538 Divergence and Curl in a Vector Field. 



Let point T be so selected that D ?l = 0. Then 



-5T-J- ac> -f- ^- — an = 0, 

 do on 



or 



S=— -I^S w 



In other words, the points for which D ?l = determine a 

 plane N1ST inclined by an angle 7 to the rectifying plane.. 

 This angle is determined by eq. (29) and characterizes the 

 amount by which the flux is skewed. Without tortuosity,, 

 that is in a two-dimensional field, 7 = and plane NN 

 coincides with bt. 



In the preceding discussion, the derivative dD 6 /3& is left 

 out of consideration, because it does not enter in the ex- 

 pression for the curl. The flux may spread to any degree in 

 the rectifying plane, without affecting the component of the 

 curl in the direction of vector D. 



Summary. 

 Divergence. 



In two dimensions : div D= -~ h tt ; 



0$ It 



In three dimensions : div D= ^ h 



0* 



\R Hr) 



Curl. 



in two dimensions : curl D= ^ 1 ; 



On p 



In thrse dimensions the projections of the curl are as- 



£oll OWS ;_ 9D p 



alono- the binomial, (curl JJk = ^- 1 ; 



& v J On p ' 



along the normal, (curlD) n = -~r- H ; 



along the vector itself, or along the tangent, 



(curlD)^. 



