Electrodynamics of Continuous Media: Course of Theoretical Physics by L D Landau & E.M. LIFSHITZ

Author:L D Landau & E.M. LIFSHITZ [LANDAU, L.D. & LIFSHITZ, E.M.]
Language: eng
Format: epub
ISBN: 9781483293752
Publisher: Elsevier
Published: 1984-09-15T00:00:00+00:00

(64.8)

The required field H(e) outside the conductor is obtained by subtracting from the solution H′ of this latter problem.

The magnetic field thus produced, like any variable field, induces electric currents in the conductor itself. In a simply-connected body, these currents appear in the form of a magnetic moment. In a non-uniformly rotating ring, the effect appears as an e.m.f.—the Stewart–Tolman effect.

Misunderstanding may arise from the appearance of the angular velocity Ω itself, and not its time derivative, in formula (64.8). We may therefore emphasize that the above discussion, and therefore the significance here attached to the quantity (64.8), pertain only to non-uniform rotation. When Ω is constant, equation (64.7) with the appropriate boundary condition at infinity is identically satisfied by H′ = , and the definition (64.5) then gives H = 0. The magnetic field which arises from the gyromagnetic effect (§36) in uniform rotation is a small quantity which is here neglected.

The derivation has also ignored the deformation of the body which results from non-uniform rotation. It can be seen that including this deformation would not affect the result if the characteristic time of variation of the angular velocity is (as we assume) much longer than the relaxation time of the conduction electrons in the deformation: the electric current in the conductor is due to the gradient of φ + ζ0/e, where φ is the field potential and ζ0 the chemical potential of the conduction electrons (see §26). A non-uniform deformation produces a gradient of ζ0, but this is compensated by the electric field which results from the thermodynamic equilibrium condition eφ + ζ0 = constant.

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