• The Spark Herald EM Fields pixel-art physics T-shirt, white tee, front view

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The Spark Herald

Electromagnetism / Lightning Command Physics

\[\nabla\cdot\vec E = \frac{\rho}{\varepsilon_0}\]
$29.99 USD
$29.99 USD
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Size guide S–5XL · inches

Energy reaches your lamp through the space around the wire, not inside it. Maxwell’s equations predict light, and Poynting showed in 1884 that energy flows where electric and magnetic fields cross. Electrons in a copper wire drift slower than a snail; the lamp lights at once because the field moves at nearly light speed. The Spark Herald on a pixel-art unisex tee; equation, symbols and sources in the panel below.

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Details

Size & fitS–5XL

Unisex heavy cotton (Gildan 5000), classic fit.

SizeWidthLengthSleeve
S182815.1
M202916.5
L223018
XL243119.5
2XL263221
3XL283322.4
4XL303423.7
5XL323525

Pour l'échelle : la taille M mesure 20 in (50.80 cm) de large, soit environ 3.143 × 1034 longueurs de Planck (lP = 1.616255 × 10−35 m). Un mètre ruban est plus rapide.

Measurements in inches, ±1.5 in tolerance.

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Returns & replacements21 days

Every item is printed to order, so we can’t accept returns or exchanges for change of mind, or if you ordered the wrong size or colour.

Print defect, misprint, damage or the wrong item? We’ll send a free replacement, or a refund if you prefer. Report it within 21 days of delivery with a photo; no need to send it back.

Full refund & replacement policy

The physics

Maxwell's four equations describe every classical electric and magnetic effect: charges make electric fields, there are no magnetic charges, and changing fields create each other. Together they predict electromagnetic waves travelling at the speed of light.

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

\[\nabla\cdot\vec E = \frac{\rho}{\varepsilon_0}\]
\[\nabla\cdot\vec B = 0\]
\[\nabla\times\vec E = -\frac{\partial\vec B}{\partial t}\]
\[\nabla\times\vec B = \mu_0\vec J + \mu_0\varepsilon_0\frac{\partial\vec E}{\partial t}\]
\[c = \frac{1}{\sqrt{\mu_0\varepsilon_0}}\]
\[\vec S = \frac{1}{\mu_0}\,\vec E\times\vec B\]
SymbolMeaningUnit
\(\vec E\) 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

  1. Maxwell (1865) A dynamical theory of the electromagnetic field, Phil. Trans. R. Soc. 155, 459
  2. Feynman Lectures on Physics Vol. II Ch. 18: The Maxwell Equations
  3. Encyclopaedia Britannica — Maxwell’s equations
  4. NIST CODATA 2022 — vacuum electric permittivity ε0
  5. NIST CODATA 2022 — vacuum magnetic permeability μ0
  6. NIST CODATA 2022 — speed of light in vacuum c
  7. Feynman Lectures on Physics Vol. II Ch. 27: Field Energy and Field Momentum

Source Maxwell, J. C. (1865). A dynamical theory of the electromagnetic field. Philosophical Transactions of the Royal Society of London, 459–512.doi.org/10.1098/rstl.1865.0008

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Field notes

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