The Magnetic Bottle

Plate 78 speaks for itself: “Earth keeps a cage of charged rain.”

The Physics

Charged particles spiral along Earth's field lines and are reflected where the field strengthens near the poles, bouncing between hemispheres in the Van Allen belts.

μ = m v⊥² / (2B)

• μ: magnetic moment, an adiabatic invariant, J T⁻¹
• m: particle mass, kg
• v⊥: speed perpendicular to B, m s⁻¹
• B: magnetic flux density, T
• α: pitch angle, rad

sin²α/B is conserved (μ invariant). Explorer 1's Geiger counter saturated in 1958.

Sources

• J. A. Van Allen et al., Jet Propulsion 28, 588 (1958).
• F. F. Chen, Introduction to Plasma Physics, Ch. 2.

On the poster

Plate 078, “The Magnetic Bottle”: the pixel-art plate with its slogan “Earth keeps a cage of charged rain.”, the key equation and the facts panel shown above. Pixelated Physics. Physics. Personified.