ELEMENTARY ELECTRICITY AND MAGNETISM 9 



meters in area, stretched across and at right angles to a uniform 

 magnetic field of intensity df. The product sdf is called the mag- 

 netic flux across the surface. That is : 



< = sdf (40) 



in which < is the magnetic flux across a plane surface of area s 

 square centimeters at right angles to a uniform magnetic field of 

 intensity df. When the plane surface is not at right angles to 

 the uniform magnetic field then : 



in which 6 is the angle between df and the normal to the surface. 

 When the field is not uniform or when the surface is curved then : 



in which A<3> is the flux across an element of the surface of 

 which the area is AJ, df is the intensity of the field at the ele- 

 ment of surface, and 6 is the angle between df and the normal 

 to the element of surface. In this case the total flux across a 

 finite surface is found by integrating equation (4^) over the finite 

 surface. 



The unit flux is the flux across one square centimeter at right 

 angles to a magnetic field of unit intensity, or it is the flux across 

 I //zth of a square centimeter at right angles to a magnetic field 

 of n units of intensity. The International Electrical Congress of 

 1900 adopted the name maxwell for the unit flux ; however, the 

 unit flux is almost universally called the line, and a given flux is 

 usually expressed as so many lines. 



The manner in which magnetic field is distributed in space is 

 mathematically identical with the manner in which velocity is 

 distributed throughout a moving incompressible liquid. The 

 stream lines in a moving incompressible liquid are closed or 

 reentrant lines.* Similarly, the lines offeree of a magnetic field 



* Unless the motion extends to infinity. 



