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Maxwellion

Maxwell’s Equations Physics

\[\nabla\cdot\vec E = \frac{\rho}{\varepsilon_0}\]
$21.99 USD
$21.99 USD
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What is light, really? Maxwellion holds the answer in four lines. Maxwell’s equations tie electric and magnetic fields to charges, currents and each other. In empty space they predict waves travelling at c = 1/√(μ0ε0), the speed of light, so light is an electromagnetic wave. Pixel-art black ceramic mug in 11 or 15 oz; equation, symbols and sources in the physics panel below.

Shipping calculated at checkout by destinationMade to order, ships in ~10 days

Details

Size & material11oz · 15oz

Black glossy ceramic mug with a C-handle. Lead- and BPA-free.

  • 11oz: 0.33 l
  • 15oz: 0.44 l
CareDishwasher & microwave safe

Dishwasher safe (top rack) or hand wash. Microwave safe.

ShippingBy destination

Shipping calculated at checkout by destination.

Made to order: about 10 days of production and handling before it ships.

Delivery times & where we ship

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 how charges and currents make electric and magnetic fields, and how changing fields make each other. Together they predict light as a self-sustaining electromagnetic wave.

Maxwellion carries four lines, and they cover every electric and magnetic effect of classical physics.

Read them in order. Electric charge is the source of electric field. There is no magnetic charge, so magnetic field lines never start or end. A changing magnetic field makes a curling electric field; that is Faraday's induction. And magnetic field curls around electric currents and around changing electric fields. James Clerk Maxwell added that last term, and it changed everything.

With it, the equations allow a disturbance in the fields to travel through empty space on its own: a changing electric field makes a magnetic field, which makes an electric field, and so on. Maxwell worked out the speed in his 1865 paper, A Dynamical Theory of the Electromagnetic Field. It came out as one over the square root of two measured electrical constants, the last line, and matched the measured speed of light. He concluded that light is an electromagnetic wave.

FOUR LINES. ALL OF LIGHT. is true for light as a classical wave: radio, visible light and X-rays all obey these equations. Photons, and how atoms emit and absorb them, need quantum electrodynamics on top.

Maxwellion does not shine. He explains why anything can.

Equations

\[\nabla\cdot\vec E = \frac{\rho}{\varepsilon_0}\]
\[\nabla\cdot\vec B = 0\]
\[\nabla\times\vec E = -\frac{\partial\vec B}{\partial t}\]
\[\begin{gathered} \nabla\times\vec B = \mu_0\vec J \\ {}+ \mu_0\varepsilon_0\frac{\partial\vec E}{\partial t} \end{gathered}\]
\[c = \frac{1}{\sqrt{\mu_0\varepsilon_0}}\]
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 \(\mathrm{N/A²}\)
\(t\) time \(\mathrm{s}\)
\(c\) speed of light in vacuum \(\mathrm{m/s}\)

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. HyperPhysics — Maxwell's Equations
  4. NIST CODATA 2022 — speed of light in vacuum c (exact)
  5. NIST CODATA 2022 — vacuum electric permittivity

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

Field notes

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