COIL OF MAXIMUM ACTION FOR A GIVEN SOURCE. 



8l 



As the length of the corresponding wire is 



\2irr. n^dr = 7rn l (a" 2 - a' 2 ), 



t) of 



the specific action of this layer is 



a - a 



+ /. 



Equating the two specific actions, we get, as a condition of the 

 maximum, 



a' 



If we add to this equation (2), which gives the value of /, we 

 might determine the dimensions a" and b of the coil. 



731. COIL OF MAXIMUM ACTION FOR A GIVEN SOURCE. 

 Without altering the dimensions of the channel, we may further 

 investigate what should be the length and diameter of the wire, in 

 order that with a given source the intensity of the magnetic field is a 

 maximum at the centre of the coil. It is necessary to introduce here 

 the elements of the source, which is defined by the electromotive 

 force, and its own resistance R' including the resistance of the con- 

 necting wires, without which the magnetic action would increase 

 indefinitely with the number of turns, or, in other words, with the 

 density of the current. 



The intensity of the current is expressed by 



E 



R + R" 

 and the action at the centre of the coil is 



(16) 





The condition of maximum of this expression is easily obtained 

 in the case of a uniform winding : if we suppose that the wire is bare, 



VOL. II. G 



