PEIRCE. — MANNER OF GROWTH OF A CURRENT. 511 



A long, solid, circular, iron cylinder, of specific resistance p and of 

 radius a, is closely surrounded by a uniformly wound coil of wire which 

 has N turns per centimeter of the length of the core ; the outer radius of 

 the coil is (a + ^ ) and the axis of the core is the z axis. A current 

 (C) in the coil is accompanied by a magnetic field (//) in the core which 

 has the direction of the z axis, and any change in the intensity of C 

 induces in the core temporary currents, the lines of which are circles 

 parallel to the xy plane with centres on the z axis. At any instant the 

 value of H and that of q, the vector which gives the density of the cur- 

 rent at any point in the core, are functions of the distance (r) from the 

 z axis alone, and are independent of z ; hence Maxwell's current equation, 



4tt<7 = Curl //, (1) 



reduces to the simple form 



4-» = -|f. (2) 



The currents in the core do not affect the intensity (ff a ) of the mag- 

 netic field at the boundary of the coil, so that at every instant 



B it = 4irNC. (3) 



Since in columnar co-ordinates 



1 3 f 9V\ 1 9 a V 3 2 V 



r 



9r\ 9r ; " r V 2 9u 2 3z 2 -' 



where Fis any scalar function, the general equation, 



4tt/x 9H 



— -57 = **W, (5) 



Aira 9H 1 9 ( 9H\ 



becomes • — = -•— [r • — , 



p d t r 3 r \ 3r J 



(6) 



where /j. is the permeability of the iron, supposed constant. 



When there are no currents in the core, the intensity (JT) of the 

 magnetic field in the core has at every point the boundary value (H a ), 

 but when positively directed eddy currents exist, the intensity of the 

 field is greater near the axis and sinks gradually, as r increases, to H a 

 at the boundary. If, then, L is the inductance of the coil per centimeter 



