Electric Power Generation from Earth’s Rotation through its Own Magnetic Field

Chyba, Christopher F.; Hand, K. P.

doi:10.1103/physrevapplied.6.014017

Cited by 7 publications

(2 citation statements)

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“…(1) always. However, this argument fails when ∇ × (v × B) = 0 (Chyba & Hand (2016, 2020), because the electric field of a static charge distribution may always be written as a potential of a scalar field: E = −∇V . But since ∇ × ∇V = 0 always, the equation…”

Section: A New Mechanismmentioning

confidence: 99%

Internal-Current Lorentz-Force Heating of Astrophysical Objects

Chyba,

Hand

2021

Preprint

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Two forms of ohmic heating of astrophysical secondaries have received particular attention: unipolargenerator heating with currents running between the primary and secondary; and magnetic induction heating due to the primary's time-varying field. Neither appears to cause significant dissipation in the contemporary solar system. But these discussions have overlooked heating derived from the spatial variation of the primary's field across the interior of the secondary. This leads to Lorentz force-driven currents around paths entirely internal to the secondary, with resulting ohmic heating. We examine three ways to drive such currents, by the cross product of: (1) the secondary's azimuthal orbital velocity with the non-axially symmetric field of the primary; (2) the radial velocity (due to non-zero eccentricity) of the secondary with the primary's field; or (3) the out-of-plane velocity (due to non-zero inclination) with the primary's field. The first of these operates even for a spin-locked secondary whose orbit has zero eccentricity, in strong contrast to tidal dissipation. We show that Jupiter's moon Io today could dissipate about 600 GW (more than likely current radiogenic heating) in the outer hundred meters of its metallic core by this mechanism. Had Io ever been at 3 jovian radii instead of its current 5.9, it could have been dissipating 15,000 GW. Ohmic dissipation provides a mechanism that could operate in any solar system to drive inward migration of secondaries that then necessarily comes to a halt upon reaching a sufficiently close distance to the primary.

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Section: A New Mechanismmentioning

confidence: 99%

Internal-Current Lorentz-Force Heating of Astrophysical Objects

Chyba,

Hand

2021

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“…Recently, Chyba and Hand made a proposal for obtaining electrical energy through electromagnetic induction in a circuit at rest on the Earth surface [89]. The circuit, viewed from an inertial frame K centered at the Earth's center, is rotating in the Earth's magnetic field.…”

Section: Electromagnetic Induction In Some Recent Research Papersmentioning

confidence: 99%

Electromagnetic induction: physics, historical breakthroughs, epistemological issues and textbooks

Giuliani¹

2021

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The discovery of Electromagnetism by Ørsted (1820) initiated an "extraordinary decennium" ended by the discovery of electromagnetic induction by Faraday (1831). During this decennium, in several experiments, the electromagnetic induction was there, but it was not seen or recognized. In 1873, James Clerk Maxwell, within a Lagrangian description of electric currents, wrote down a 'general law of electromagnetic induction' given by, in modern form and with standard symbols:In Maxwell's derivation, the velocity appearing in this equation, is the velocity of the line element dl. A modern reformulation of Maxwell's general law, starts with the definition of the induced emf as the• dl, where v c is the velocity of the charge. It is shown that, this apparently minor difference, is fundamental. The general law is a local law: it correlates what happens in the line at the instant t to the values of quantities at the points of the line at the same instant t. For rigid circuits, it is Lorentz invariant. If expressed in terms of the magnetic field, it allows -in the approximation of low velocities -the derivation of the "flux rule", for filiform circuits.The "flux rule" is a calculation tool and not a physical law because it not always yields the correct prediction, it does not say where the induced emf is localized, it requires ad hoc choices of the integration paths and -last but not least -because, if physically interpreted, it implies physical interactions with speeds higher than that of light. Maxwell's general law has been rapidly forgotten; instead, the "flux rule" has deeply taken root. The reasons appear to be various. One is plausibly related to the idea that the vector potential does not have physical meaning, a stand clearly assumed by Hertz and Heaviside at the end of the Nineteenth century. An analysis of university textbooks, spanned over one century, assumed to be representative on the basis of the authors and/or on their popularity or diffusion, suggests that other reasons are related to the habit of presenting electromagnetic phenomena following the historical development and to the epistemological stand according to which physical laws must be derived from experiment without the need of recurring, soon or later, to an axiomatic presentation of the matter. On the other hand, the rooting of the "flux rule" has been certainly favored by its calculation utility: this practical feature has overshadowed its predictive and epistemological weakness.

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