Displacera

Displacera, a hooded field-weaver, holds a glowing disc of light between his hands.

The Physics

Ampère's law broke down at a charging capacitor: current flows in the wire but not across the gap. James Clerk Maxwell fixed it in 1861–65 by adding a term for the changing electric field in the gap, which makes a magnetic field just as a real current does (“A Dynamical Theory of the Electromagnetic Field”, Phil. Trans. 155, 459, 1865). With it, the equations predicted electromagnetic waves travelling at the speed of light.

J_d = ε₀ ∂E/∂t

• J_d: displacement current density (A/m²)
• ε₀: permittivity of free space (F/m)
• ∂E/∂t: rate of change of the electric field (V m⁻¹ s⁻¹)

Light itself is changing electric and magnetic fields keeping each other going through this term. Hertz confirmed the waves in 1887–88.

Honest caveat: No charge actually crosses the gap; the name is a leftover from Maxwell's mechanical model.

On the sticker

Displacera cups a glowing cyan disc of light between his hands. Printed text: DISPLACERA with the line J = ε0 ∂E/∂t. Pixel-art kiss-cut vinyl sticker, white, in 2″, 3″, 4″ and 6″ sizes.