94 MATHEMATICAL FORMULAE AND ELLIPTIC FUNCTIONS 



4.23 



1. VAB = grad AB = (AV)B + (BV)A + V.A curl B + V.E curl A. 



2. V VAB = div FAB = B curl A - A curl B. 



3. FVFAB = (BV)A - (AV)B + A div B - B div A. 



4. div </>A = c/> div A + AV</>. 



5. curl </>A = V- V</>A + </> curl A = F-grad </>.A + curl A. 



6. VA 2 = 2(AV)A + 2 FA curl A. 



7. C(AV)B = A(CV)B + AFC curl B. 



8. BVA 2 = 2A(BV)A. 



4.24 R is a radius vector of length r and r a unit vector in the direction of R, 



R = rr, 



_. i i _ i 



i. V - = - -rR = -- 



r r 3 r 2 



2. 



- R = r = grad r 



5. FVR = curl R = o. 



6. VR = div R = 3. 







8. 



10. (AV)R = A. 



4.30 dS = an element of area of a surface regarded as a vector whose direction 

 is that of the positive normal to the surface. 

 dV = an element of volume a scalar. 



