Shielda

Shielda glows with charge, but a swarm of opposite charges mutes her beyond arm's length.

The Physics

Put a charge in a plasma and opposite charges crowd round it, hiding it from far away. Its potential falls off exponentially over the Debye length. A gas counts as a plasma only if it is much bigger than the Debye length and holds many particles in a Debye sphere.

λ_D = √(ε₀ k_B T_e / (n_e e²)), φ(r) = q e^(−r/λ_D) / (4πε₀ r), N_D = (4/3)π n_e λ_D³ ≫ 1

• λ_D: Debye length (m)
• ε₀: vacuum permittivity, 8.8541878128 × 10⁻¹² F/m
• k_B: Boltzmann constant (J/K)
• T_e: electron temperature (K)
• n_e: electron number density (m⁻³)
• e: elementary charge, 1.602176634 × 10⁻¹⁹ C (exact)
• φ: electric potential (V)
• q: test charge (C)
• r: distance (m)
• N_D: electrons in a Debye sphere

In the solar corona (n_e ~ 10¹⁵ per m³, T_e ~ 100 eV), λ_D ≈ 2 mm. Peter Debye and Erich Hückel worked out the same screening in salt solutions in 1923.

On the shirt

Front: Shielda, the pixel-art character, with the title. Back: the Debye length, the screened potential, the plasma criterion, the solar-corona example and the 1923 electrolyte credit. Printed on a unisex tee.