174 



PROCEEDINGS OF THE AMERICAN A< LDEMY. 



straight iron wires, placed close together (Figure Go), and if, after a 

 steady current of intensity Ej w lias been running for some time through 



the solenoid, so that there is a magnetic field of 

 uniform intensity //„ = inAh' w in the core, the 

 applied electromotive force be suddenly shunt ed 

 out of the solenoid circuit, the current (6') in tin- 

 coil will gradually die out. At any instant the 

 field, in so much of the space A as is occupied by 

 air, is 4 -XC, for eddy currents in the wires act 

 like solenoid sheets and do not affect the field 

 without the wires. Within each wire there are 

 eddy currents, of course, and at every point in the wire, at every 

 instant, the field intensity, II, must satisfy the equation 



ll'.l BE CO. 



ell 

 dt 



4 ~/u |_ da? ' jr _ 



65 



The induction flux through the turns of the solenoid per centimeter 

 of its length shall be p, so that 



E 



dp 



— = ir 



dt 



= wC, or, in this case, 



dp 

 It 



= - wC. 



If there are n' 1 wires in the core and the area of the cross-section of 

 each of them is D, 



p = ±TrX 2 C(A - n*B) + fi 



*SS* 



,l.i da 



(66) 



where the double integral is to be extended over the cross-sections of all 

 the wires : hence 



tvC+(A -, /■=//) I *N' •'','' + .«*V /'/''// ■'/.'■'/'/ = <>; (G7) 

 and if the wires fill the square space as full as possible, 



A - n*B= 0.2] l«i .1. nearly. 



If II S represents the strength of the magnetic field in the air space 

 within the solenoid, 



lis H {A — >r/)') - 4 



W <tt if 



If 



dH 



dt ' 



dxdy = 0. (68) 



