. The battery's charges set up an electric field around the wires; the current sets up a magnetic field circling them. Their cross product points from the battery, through the space beside the wires, into the lamp. Energy reaches the lamp through the fields around the wire, with the wire guiding them. Feynman works through the same surprise in Chapter 27 of the second volume of his Lectures, with a charging capacitor whose energy enters not along the wires but from the sides.
Meanwhile the electrons themselves barely move. In a copper wire with a cross-section of one square millimetre carrying one ampere, the free electrons drift at about seven hundredths of a millimetre per second, slower than a snail. The lamp lights almost at once because the field travels at nearly the speed of light, not because any electron made the trip.
Lightning, the Herald's signature, is the same physics with the insulation removed: a field strong enough to tear electrons off air molecules, opening a conducting channel through the sky.
The Spark Herald never rides the wire. They travel beside it, at the speed of light.
Equations
| Symbol | Meaning | Unit |
|---|---|---|
| \(\vec E\) | electric field | \(\mathrm{V/m}\) |
| \(\vec B\) | magnetic flux density | \(\mathrm{T}\) |
| \(\rho\) | charge density | \(\mathrm{C/m³}\) |
| \(\vec J\) | current density | \(\mathrm{A/m²}\) |
| \(\varepsilon_0\) | vacuum permittivity | \(\mathrm{F/m}\) |
| \(\mu_0\) | vacuum permeability | \(\mathrm{N/A²}\) |
| \(c\) | speed of light | \(\mathrm{m/s}\) |
| \(\vec S\) | Poynting vector (electromagnetic energy flux) | \(\mathrm{W/m²}\) |
Sources
- Maxwell (1865) A dynamical theory of the electromagnetic field, Phil. Trans. R. Soc. 155, 459 (opens in a new tab)
- Feynman Lectures on Physics Vol. II Ch. 18: The Maxwell Equations (opens in a new tab)
- Encyclopaedia Britannica — Maxwell’s equations (opens in a new tab)
- NIST CODATA 2022 — vacuum electric permittivity ε0 (opens in a new tab)
- NIST CODATA 2022 — vacuum magnetic permeability μ0 (opens in a new tab)
- NIST CODATA 2022 — speed of light in vacuum c (opens in a new tab)
- Feynman Lectures on Physics Vol. II Ch. 27: Field Energy and Field Momentum (opens in a new tab)
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