THE INFLUENCE OF FREQUENCY UPON THE 

 SELF-INDUCTANCE OF COILS. 



By J. G. Coffin. 



Presented by A. 6. Webster, January 10, 1906. Received February 14, 1906. 



It is well known, through the work of Lord Rayleigh, 1 and Stefan, 2 

 that currents of high frequency in straight wires distribute themselves 

 over the cross-section of the wires very differently from steady currents. 



The values of the resistance of such wires, as well as their self-induc- 

 tance, thereby suffer a change. Resistance undergoes a large increase, 

 self-inductance a small decrease. The theory for straight wires has been 

 hitherto directly applied to wires wound on coils, in want of a better 

 theory for such a case. 



Recently, Max Wien 3 and A. Sommerfeld 4 have attacked successfully 

 the problem for wire coils. 



Max Wien's results, however, are only applicable to small frequencies, 

 while those of Sommerfeld, although valid for all frequencies, gave only 

 the change in resistance. 



In the following will be found the derivation of a formula by a method 

 based on that of Sommerfeld for the change of self-inductance with the 

 frequency. 



By means of this theory we shall derive a method of assigning the 

 correction to be applied to any coil of a single layer. Its extension to 

 coils of more than one layer is reserved for a future communication. 

 The theory 5 shows that with increasing frequency the currents tend to 

 flow more and more on the inside surface of the coil. The maximum 

 change in self-inductance is then the change due to a diminution of the 

 mean radius of the coil of one half the diameter of the wire, with which 

 the coil is wound. 



1 Phil. Mag., 21, 381 (1886). 



3 Wied. Ann., 41, 400 (1890). 



3 Max Wien, Ann. d. Phys., 14, 1 (1904). 



* A. Sommerfeld, Ann. d. Phys., 15, 673 (1904). 



Max Wien, loc. cit. 



