Page:Electricity (1912) Kapp.djvu/169

Rh far the present case is covered by the previous argument. But we do not want to carry our unit pole from infinity on the right to infinity on the left; we want to carry it fairly close round the coil, say along the dotted line from D to E and round to D again. The dotted line forms the closed magnetic path, whilst the coil forms the electric path, both being interlinked. For reasons already stated, the exact shape of the path is immaterial. As long as we start and finish the journey at the same point, the same amount of energy is required to perform it. Let us then make the journey in the following way: Go from Da long way vertically downwards. This part of the journey costs no energy, since all the lines of force are crossed at right angles. Then go in a wide sweep to A. Also this part of the journey costs no energy, since it is made in a region where there is no force at all. It is only when we travel from A to O that we get into a region where we encounter opposing (or helping) forces. By passing from A through O to B we expend (or recover) the energy represented by 4πni, whilst the journey from B to D is again performed without recovery or expenditure of energy. If, then, the dotted line represents the magnetic