14 T11K MAGNETIC CIRCUIT [ART. 8 



8. Flux Density. It is often of importance to consider the flux 

 density ,.or the value of a flux per unit of cross-section perpendicular 

 to the direction of the lines of force. Flux density is usiuilly 

 denoted by B, and is measured in maxwells (or its multiples) per 

 square centimeter. 1 "When the flux is distributed uniformly over 

 the cross-section of a path, the flux density 



(11) 



where A is the area of the cross-section of the path. If the flux is 

 distributed non -uniformly, an infinitesimal flux d<P passing through 

 a cross-section dA must be considered. In the limit, the flux den- 

 sity at a point corresponding to dA is 



(12) 



The areas A and dA are understood to be at all points normal 

 to the direction of the field. Solving these two equations for the 

 flux we find 



= B-A, ....... (13) 



or 



A B-dA, ...... (14) 



= C 



/o 



the integration being extended over the whole cross-section of the 

 path. Expressed in words, these last two formulae mean that 

 the total flux passing through a surface is equal to the sum of the 

 fluxes passing through the different parts of that surface. 



Magnetic flux density is analogous to current density U, and 

 to dielectric flux density D treated in the Electric Circuit. The 

 student will find no difficulty in interpreting eqs. (11) to (14) 

 from the point of view of the electric and electrostatic circuits. 



The relation between B and H is obtained from eq. (1) in which 

 the value of (R is obtained from eq. (4). Namely, we have 



or 



1 Some writers express flux density in gausses, one gauss being equal to 

 one maxwell per square centimeter. The unit kilogauss, equal to one kilo- 

 maxwell per square centimeter, is also used. While the terms gauss and 

 kilogauss are convenient abbreviations, no use is made of them in this hook 

 in order to keep the relation between a flux and the cross-section of its path 

 explicitly before the student. 



