KDlltfyfic cJf 



niegrals 



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H=i^[^.lvri?iirfX dx7vj^l 



O 



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Some simple engineering prob- ^ ! 



lems require advanced mathe- 

 matics in their solution. This i 

 is true, for example, in the ' \ \ \ 

 computation of the magnetic 

 field outside the spiral grid 

 a vacuum tube, a problem of 

 interest to Bell Telephone Lab- 

 oratories. If the grid is closely 



a a 





^ 



_^ coiled, the current can be 



treated as a continuous cylin- 

 drical sheet, of radius a. Then 

 y / ^ the component of the magnetic 

 field parallel to the axis of the 

 ' grid at a distance r from the 



axis is given by the above func- 

 tion of two Elliptic Integrals 

 whose "modulus" is k = a/r. 



//" 



274 



