THE MAGNETIC MEASUREMENT OF CURRENT. 25 



in the element cc. Then, according to equation (3) of Art. 



1 6, we have: 



2irr z lz'dx 



Every element of the long coil produces at p a field which is in 

 the same direction (parallel to the axis of the coil), and therefore 

 the field at p due to the entire coil is found by integrating (i) 

 between the limits x = B to x = + A. For a very long 

 coil the limits of the integration are from x <*> to # = + <, 

 and in this case we get : 



H = 47TZ/ (2) 



where H is the strength of the magnetic field inside of a very 

 long coil having z turns of wire per unit of length, and / is 

 the current in the coil in abamperes. 



i-z.dx turns 



Fig. 20. 



According to the above derivation, equation (2) gives the inten- 

 sity of the magnetic field along the axis of a very long cylindrical 

 coil, but as a matter of fact, the magnetic field inside of the coil 

 is uniform, that is to say, it has everywhere the same intensity 

 and it is everywhere in the same direction. 



1 8. Contribution to the magnetic field at a given point by one 

 element of an electric wire. The region surrounding an electric 

 circuit is a magnetic field, and each element of the circuit (each 



