ELEMENTARY ELECTRICITY AND MAGNETISM. 19 



13. Magnetic field inside of a long solenoid. A winding of 

 wire is called a coil. The usual form of coil consists of wire 

 wound on a spool. When the spool is very short and large in 

 diameter the coil is called a circular coil. The intensity of mag- 

 netic field at the center of a circular coil is discussed in the fore- 

 going article. When the spool is very long in comparison with 

 its diameter the coil is called a solenoid. The solenoid is usually 

 made by winding one or more layers of wire on a long tube. 



The magnetic field in a long solenoid is uniform, that is, the 

 field has the same intensity at every point inside of the solenoid 

 and the same direction, namely, parallel to the axis of the 

 solenoid. 



The intensity in gausses of the magnetic field inside of a long 



solenoid is : 



(9) 



in which z is the number of turns of wire per centimeter length 

 of solenoid, and / is the current in abamperes. Equation (9) 



may be written : 



Z 



W = 47T'-j'f (10) 



in which Z is the total number of turns of wire on the solenoid 

 and / is the length of the solenoid in centimeters. 



Discussion of equation (9). The equation gives the intensity of the magnetic 

 field at every point in a long solenoid, except at points near the ends of the sole- 

 noid, and it is true whatever 

 the shape of the section of the 



solenoid. The following proof J 

 of equation (9) applies how- 

 ever to points in the axis of _ 

 a cylindrical solenoid. 



Let Fig. 10 represent a por- 

 tion of a long cylindrical solen- { 



oid of radius r, having z turns 

 of wire per centimeter of length Fig. 10. 



and carrying current /. Let/ 



be the point, in the axis of the solenoid, at which the field intensity is to be deter- 

 mined. Each element of the solenoid contributes its share to the intensity of field 



