By P. H Roberts
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Additional resources for An introduction to magnetohydrodynamics
A,I. s~L _ _;ss r'l e , ~ A2 A2 (a) time t (b) time l + lSt Fig. 4. The boundary condition on the electric field at a moving surface. The elementary rectangular circuit A , A 2 C 2 C , is fixed in space, and the surface S intersects it at FG (at time t) and F'G' (at time t + ot). -----~-------,---- The Equations of Magnetohydrodynamics Since (5) implies (12), (86) implies (87). For time dependent fields, (6) implies (7) and therefore (88) implies (83). In the case of solid conductors, (86) is not really a constraint on the solution, rather, it is a definition of J.
The difference in flux is therefore -/(BI -Bz)(FF/) = -IUn(B 1 -Bz)Dt. The rate of change of flux through r is therefore -lUn(B I - B z ) = I(E1 - E z), by (6), where E denotes the component of E in the direction of J. This agrees with (88). A,I. s~L _ _;ss r'l e , ~ A2 A2 (a) time t (b) time l + lSt Fig. 4. The boundary condition on the electric field at a moving surface. The elementary rectangular circuit A , A 2 C 2 C , is fixed in space, and the surface S intersects it at FG (at time t) and F'G' (at time t + ot).
Across any layer in which the physical properties of a medium change rapidly, some of the field variables must also change rapidly. When such a layer is idealized as an abrupt surface of discontinuity separating two homogeneous regions, these same field variables suffer discontinuities across it. in cannot alter greatly. Thus, by (8), there will be a comparatively t If the fluid is poorly conducting, there is little connection between Band p, and the stresses mjJ and -pOll balance separately. This combination of conventional electrodynamics and hydrostatics is not particularly interesting, and by , magnetostatics ' we will imply that the fluid is highly conducting.