By Henry William Watson
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Additional resources for The Mathematical Theory of Electricity and Magnetism
35 VECTOR POTENTIAL. ] It will be observed that the magnetic induction components satisfy the no-convergence condition da db dc + T + dz T T= ax ay ' but that the magnetic force components a, /3, y do not generally do so on the other hand, a, /3, and y are always derived from a potential, but a, b, and c are not so, unless the components of ; magnetisation A, B, and C are so derived. The magnetic induction and magnetic force are the same in all regions devoid of magnetic matter. ] Since the flux of magnetic induction is zero for any must be the same through all bounded by the same closed curve, and therefore must closed surface whatever, this flux surfaces be equal to a line integral taken round the curve.
191, above referred to, that if a small cylinder be taken whose base is dS and height very small in comparison with the linear magnitude of dS, then the average force within this cylinder normal to dS arising from the included magnetic molecules Whence it is 4770-, or in the magnetic notation follows that if a crevasse be formed by emptying this cylinder of the included molecules, the average force within the cylinder normal to dS arising from, the rest of the field is in other words, this force is the magnetic induction as above defined.
47rm(lB Treating the other double integrals in the same way, for the sum mA). T7 <^C &c. = &c. ] When the magnetisation is lamellar A, J3, and derivable from a potential 0, and therefore in this case a> C d, are and c are so likewise. Referring to Art. 304, we see that in such a mass the quantity in that Article called fi, or r^ ~a dS, the potential of magnetic induction, and that the components of this induction are is 39 INDUCED MAGNETISM. 3 1 5-] In this case rrr(d
The Mathematical Theory of Electricity and Magnetism by Henry William Watson