Cosmology

EstablishedDirect evaluation of Ferraro's law, the equatorial potential, and the printed LC product.

Isorotation Potential

The steady induction law fixes the angular velocity on each poloidal line. The 11-year product is the invert of a printed inductance and capacitance.

Last updated: 8 October 2026

Reading this entry

The isorotation page applies Ferraro's law, keeping Ω constant on each poloidal line, and evaluates the equatorial potential per tesla for a radiative interior near 430 nHz out to 0.713 R_☉. The printed Sun–Sirius inductance and capacitance invert to the 11.004 yr product.

What this is used for

Stellar-types, coronal-hole, and local-stream pages use this potential and this LC invert when they quote the Hale half-period and the shear at the convection-zone base. The coaxial return supplies a second period, 27.02 yr, from its own L and C, and the dynamo-flow seat stays closed.

Walk through

Steady ideal induction gives (B·∇)Ω = 0, so Ω is constant on each poloidal line, and one rate is 430 nHz out to 0.713 R_☉. On an equatorial path at R_c = 0.70 R_☉ with Ω = 2π × 430 nHz the potential is ½ Ω R_c² = 3.204×10¹¹ V per tesla. The sidereal period 24.47 d is 473 nHz, the velocity jump is 132 m s⁻¹, and that jump matches B_φ = Δv √(μ₀ ρ) = 1.62 T. The printed pair L = 1.35×10¹¹ H and C = 9.05×10⁴ F gives π√(LC) = 11.00366 yr, printed as 11.004 yr and doubled as 22.01 yr, and a coaxial return at 100 AU with b/a = 2 gives L = 1.13×10¹⁰ H, C = 6.53×10⁶ F, and π√(LC) = 27.02 yr.

In steady ideal induction, . The angular velocity is constant along each poloidal field line. One such is the scored radiative interior, nearly solid-body at about out to .

Uniform axial field, equatorial path, , . An axial current is parallel to and produces no homopolar potential.

The equatorial sidereal rate, , is . The velocity jump against the interior is . At the scored convection-zone base density that jump matches . A rope is . The unquenched winding of a seed reaches that match in a few days and, continued with no back-reaction, runs past it.

Left: magnetic pressure over gas pressure versus field, crossing unity near a few thousand tesla. Right: toroidal field wound from a 1 T seed, stopping at the 1.62 T shear match if the back-reaction is kept. — Gas pressure at the scored base is . Magnetic pressure equals that gas pressure at .

The printed Sun–Sirius pair is and .

The three-decimal print of the same product is . Twice the six-figure value is , which prints as .

That period is the invert of the printed pair: the sheath voltage that returns the capacitance is . A coaxial return on the same Sirius length, inner radius and , produces both factors.

Two bars. The coaxial return on the Sirius length gives 27.02 years. The printed pair is 11.00366 years, which prints as 11.004 years. — The coaxial period is . It does not depend on . The full ring is .

The homopolar potential is axisymmetric. Hale polarity is one dipole under the -effect. The dynamo-flow seat stays closed.

Integrity

Ferraro's law, the potential per tesla, the shear-match field, the printed invert, and the coaxial pair are direct evaluations. The dynamo-flow seat stays closed. This page charters no ledger row and does not promote.

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