• Pixel-art sticker of Quickel, personifying Speed of Light, with the caption “Two Constants, One Speed.”

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Quickel

Speed of Light Physics

\[c = \frac{1}{\sqrt{\mu_0 \varepsilon_0}}\]
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Meet Quickel, a light beam whose speed came from two constants of electricity and magnetism. In the 1860s Maxwell showed changing fields make a wave whose speed, from μ₀ and ε₀, is about 2.998 × 10⁸ m/s. It matched light, so light is electromagnetic. Pixel-art kiss-cut sticker in 2, 3, 4 and 6 inches; equation, symbols and sources in the physics panel below.

Size
Surface

Flat $6 shipping worldwideMade to order, ships in 2–5 business days

Details

Size3″ × 3″

3″ × 3″ kiss-cut sticker.

Shipping

Flat $6 shipping on every order, worldwide, whatever's in it.

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

Meet Quickel, a beam of light whose speed was worked out from two constants of electricity and magnetism.

In the 1860s James Clerk Maxwell combined the laws of electricity and magnetism. He found that a changing electric field makes a magnetic field, and a changing magnetic field makes an electric field. Together they can keep each other going as a wave travelling through empty space.

The speed of that wave is c = 1/√(μ₀ε₀). Using μ₀ ≈ 1.2566 × 10⁻⁶ H/m and ε₀ ≈ 8.854 × 10⁻¹² F/m, √(μ₀ε₀) ≈ 3.336 × 10⁻⁹ s/m, so c ≈ 2.998 × 10⁸ m/s.

That matched the measured speed of light, so Maxwell concluded that light itself is an electromagnetic wave. In it the electric and magnetic fields wiggle at right angles to each other and to the direction of travel.

Since 1983 the speed of light has been fixed at exactly 299,792,458 m/s, and the metre is defined from it.

Equations

\[c = \frac{1}{\sqrt{\mu_0 \varepsilon_0}}\]
SymbolMeaningUnit
\(c\) speed of light in vacuum \(\mathrm{m/s}\)
\(\mu_0\) vacuum magnetic permeability \(\mathrm{H/m}\)
\(\varepsilon_0\) vacuum electric permittivity \(\mathrm{F/m}\)

Sources

  1. OpenStax University Physics Vol. 2 — Maxwell's Equations and Electromagnetic Waves
  2. NIST CODATA — vacuum magnetic permeability μ₀
  3. NIST CODATA — vacuum electric permittivity ε₀

Field notes

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