350 
PROFESSOR J. H. POYXTING OX THE TRAXSFER 
Applications of the Law of Transfer of Energy. 
(1.) A straight wire conveying a current. 
In this case very near the wire, and within it, the lines of magnetic force are circles 
round the axis of the wire. The lines of electric force are along the wire, if we take 
it as proved that the flow across equal areas of the cross section is the same at all 
parts of the section. If A B, fig. 1, represents the wire, and the current is from A to B, 
Fig. 1. 
then a tangent plane to the surface at any point contains the directions of both the 
electromotive and magnetic intensities (we shall write E.M.I. and M.I. for these 
respectively in what follows), and energy is therefore flowing in perpendicularly 
through the surface, that is, along the radius towards the axis. Let us take a portion 
of the wire bounded by two plane sections perpendicular to the axis. Across the 
ends no energy is flowing, for they contain no component of the E.M.I. The whole of 
the energy then enters in through the external surface of the wire, and by the general 
theorem the amount entering in must just account for the heat developed owing to 
the resistance, since if the current is steady there is no other alteration of energy. It 
is, perhaps, worth while to show independently in this case that the energy moving 
in, in accordance with the general law, will just account for the heat developed. 
Let r be the radius of the wire, i the current along it, a the magnetic intensity at 
the surface, P the electromotive intensity at any point within the wire, and Y the 
difference of potential between the two ends. Then the area of a length l of the wire 
is 2nrl, and the energy entering from the outside per second is 
area x E.M.I. x M.I. _ 2irrl.V.a. 
47T 477 
2 r 7ri'oc.Yl 
477 
_ 4777 V 
477 
=iV 
