174 



PROCEEDINGS OF THE AMERICAN ACADEMY. 



straight iron wires, placed close together (Figure 60), and if, after a 



steady current of intensity Elw has been running for some time through 



the solenoid, so that there is a magnetic field of 



r ^^rW^ uniform intensity ^o = 4 ttNE/w in the core, the 



^r)rY~)(p applied electromotive force be suddenly shunted 



OOCXD ^^^ ^^ ^^® solenoid circuit, the current (C) in the 



OOOOO coil will gradually die out. At any instant the 



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

 OOQQQ air, is 4 ttNC, for eddy currents in the wires act 

 TiGURE 60. 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, H, must satisfy the equation 



dH 



dt 





(65) 



The induction flux through the turns of the solenoid per centimeter 

 of its length shall be j), so that 



E — J- = wC, or, in this case, ■— = — wC. 

 at at 



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

 each of them is B, 



p = A 7rN^C{A - n^B) + ixN ffH-dx dy 



(66) 



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

 the wires ; hence 





"""IS 



dH 



dt ' 



dccdy = 0; (67) 



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



A—n'B = 0.2146 A, nearly. 



If Hs represents the strength of the magnetic field in the air space 

 within the solenoid, 



H^+il^i^A-n'B/J^ + '"-'' 



w 



dt 



w 



'If 



dH 



dt ' 



dxdy = 0. (68) 



