• Pixel-art sticker of Gaussum, personifying Gauss's Law, with the caption “Count The Flux, Find The Charge.”

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Gaussum

Gauss's Law Physics

\[\Phi_E = \frac{Q}{\varepsilon_0}\]
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Meet Gaussum, a charge inside a bubble who shows the bubble's size does not matter. Gauss's law says the total electric flux out of any closed surface depends only on the charge inside. For 1 nC it is about 113 N·m²/C, whether the bubble is 1 cm or 1 km across. 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.

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

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Returns & replacements21 days

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The physics

Meet Gaussum, a charge inside a bubble who shows that the bubble's size does not matter.

Electric field lines spread out from a positive charge. Electric flux measures how much field passes through a surface. Gauss's law says that the total flux out through any closed surface depends only on the charge enclosed inside it, Φ_E = Q/ε₀.

For a charge of 1 nC, the flux through the closed surface is 10⁻⁹ / (8.85 × 10⁻¹²) ≈ 113 N·m²/C. That holds whether the bubble is 1 cm or 1 km across, and whether it is a sphere or a lumpy shape, because the net number of field lines crossing outward stays the same.

Charges outside the surface add nothing to the total, since each of their field lines enters and then leaves again.

With symmetric shapes such as spheres, cylinders and flat sheets, Gauss's law turns hard field calculations into short ones, and it is one of Maxwell's four equations of electromagnetism.

Equations

\[\Phi_E = \frac{Q}{\varepsilon_0}\]
Symbols
SymbolMeaningUnit
\(\Phi_E\) electric flux through a closed surface \(\mathrm{N·m²/C}\)
\(Q\) charge enclosed \(\mathrm{C}\)
\(\varepsilon_0\) vacuum electric permittivity \(\mathrm{F/m}\)