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By P. H Roberts

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103) Also we must have

B = 0 on a given surface S into a corresponding condition on A. B = 0, and let B = O. Since div B = 0 everywhere, we may introduce A and A, and (92) must hold. Now,since B = O,A = - grad \f for some \f. Thus (96) n x A = -n x grad \f, on S for some \f. (d) Mechanical conditions (v #- 0). g. a shock or detonation front), or (ii) a surface separating two immiscible fluids, or (iii) a fluidsolid interface (medium 2, say, being the stationary solid). We shall have no occasion to consider (i). In cases (ii) and (iii) we have, by applying (48) to the volume of Fig.

3(a)] and using the divergence theorem. g. 13), and we will not repeat it here. In a similar way, equations (5) and (6) may < x Medium I Medium 2 x Fig. 2 (b) Fig. 3. Elementary volumes and circuits: (a) The penny-shaped disk (b) The rectangular circuit The dimensions of these are small compared with the radii of curvature of the surface and with the length scales of the fields considered. g. g. M. 6) , . I I t 1 ~--------~--------- The Equations of Magnetohydrodynamics be integrated round a contour crossing S [Fig.

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