a • (b X C) = b • (C X a) = C • (a X b) a x (b x c) = (a• c)b-(a• b)c (a x b) • (c x d) = (a· c)(b • d)-(a· d)(b • c) V x Vl/f = 0 V • (V x a) = 0 V x (V x a) = V(V • a)-V 2 a V • (l/fa) = a • Vl/f + l/JV • a V X (l/fa) = Vl/f X a + l/JV X a V(a • b) = (a• V)b + (b • V)a + a x (V x b) + b x (V x a) V · (a x b) = b • (V x a)-a• (V x b) V x (a x b) = a(V • b)-b(V • a) + (b · V)a-(a• V)b If x is the coordinate of a point with respect to some origin, with magnitude r = lxl, n = x/r is a unit radial vector, and f(r) is a well-behaved function of r, then V · x = 3 Vxx=O 2 af V · [nf(r)] =-f +-r ar V x [nf(r)] = 0 (a · V)nf(r) = f(r) [a-n(a • n)] + n(a • n) af r ar V (x • a) = a + x(V • a) + i(L x a) where L = ~ (x x V) is the angular-momentum operator. l
CITATION STYLE
Jackson, J. D. (2003). Electrodynamics, Classical. In digital Encyclopedia of Applied Physics. Wiley. https://doi.org/10.1002/3527600434.eap109
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