• Pixel-art sticker of Voltaro, personifying Electric Potential of a Point Charge, with the caption “Closer In, Higher Up.”

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Voltaro

Electric Potential of a Point Charge Physics

\[V = \frac{k q}{r}\]
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$4.99 USD
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Meet Voltaro, a positive charge ringed by circles of equal potential. The potential around a point charge falls as one over the distance: 1 nC gives about 90 V at 10 cm and about 180 V at 5 cm. Pushing a positive test charge closer takes work. 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 Voltaro, a positive charge surrounded by rings of equal potential.

Electric potential tells you how much energy each coulomb of charge would have at a point. Around a single point charge q, the potential at a distance r is V = kq/r, where k ≈ 8.99 × 10⁹ N·m²/C² is the Coulomb constant.

For a charge of 1 nC, the potential 10 cm away is 8.99 × 10⁹ × 10⁻⁹ / 0.1 ≈ 90 V. Halve the distance to 5 cm and the potential doubles to about 180 V. The rings of equal potential around the charge are called equipotentials.

A positive test charge moving inward has to climb this potential hill, so work must be done to push it closer. Let it go and it rolls away, turning that stored energy into motion.

Potential falls off as 1/r, more gently than the field, which falls as 1/r². Because it is a number with no direction, adding potentials from several charges is easy.

Equations

\[V = \frac{k q}{r}\]
SymbolMeaningUnit
\(V\) electric potential \(\mathrm{V}\)
\(k\) Coulomb constant \(\mathrm{N·m²/C²}\)
\(q\) source charge \(\mathrm{C}\)
\(r\) distance from the charge \(\mathrm{m}\)

Sources

  1. OpenStax University Physics Vol. 2 — Calculations of Electric Potential
  2. NIST CODATA — vacuum electric permittivity ε₀

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