The London, Edinburgh and Dublin philosophical magazine and journal of science . sities of tbe several magnets vary as thet| power of their distance from the centre. Images due to Generation of Circular Currents coaxial witha Spherical Sheet, fyc. 10. A circular current whose axis passes through the centreof the sphere is equivalent to a magnetic shell forming a spheri-cal cap on the surface of a concentric sphere, this cap beingbounded by the current. It is thus evident that the imagesdue to the sudden generation of such a current are also circularcurrents, which move in the manner described
The London, Edinburgh and Dublin philosophical magazine and journal of science . sities of tbe several magnets vary as thet| power of their distance from the centre. Images due to Generation of Circular Currents coaxial witha Spherical Sheet, fyc. 10. A circular current whose axis passes through the centreof the sphere is equivalent to a magnetic shell forming a spheri-cal cap on the surface of a concentric sphere, this cap beingbounded by the current. It is thus evident that the imagesdue to the sudden generation of such a current are also circularcurrents, which move in the manner described in the pre-ceding sections. There is no need to restrict the results tocircular currents as the same arguments are equally applicablewhen the inducing current flows in any closed curve traced ona spherical surface concentric with the sheet, the images inthis case being currents in similar curves. It remains to statethe relation between the intensities of the currents in theimages and that of the inducing current. (i.) Let A A7 (fig. 4) be the wire in which an inducing Fio% current of intensity I is suddenly generated outside the at time t the image for inside points will be a current inPPand for outside points a current in QQ, where OP=^R/aOAand OQ = e~*R/aa2/OA. Suppose the currents replaced bytheir equivalent magnetic shells on spherical surfaces centredat 0, and let corresponding elements of these shells be magnetic moments of the elements of PP, QQ, and AAare respectively as OP! : OQI : OA* ; and the areas of theseelements areas OP2: OQ2 : OA2; hence the strengths of theshells are as OP~* : OQ-* : OA-*, and the current-intensities Plane, Cylindrical, and Spherical Current-Sheets. 393 are in the same ratio. Thus finally, if V and I be the inten-sities of the image-currents at time t in PPand QQ, we have i=-(sri=-^K2i> *w—(ST1—*;1- It will be noticed that V increases as its circuit QQapproaches the centre, while I decreases as its circuit PP7re
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Keywords: ., bookcentury1800, bookdecade1840, booksubjectscience, bookyear1840
