Miscellaneous papers . ofthe order of 1 Daniell in 50 in., that is, very small , a term of the form const/p may have to be addedto the above value of <£. Its value depends on the quantityof free electricity on the earth, although it does not vanishwith this quantity; but the order of magnitude of the cal-culated forces is not altered by the presence of this term. III. When a sphere of any arbitrary magnetic properties rotates Sphericalin a liquid, which is itself a conductor, and makes electric ^f^contact with the surface of the sphere, the sphere will inducecurrents in the li
Miscellaneous papers . ofthe order of 1 Daniell in 50 in., that is, very small , a term of the form const/p may have to be addedto the above value of <£. Its value depends on the quantityof free electricity on the earth, although it does not vanishwith this quantity; but the order of magnitude of the cal-culated forces is not altered by the presence of this term. III. When a sphere of any arbitrary magnetic properties rotates Sphericalin a liquid, which is itself a conductor, and makes electric ^f^contact with the surface of the sphere, the sphere will inducecurrents in the liquid. In general these no longer flow inconcentric spherical shells, but traverse the magnet. 108 INDUCTION IN ROTATING SPHERES The determination of these currents presents no furtherdifficulty apart from self-induction. I shall not enter in detailinto the calculations. Fig. 10 represents the simplest homogeneous magnetic sphere rotates about its magneticaxis. The figure drawn represents the lines of flow in a. Fig. 10. meridional section. The form of the lines of flow does notdepend upon the resistances of the magnet and the the intensity vanishes when either resistance becomesinfinitely great. § 8. Solution for the Formulae of the Potential Law. So far we have assumed for the induced electromotiveforces the expressions which Jochmann has deduced for themfrom Webers fundamental law. We shall now inquire whatchanges the results undergo when we use the formulae whichfollow from the potential law and are given in vol. lxxviii. ofBorchardts Journal} If 3E, |f, % denote the electromotive forces hitherto assumed,%, J?, % those which follow from the potential law, we have 1 Helmholtz, Wiss. Abhandl. vol. i. p. 702. II INDUCTION IN ROTATING SPHERES 109 ox S=g- = co(Vx - Uy). We see at once that we may retain the previous solutionsunaltered as regards u, v, w} -*Jr, H. The only alteration whichmu
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Keywords: ., bookcentury1800, bookdecade1890, booksubjectphysics, bookyear1896
