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AI Overview There isn't a single "eddy flux density" formula; instead, eddy currents (which cause flux changes) are found using Maxwell's equations (often numerically), but the resulting magnetic flux density (B) is calculated as B = Φ/A (Flux/Area) or B…
AI Overview

There isn't a single "eddy flux density" formula; instead, eddy currents (which cause flux changes) are found using Maxwell's equations (often numerically), but the resulting magnetic flux density (B) is calculated toas B = Φ/A (Flux/Area) or B = μH (permeability times field strength), with eddy current losses themselves often estimated by Steinmetz's equation for power loss (Pₑ ∝ ƒ² B²ₘₐₓ), showing eddy currents are part of the complex system, not a simple direct calculation from one formula.

https://news.1rj.ru/str/orgonecontinuum/3062
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In Lord Kelvin's (William Thomson's) vortex theory of the atom and his later superfluid ether models, magnetic phenomena are treated using the mathematics of hydrodynamics rather than the abstract fields of Maxwell or the space-time curvature of Einstein.

1. The Fundamental Identity: Magnetic Field as Vorticity

In Kelvin's superfluid ether, the magnetic field 𝐁 is directly identified with the vorticity 𝛚 of the ether fluid.

Vorticity Formula: 𝛚 = ∇ ⨯ 𝐯
   
Where 𝐯 is the local velocity of the ether.

Equivalence: 𝐁 ∝ 𝛚.

In this framework, magnetic "flux" is not an abstract field line but the literal circulation (𝚪) of the ether fluid around a vortex filament. 

2. Magnetic Eddy Flux Density (Circulation)

The "density" of magnetic flux in a vortex-based ether corresponds to the strength of the vortex filaments per unit area.

Circulation 𝚪:
𝚪 = 𝐯 ⋅ d𝐥 = (∇ ⨯ 𝐯) ⋅ d𝐒 = ∬  𝛚 ⋅ d𝐒.

Flux Density Relationship: Just as magnetic flux 𝚽 = 𝐁 ⋅ d𝐒, Kelvin's model views this as the integral of the ether's rotational velocity over the area. 

3. Kinetic Energy and Magnetic Energy Density

In Maxwell's theory, magnetic energy density is 𝐁²/2μ₀. In Kelvin’s superfluid ether, this energy is the kinetic energy of the ether's rotation:

Energy Density Formula: 𝑢ₘₐ₉ = ½ 𝜌|𝐯|²

Where 𝜌 is the density of the ether fluid and 𝐯 is its rotational (eddy) velocity.

The magnetic force is then interpreted as the hydrodynamic pressure gradient resulting from these velocity distributions.
Summary Formulae for Kelvin's Model

Magnetic Induction: 𝐁 = k(∇ ⨯ 𝐯) (where k is a proportionality constant related to ether density).

Magnetic Flux (Circulation): 𝚽 = 𝐯 ⋅ d𝐥.

Vortex Motion (Force): 𝐅 = 𝛒 (𝐯 ⨯ 𝛚) (Analogous to the Lorentz force 𝐣 ⨯ 𝐁).
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AI Overview

Lord Kelvin's ether theory did not produce specific, lasting, or currently used formulae for calculating magnetic eddy flux density. His model was a conceptual framework based on stable, knotted vortices in a hypothetical, ideal, incompressible, and frictionless fluid ether that was meant to explain the nature of atoms and light, not to replace or extend the specific quantitative equations of Maxwell's theory.

Context of Kelvin's Ether Theory

Conceptual, not Quantitative: Kelvin's (William Thomson's) primary contribution was the idea of vortex atoms as a model for matter, which inspired the mathematical field of knot theory. He viewed magnetic forces as analogous to the forces between these ethereal vortices.

Failed Model: Kelvin's vortex atom theory was ultimately incorrect and failed to gain universal acceptance or provide quantitative predictions that matched experimental results as precisely as Maxwell's emerging theory.

Maxwell's Equations Prevailed: James Clerk Maxwell developed a successful, abstract mathematical theory of electromagnetism that described the behavior of electric and magnetic fields and electromagnetic waves without needing a detailed mechanical model of the ether itself. Modern physics is built upon Maxwell's equations (and their integration into Einstein's relativity and quantum mechanics), not Kelvin's vortex model.

Modern Scientific Perspective

Modern physics has entirely abandoned the concept of a luminiferous, mechanical ether in favor of Einstein's theories of relativity and quantum field theory, where electromagnetic fields are viewed as fundamental entities or quantum excitations of fields, not as mechanical motions within a fluid medium.

Therefore, there are no established, scientifically valid formulae within Kelvin's obsolete ether theory that can be used to calculate magnetic eddy flux density. Standard calculations for magnetic flux density use the well-established equations derived from Maxwell's theory, such as 𝚽ʙ = ∬ᴀ B⃗ · dA⃗
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