• Pixel-art sticker of Paralix, personifying Parallel Currents, with the caption “Same-Way Currents Pull Together.”

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Paralix

Parallel Currents Physics

\[\frac{F}{L} = \frac{\mu_0 I_1 I_2}{2\pi d}\]
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Meet Paralix, a pair of wires who lean in whenever their currents flow the same way. Same-direction currents attract; opposite ones repel. Two wires 10 cm apart carrying 10 A each feel about 2 × 10⁻⁴ N per metre, an effect that once defined the ampere. 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 Paralix, a pair of wires who lean in whenever their currents flow the same way.

Every current makes a magnetic field that circles around its wire. A second wire nearby sits inside that field, and the moving charges in it feel a magnetic force. When the two currents run in the same direction the force pulls the wires together. When they run in opposite directions it pushes them apart.

The force on each metre of wire is F/L = μ₀I₁I₂/(2πd). Two wires 10 cm apart, each carrying 10 A, feel about 2 × 10⁻⁴ N on every metre. That is tiny, but in a power station busbar carrying thousands of amps it becomes strong enough to bend metal during a fault.

Double either current and the force doubles. Move the wires twice as far apart and it halves.

For decades this effect defined the ampere itself: one amp was the current that gave a force of 2 × 10⁻⁷ N per metre between wires 1 m apart.

Equations

\[\frac{F}{L} = \frac{\mu_0 I_1 I_2}{2\pi d}\]
Symbols
SymbolMeaningUnit
\(F/L\) force per unit length of wire \(\mathrm{N/m}\)
\(\mu_0\) vacuum magnetic permeability \(\mathrm{H/m}\)
\(I_1\) current in the first wire \(\mathrm{A}\)
\(I_2\) current in the second wire \(\mathrm{A}\)
\(d\) distance between the wires \(\mathrm{m}\)